Commiting rest of the files for selecting Random Effects.

05-Research_Program-Affective_Provo/01-Fixation_Duration_Research/01-LME_Model_Structure/01-Scripts/Step-2-Testing_Best_CorrelatedSlopes_for_Selected_Random_Intercept.R

@@ -0,0 +1,3506 @@
+# ============================================================
+# COPYRIGHT, LICENSING, AND SCHOLARLY CITATION
+# ============================================================
+# Copyright (c) 2026 Mohit Gupta
+# License: MIT
+# SPDX-License-Identifier: MIT
+#
+# This script contains original computational software
+# developed by Mohit Gupta for the AffLex-Provo
+# Research Program.
+#
+# Citation:
+# Researchers using this software in published research
+# are strongly requested to cite the AffLex-Provo repository:
+# https://huggingface.co/datasets/mohitg2/AffLex-Provo
+#
+# Third-party datasets and externally sourced materials
+# remain subject to their respective original licenses.
+#
+# See the applicable repository LICENSE file for the
+# complete MIT License terms.
+# ============================================================
+
+# ============================================================
+# CELL 1.1 — PACKAGE INSTALLATION AND INITIALIZATION (Affective Provo)
+# ============================================================
+#
+#
+# REQUIRED R VERSION: R version 4.5.2 (2025-10-31)
+#
+#
+# Purpose:
+#   Ensure that all R packages required by the Step 2 analysis
+#   pipeline are installed and loaded.
+#
+# Required packages:
+#   readr        → CSV import
+#   readxl       → Excel import
+#   openxlsx     → Excel export and formatting
+#   dplyr        → data manipulation
+#   tidyr        → missing-data handling
+#   stringr      → string utilities
+#   purrr        → functional/list operations
+#   lme4         → linear mixed-effects models
+#   optimx       → additional optimizers used by lme4::allFit()
+#   dfoptim      → additional optimizers used by lme4::allFit()
+#   future       → parallel-processing infrastructure
+#   future.apply → future-based apply functions
+#   progressr    → progress-handling utilities
+#   here         → portable project-root paths
+#
+# Procedure:
+#   1. Define the complete set of required packages.
+#   2. Identify packages that are not currently installed.
+#   3. Install only the missing packages from CRAN.
+#   4. Load all required packages.
+#
+# Notes:
+#   - Existing package installations are left unchanged.
+#   - Packages are installed only when absent.
+#   - suppressPackageStartupMessages() keeps notebook output clean.
+#   - Package versions are recorded later by sessionInfo() in
+#     the runtime log.
+# ============================================================
+
+
+# ------------------------------------------------------------
+# 1. Define Required Packages
+# ------------------------------------------------------------
+
+REQUIRED_PACKAGES <- c(
+  "readr",
+  "readxl",
+  "openxlsx",
+  "dplyr",
+  "tidyr",
+  "stringr",
+  "purrr",
+  "lme4",
+  "optimx",
+  "dfoptim",
+  "future",
+  "future.apply",
+  "progressr",
+  "here"
+)
+
+
+# ------------------------------------------------------------
+# 2. Identify Missing Packages
+# ------------------------------------------------------------
+
+MISSING_PACKAGES <- REQUIRED_PACKAGES[
+  !vapply(
+    REQUIRED_PACKAGES,
+    requireNamespace,
+    quietly = TRUE,
+    FUN.VALUE = logical(1)
+  )
+]
+
+
+# ------------------------------------------------------------
+# 3. Install Missing Packages
+# ------------------------------------------------------------
+
+if (length(MISSING_PACKAGES) > 0) {
+
+  message(
+    "Installing missing package(s): ",
+    paste(MISSING_PACKAGES, collapse = ", ")
+  )
+
+  install.packages(
+    MISSING_PACKAGES,
+    repos = "https://cloud.r-project.org",
+    dependencies = TRUE
+  )
+
+} else {
+
+  message("All required packages are already installed.")
+}
+
+
+# ------------------------------------------------------------
+# 4. Load Required Packages
+# ------------------------------------------------------------
+
+suppressPackageStartupMessages({
+
+  library(readr)
+  library(readxl)
+  library(openxlsx)
+
+  library(dplyr)
+  library(tidyr)
+  library(stringr)
+  library(purrr)
+
+  library(lme4)
+  library(optimx)
+  library(dfoptim)
+
+  library(future)
+  library(future.apply)
+
+  library(progressr)
+
+  library(here)
+})
+
+
+# ------------------------------------------------------------
+# 5. Confirm Package Initialization
+# ------------------------------------------------------------
+
+message(
+  "Package initialization complete: ",
+  length(REQUIRED_PACKAGES),
+  " required packages available."
+)
+
+
+
+
+
+
+
+
+
+
+# ============================================================
+# CELL 1.2 — HARD THREAD CAPS
+# ============================================================
+# Purpose:
+#   Restrict low-level numerical libraries to a single thread.
+#
+# Rationale:
+#   Mixed-effects models and allFit() may perform substantial
+#   numerical computation. If process-level parallelism is used
+#   later, unrestricted BLAS/OpenMP threading inside individual
+#   workers can cause:
+#
+#     - CPU oversubscription
+#     - memory contention
+#     - reduced performance
+#     - computational instability
+#
+# Strategy:
+#   Restrict low-level numerical libraries to one thread.
+#   Any intentional parallelism should occur at the R-process
+#   level rather than within each numerical operation.
+#
+# Controlled libraries:
+#   - VECLIB / macOS Accelerate
+#   - OpenMP
+#   - OpenBLAS
+#   - Intel MKL
+#   - NumExpr
+#
+# Notes:
+#   - This does NOT change the statistical model.
+#   - This does NOT change the analysis sample.
+#   - This should be configured before heavy model fitting.
+# ============================================================
+
+Sys.setenv(
+  VECLIB_MAXIMUM_THREADS = "1",
+  OMP_NUM_THREADS = "1",
+  OPENBLAS_NUM_THREADS = "1",
+  MKL_NUM_THREADS = "1",
+  NUMEXPR_NUM_THREADS = "1"
+)
+
+
+
+
+
+
+
+
+
+
+# ============================================================
+# CELL 1.3 — CORRELATED RANDOM-SLOPE CONFIGURATION
+# ============================================================
+# Purpose:
+#   Define the random-effects configuration used during Step 2,
+#   which evaluates candidate participant-level random slopes.
+#
+# Step 1 established the random-intercept structure.
+#
+# Step 2 now evaluates whether lexical and affective
+# fixed-effect predictors should additionally vary by
+# participant as random slopes.
+#
+# ------------------------------------------------------------
+# Additional Random Intercept
+# ------------------------------------------------------------
+# ADDITIONAL_INTERCEPT:
+#   Specifies the crossed random-intercept grouping factor
+#   retained alongside Participant_ID.
+#
+# USE_ADDITIONAL_INTERCEPT:
+#   TRUE  → include the additional crossed random intercept
+#   FALSE → use participant grouping only
+#
+# With the current configuration:
+#
+#   (1 + candidate slopes | Participant_ID)
+#   + (1 | Word_Unique_ID)
+# ------------------------------------------------------------
+
+ADDITIONAL_INTERCEPT <- "Word_Unique_ID"
+USE_ADDITIONAL_INTERCEPT <- TRUE
+
+
+# ------------------------------------------------------------
+# Random-Slope Correlation Structure
+# ------------------------------------------------------------
+# USE_UNCORRELATED_SLOPES:
+#
+#   FALSE:
+#       (1 + slopes | Participant_ID)
+#
+#       Participant intercepts and random slopes are allowed
+#       to correlate.
+#
+#   TRUE:
+#       (1 + slopes || Participant_ID)
+#
+#       Participant intercepts and random slopes are modeled
+#       without correlation parameters.
+#
+# This Step 2 script evaluates CORRELATED random slopes, so the
+# setting should remain FALSE.
+# ------------------------------------------------------------
+
+USE_UNCORRELATED_SLOPES <- FALSE
+
+
+# ------------------------------------------------------------
+# Candidate-Slope Complexity Limit
+# ------------------------------------------------------------
+# MAX_SLOPES_PER_CANDIDATE controls the maximum number of
+# participant-level random slopes allowed in a candidate model.
+#
+# Inf:
+#   Do not impose an artificial maximum.
+#
+# A smaller value may be used in a separate sensitivity or
+# stability analysis if highly complex structures prove
+# computationally unstable.
+# ------------------------------------------------------------
+
+MAX_SLOPES_PER_CANDIDATE <- Inf
+
+
+# ------------------------------------------------------------
+# Console Confirmation
+# ------------------------------------------------------------
+
+if (USE_ADDITIONAL_INTERCEPT) {
+  message("Random-intercept structure: Participant_ID + ", ADDITIONAL_INTERCEPT)
+} else {
+  message("Random-intercept structure: Participant_ID only")
+}
+
+message(
+  "Participant random slopes: ",
+  if (USE_UNCORRELATED_SLOPES) "UNCORRELATED" else "CORRELATED"
+)
+
+message("Maximum slopes per candidate: ", MAX_SLOPES_PER_CANDIDATE)
+
+
+
+
+
+
+
+
+
+
+# ============================================================
+# CELL 1.4 — ROOT-ANCHORED PROJECT PATHS
+# ============================================================
+# Purpose:
+#   Define portable input and output paths using the 'here'
+#   package.
+#
+# Input:
+#   02-Data/
+#     03-Analysis_Ready/
+#       03_Affective_Provo.csv
+#
+# Dataset:
+#   Affective Provo guarantees complete mandatory:
+#
+#   Lexical predictors:
+#       - Word_Length
+#       - Response_Proportion
+#       - Lg10WF
+#
+#   Affective predictors:
+#       - V.Mean.Y
+#       - A.Mean.Y
+#       - D.Mean.Y
+#
+# Important:
+#   Eye-tracking outcomes have NOT been used to determine
+#   inclusion in the exported Affective Provo dataset.
+#
+#   DV-specific duration filtering therefore occurs later in
+#   this Step 2 analysis pipeline, as it did in Step 1.
+#
+# Output:
+#   05-Research_Program-Affective_Provo/
+#     01-LME_Model_Structure/
+#       02-Results/
+#
+# Step 1 and Step 2 intentionally use the same results
+# directory. Step-specific filenames distinguish their outputs.
+# ============================================================
+
+PROJECT_ROOT <- here()
+
+RAW_DATA_PATH <- here(
+  "02-Data",
+  "03-Analysis_Ready",
+  "03_Affective_Provo.csv"
+)
+
+OUTPUT_DATA_DIR <- here(
+  "05-Research_Program-Affective_Provo",
+  "01-Fixation_Duration_Research",
+  "01-LME_Model_Structure",
+  "02-Results"
+)
+
+dir.create(
+  OUTPUT_DATA_DIR,
+  recursive = TRUE,
+  showWarnings = FALSE
+)
+
+stopifnot(
+  file.exists(RAW_DATA_PATH)
+)
+
+message("PROJECT_ROOT: ", PROJECT_ROOT)
+message("RAW_DATA_PATH: ", RAW_DATA_PATH)
+message("OUTPUT_DATA_DIR: ", OUTPUT_DATA_DIR)
+
+
+# ============================================================
+# 1.5 RUNTIME LOG — START
+# ============================================================
+
+LOG_PATH <- file.path(
+  OUTPUT_DATA_DIR,
+  "Step-2_Runtime_Log_Affective_Provo_Correlated_Slopes.txt"
+)
+
+log_con <- file(
+  LOG_PATH,
+  open = "wt"
+)
+
+sink(log_con, split = TRUE)
+sink(log_con, type = "message")
+
+cat(
+  paste0(
+    "\n",
+    strrep("=", 80), "\n",
+    "STEP 2 — CORRELATED RANDOM-SLOPE ANALYSIS\n",
+    "Dataset: Affective Provo\n",
+    "Started: ", format(Sys.time(), "%Y-%m-%d %H:%M:%S"), "\n",
+    "R version: ", R.version.string, "\n",
+    strrep("=", 80), "\n\n"
+  )
+)
+
+
+
+
+
+
+# ============================================================
+# CELL 2 — SHARED HELPER FUNCTIONS
+# ============================================================
+# Purpose:
+#   Define reusable utility functions used throughout the
+#   correlated random-slope model-selection pipeline.
+#
+# Includes:
+#   - Random-slope candidate generation
+#   - Runtime formatting
+#   - Excel sheet-name sanitization
+#   - Row-count auditing for fair AIC/BIC comparison
+#   - Structured Excel export with safe sheet replacement
+#
+# Design principles:
+#   - Functions are reusable across DVs.
+#   - Functions are shared by Paper 1 (Affective Provo) and
+#     Paper 2 (Lexical Provo).
+#   - No model fitting occurs in this cell.
+#   - No analysis-specific row filtering occurs in this cell.
+#   - File-writing side effects occur only in the explicitly
+#     defined Excel-export function.
+# ============================================================
+
+
+# ------------------------------------------------------------
+# 2.1 Random-Slope Candidate Generator
+# ------------------------------------------------------------
+# Purpose:
+#   Generate all candidate participant-level random-slope
+#   structures from a supplied set of slope variables.
+#
+# Behavior:
+#   - Always includes the random-intercept-only candidate:
+#
+#         "1"
+#
+#   - Generates every combination of the supplied slopes.
+#
+#   - max_slopes can optionally restrict the maximum number
+#     of slopes included in any candidate structure.
+#
+# Example for the Len-Freq-Pred baseline:
+#
+#   slope_vars = c(
+#       "Word_Length",
+#       "Response_Proportion",
+#       "Lg10WF"
+#   )
+#
+# Candidate structures include:
+#
+#   "1"
+#   "1 + Word_Length"
+#   "1 + Response_Proportion"
+#   "1 + Lg10WF"
+#   "1 + Word_Length + Response_Proportion"
+#   ...
+#   "1 + Word_Length + Response_Proportion + Lg10WF"
+#
+# The generated strings are later inserted into the
+# participant-level random-effects term.
+#
+# For correlated slopes:
+#
+#   (1 + slopes | Participant_ID)
+#
+# For uncorrelated slopes:
+#
+#   (1 + slopes || Participant_ID)
+# ------------------------------------------------------------
+
+generate_re_candidates <- function(slope_vars, max_slopes = Inf) {
+  candidates <- c("1")
+
+  if (length(slope_vars) == 0) return(candidates)
+
+  for (r in seq_along(slope_vars)) {
+    if (is.finite(max_slopes) && r > max_slopes) next
+
+    combos <- combn(slope_vars, r, simplify = FALSE)
+
+    candidates <- c(
+      candidates,
+      vapply(
+        combos,
+        function(x) paste("1 +", paste(x, collapse = " + ")),
+        character(1)
+      )
+    )
+  }
+
+  unique(candidates)
+}
+
+
+# ------------------------------------------------------------
+# 2.2 Runtime Formatter
+# ------------------------------------------------------------
+# Purpose:
+#   Convert elapsed execution time in seconds into a compact
+#   human-readable representation.
+#
+# Output examples:
+#   12.5 seconds → "12.5s"
+#   492 seconds  → "8.2m"
+#   4860 seconds → "1.35h"
+# ------------------------------------------------------------
+
+fmt_secs <- function(s) {
+  if (is.null(s) || !is.finite(s)) return("NA")
+
+  s <- as.numeric(s)
+
+  if (s < 60) return(sprintf("%.1fs", s))
+  if (s < 3600) return(sprintf("%.1fm", s / 60))
+
+  sprintf("%.2fh", s / 3600)
+}
+
+
+# ------------------------------------------------------------
+# 2.3 Excel Sheet-Name Sanitizer
+# ------------------------------------------------------------
+# Purpose:
+#   Ensure dynamically generated worksheet names comply with
+#   Microsoft Excel naming restrictions.
+#
+# Excel restrictions handled:
+#   - Maximum worksheet-name length = 31 characters
+#   - Prohibited characters:
+#
+#         \ / * [ ] : ?
+#
+# This prevents worksheet-creation errors during repeated
+# automated exports.
+# ------------------------------------------------------------
+
+safe_sheet_name <- function(name) {
+  name <- str_replace_all(name, "[\\\\/*\\[\\]:?]", "_")
+  str_sub(name, 1, 31)
+}
+
+
+# ------------------------------------------------------------
+# 2.4 Row-Count Audit for Fair Model Comparison
+# ------------------------------------------------------------
+# Purpose:
+#   Audit the analysis sample used for AIC/BIC comparison.
+#
+# Why this matters:
+#   Candidate random-slope models for the SAME DV must be
+#   compared on exactly the same observations. Otherwise,
+#   differences in AIC/BIC could reflect differences in sample
+#   composition rather than differences in model structure.
+#
+# Reports:
+#   original_rows
+#       → rows supplied to the audit function
+#
+#   dv_nonmissing_rows
+#       → rows with a non-missing value for the current DV
+#
+#   complete_case_rows_used_for_AIC_BIC
+#       → rows complete across the current DV and all variables
+#         specified in required_cols
+#
+#   rows_dropped_for_complete_case
+#       → rows removed because at least one required value
+#         was missing
+#
+#   pct_dropped
+#       → percentage of supplied rows removed by complete-case
+#         filtering
+#
+# Important:
+#   This helper audits MISSINGNESS only.
+#
+#   It does NOT automatically impose DV > 0.
+#
+#   For duration-based analyses, the positive-duration
+#   restriction must be applied during the analysis-data
+#   preparation stage before candidate models are compared.
+#
+# Safety:
+#   Required columns are validated explicitly. Missing required
+#   variables cause the pipeline to stop rather than being
+#   silently omitted from the audit.
+# ------------------------------------------------------------
+
+dv_rowcount_summary <- function(df, dv, required_cols, label = "") {
+
+  cols_needed <- unique(c(dv, required_cols))
+
+  missing_required <- setdiff(cols_needed, names(df))
+
+  if (length(missing_required) > 0) {
+    stop(
+      "Row-count audit cannot proceed. Missing required variable(s): ",
+      paste(missing_required, collapse = ", ")
+    )
+  }
+
+  original_n <- nrow(df)
+  dv_nonmissing <- sum(!is.na(df[[dv]]))
+
+  complete_n <- df %>%
+    select(all_of(cols_needed)) %>%
+    drop_na() %>%
+    nrow()
+
+  dropped <- original_n - complete_n
+
+  tibble(
+    label = ifelse(nchar(label) > 0, label, dv),
+    dv = dv,
+    original_rows = original_n,
+    dv_nonmissing_rows = dv_nonmissing,
+    complete_case_rows_used_for_AIC_BIC = complete_n,
+    rows_dropped_for_complete_case = dropped,
+    pct_dropped = if (original_n > 0) dropped / original_n * 100 else NA_real_,
+    required_cols_used = paste(required_cols, collapse = ", ")
+  )
+}
+
+
+# ------------------------------------------------------------
+# 2.5 Structured Excel Export
+# ------------------------------------------------------------
+# Purpose:
+#   Save correlated random-slope model-selection outputs to a
+#   structured multi-sheet Excel workbook.
+#
+# Sheets created for each DV:
+#
+#   <DV>_ranking
+#       → candidate random-slope model ranking
+#
+#   <DV>_audit
+#       → model-fitting / convergence audit information
+#
+#   <DV>_rowcounts
+#       → sample-size and complete-case diagnostics
+#
+# Repeated-execution behavior:
+#   - Creates the workbook if it does not already exist.
+#   - Loads the existing workbook when rerunning the analysis.
+#   - Removes only the sheets corresponding to the current DV.
+#   - Recreates those sheets with the updated results.
+#   - Preserves sheets belonging to other DVs.
+#
+# Safety:
+#   - Normalizes the output path.
+#   - Creates the parent directory when necessary.
+#   - Sanitizes dynamically generated worksheet names.
+#   - Saves with overwrite = TRUE after the workbook has been
+#     updated in memory.
+# ------------------------------------------------------------
+
+save_re_outputs_to_excel <- function(
+  excel_path,
+  dv,
+  df_results,
+  df_audit,
+  rowcount_summary
+) {
+
+  excel_path <- normalizePath(
+    excel_path,
+    winslash = "/",
+    mustWork = FALSE
+  )
+
+  dir.create(
+    dirname(excel_path),
+    recursive = TRUE,
+    showWarnings = FALSE
+  )
+
+  rank_sheet <- safe_sheet_name(paste0(dv, "_ranking"))
+  audit_sheet <- safe_sheet_name(paste0(dv, "_audit"))
+  rows_sheet <- safe_sheet_name(paste0(dv, "_rowcounts"))
+
+  if (file.exists(excel_path)) {
+
+    wb <- loadWorkbook(excel_path)
+
+    if (rank_sheet %in% names(wb)) removeWorksheet(wb, rank_sheet)
+    if (audit_sheet %in% names(wb)) removeWorksheet(wb, audit_sheet)
+    if (rows_sheet %in% names(wb)) removeWorksheet(wb, rows_sheet)
+
+  } else {
+
+    wb <- createWorkbook()
+  }
+
+  addWorksheet(wb, rank_sheet)
+  writeData(wb, rank_sheet, df_results)
+
+  addWorksheet(wb, audit_sheet)
+  writeData(wb, audit_sheet, df_audit)
+
+  addWorksheet(wb, rows_sheet)
+  writeData(wb, rows_sheet, rowcount_summary)
+
+  saveWorkbook(
+    wb,
+    excel_path,
+    overwrite = TRUE
+  )
+
+  message(
+    "Saved correlated random-slope results: ",
+    excel_path
+  )
+}
+
+
+
+
+
+
+
+
+
+# ============================================================
+# CELL 3 — LOAD AND VALIDATE AFFECTIVE PROVO
+# ============================================================
+# Purpose:
+#   Load the analysis-ready Affective Provo dataset and prepare
+#   variable names for the correlated random-slope pipeline.
+#
+# Input:
+#   03_Affective_Provo.csv
+#
+# Dataset guarantees:
+#   Every observation has complete mandatory:
+#
+#   Lexical predictors:
+#       - Word_Length
+#       - Response_Proportion
+#       - Lg10WF
+#
+#   Affective predictors:
+#       - V.Mean.Y
+#       - A.Mean.Y
+#       - D.Mean.Y
+#
+# Procedure:
+#   1. Load the Affective Provo dataset.
+#   2. Preserve the loaded dataset in df_main.
+#   3. Create df as the working modeling copy.
+#   4. Rename VAD variables for model readability.
+#   5. Validate mandatory predictors.
+#
+# IMPORTANT:
+#   No eye-tracking filtering occurs here.
+#
+#   No DV > 0 filtering occurs here.
+#
+#   No predictor standardization occurs here.
+#
+#   Predictors will be standardized AFTER the DV-specific
+#   analysis sample has been constructed. This ensures that
+#   scaling is based on the observations actually entering
+#   each duration-DV model comparison.
+#
+#   Consequently, FFD, GD, GPT, and TDT may be standardized
+#   using slightly different means/SDs if their eligible
+#   analysis samples differ.
+# ============================================================
+
+
+# ------------------------------------------------------------
+# 3.1 Load Affective Provo
+# ------------------------------------------------------------
+
+df_main <- read_csv(
+  RAW_DATA_PATH,
+  show_col_types = FALSE
+)
+
+message(
+  "Affective Provo rows loaded: ",
+  format(nrow(df_main), big.mark = ",")
+)
+
+
+# ------------------------------------------------------------
+# 3.2 Create Modeling Copy
+# ------------------------------------------------------------
+# df_main preserves the loaded analysis-ready dataset.
+# Subsequent preparation occurs on df.
+# ------------------------------------------------------------
+
+df <- df_main
+
+
+# ------------------------------------------------------------
+# 3.3 Rename Affective Predictors
+# ------------------------------------------------------------
+# Rename the original VAD columns to concise names used in
+# subsequent model formulas:
+#
+#   V.Mean.Y → Valence
+#   A.Mean.Y → Arousal
+#   D.Mean.Y → Dominance
+# ------------------------------------------------------------
+
+rename_map <- c(
+  "V.Mean.Y" = "Valence",
+  "A.Mean.Y" = "Arousal",
+  "D.Mean.Y" = "Dominance",
+  "Word_Length" = "Length",
+  "Response_Proportion" = "Predictability",
+  "Lg10WF" = "Frequency"
+)
+
+for (k in names(rename_map)) {
+  if (k %in% names(df)) {
+    names(df)[names(df) == k] <- rename_map[[k]]
+  }
+}
+
+
+# ------------------------------------------------------------
+# 3.4 Validate Mandatory LFP + VAD Predictors
+# ------------------------------------------------------------
+# Affective Provo should contain complete LFP + VAD predictors
+# by construction. Missing columns or missing values therefore
+# indicate an incorrect/incomplete input dataset and should
+# stop the analysis rather than being silently filtered.
+# ------------------------------------------------------------
+
+REQUIRED_PREDICTORS <- c(
+  "Length",
+  "Predictability",
+  "Frequency",
+  "Valence",
+  "Arousal",
+  "Dominance"
+)
+
+missing_columns <- setdiff(
+  REQUIRED_PREDICTORS,
+  names(df)
+)
+
+if (length(missing_columns) > 0) {
+  stop(
+    "Missing mandatory Affective Provo predictor(s): ",
+    paste(missing_columns, collapse = ", ")
+  )
+}
+
+if (anyNA(df[REQUIRED_PREDICTORS])) {
+  stop(
+    "Affective Provo contains missing values in one or more ",
+    "mandatory LFP + VAD predictors."
+  )
+}
+
+
+# ------------------------------------------------------------
+# 3.5 Confirm Dataset Readiness
+# ------------------------------------------------------------
+
+message("Mandatory LFP + VAD predictors: complete.")
+message("Predictors remain UNSCALED at this stage.")
+message("DV-specific filtering and standardization will occur later.")
+
+
+
+
+
+
+
+
+
+# ============================================================
+# CELL 4 — DVs, CORRELATED-SLOPE CANDIDATES, AND RESOURCE PLAN
+# ============================================================
+# Purpose:
+#   Define the duration-based dependent variables, generate all
+#   candidate participant-level correlated random-slope
+#   structures, and determine a conservative computational
+#   execution plan.
+#
+# Paper 1 candidate slopes:
+#
+#   Lexical predictors:
+#       - Length
+#       - Predictability
+#       - Frequency
+#
+#   Affective predictors:
+#       - Valence
+#       - Arousal
+#       - Dominance
+#
+# Random-slope framework:
+#
+#   Candidate slopes are added at the Participant_ID level:
+#
+#       (1 + candidate_slopes | Participant_ID)
+#
+#   Because USE_UNCORRELATED_SLOPES = FALSE in Cell 1.3,
+#   participant intercepts and random slopes are allowed to
+#   correlate.
+#
+#   The additional crossed random intercept configured in
+#   Cell 1.3 is retained separately:
+#
+#       + (1 | Word_Unique_ID)
+#
+# Candidate generation:
+#   With 6 possible slopes and no complexity cap:
+#
+#       2^6 = 64 candidate structures
+#
+#   including the participant random-intercept-only candidate.
+#
+# Computational planning:
+#   - Detect available logical CPUs.
+#   - Estimate available system RAM.
+#   - Reserve CPU and RAM headroom for system stability.
+#   - Limit process-level workers according to:
+#         TASKS_PER_DV
+#         CPU_BUDGET
+#         RAM_BUDGET_WORKERS
+#   - Restrict low-level numerical threading to prevent
+#     oversubscription.
+#
+# Important:
+#   - This cell defines candidate structures only.
+#   - No model fitting occurs here.
+#   - No DV-specific filtering occurs here.
+#   - No predictor standardization occurs here.
+#   - Standardization will occur after construction of each
+#     DV-specific analysis sample.
+# ============================================================
+
+
+# ------------------------------------------------------------
+# 4.1 Define Duration-Based Dependent Variables
+# ------------------------------------------------------------
+
+DVS <- c(
+  "IA_FIRST_FIXATION_DURATION",   # Stage 1: FFD
+  "IA_FIRST_RUN_DWELL_TIME",      # Stage 2: GD
+  "IA_REGRESSION_PATH_DURATION",  # Stage 3: GPT
+  "IA_DWELL_TIME"                 # Stage 4: TDT
+)
+
+
+# ------------------------------------------------------------
+# 4.2 Define Candidate Participant-Level Random Slopes
+# ------------------------------------------------------------
+# Paper 1 evaluates whether lexical and/or affective predictor
+# effects vary across participants.
+# ------------------------------------------------------------
+
+SLOPES <- c(
+  "Length",
+  "Predictability",
+  "Frequency",
+  "Valence",
+  "Arousal",
+  "Dominance"
+)
+
+
+# Validate candidate-slope variables before generating models
+missing_slopes <- setdiff(SLOPES, names(df))
+
+if (length(missing_slopes) > 0) {
+  stop(
+    "Missing candidate random-slope variable(s): ",
+    paste(missing_slopes, collapse = ", ")
+  )
+}
+
+
+
+
+# ------------------------------------------------------------
+# 4.3 Generate Candidate Random-Slope Structures
+# ------------------------------------------------------------
+
+CANDIDATES <- generate_re_candidates(
+  SLOPES,
+  max_slopes = MAX_SLOPES_PER_CANDIDATE
+)
+
+NUM_MODELS <- length(CANDIDATES)
+NUM_DVS <- length(DVS)
+
+# Full pipeline = all four DVs combined
+TOTAL_PIPELINE_MODELS <- NUM_DVS * NUM_MODELS
+
+# Each DV is executed manually, one at a time
+TASKS_PER_DV <- NUM_MODELS
+
+message("Candidate slope variables : ", length(SLOPES))
+message("Candidate structures / DV : ", NUM_MODELS)
+message("Duration DVs              : ", NUM_DVS)
+message("Full pipeline models      : ", TOTAL_PIPELINE_MODELS)
+message("Tasks per manual DV run   : ", TASKS_PER_DV)
+
+
+# ------------------------------------------------------------
+# 4.4 System RAM Detection Helper
+# ------------------------------------------------------------
+# Detect total physical RAM in GB.
+#
+# Supported:
+#   - macOS
+#   - Linux
+#
+# Returns NA if RAM detection fails, in which case a conservative
+# fallback worker limit is used below.
+# ------------------------------------------------------------
+
+get_total_ram_gb <- function() {
+  out <- NA_real_
+  os <- Sys.info()[["sysname"]]
+
+  suppressWarnings({
+    if (os == "Darwin") {
+      mem <- as.numeric(system("sysctl -n hw.memsize", intern = TRUE))
+      if (is.finite(mem)) out <- mem / (1024^3)
+
+    } else if (os == "Linux") {
+      memline <- system("grep MemTotal /proc/meminfo", intern = TRUE)
+      memkb <- as.numeric(str_extract(memline, "\\d+"))
+      if (is.finite(memkb)) out <- memkb / (1024^2)
+    }
+  })
+
+  if (length(out) == 0) out <- NA_real_
+
+  out
+}
+
+
+# ------------------------------------------------------------
+# 4.5 Initialize Hardware and Resource Assumptions
+# ------------------------------------------------------------
+
+TOTAL_RAM_GB <- get_total_ram_gb()
+
+# Approximate memory allowance per concurrent lmer task.
+# This is a planning heuristic rather than a measured guarantee.
+EST_RAM_PER_WORKER_GB <- 2.5
+
+# Reserve RAM for the operating system and other processes.
+RAM_HEADROOM_GB <- NA_real_
+
+# Conservative fallback if RAM detection fails.
+RAM_BUDGET_WORKERS <- 1
+
+
+# Detect logical CPUs
+TOTAL_CPUS <- parallel::detectCores(logical = TRUE)
+
+if (is.na(TOTAL_CPUS)) TOTAL_CPUS <- 1
+
+
+# Reserve CPU capacity for the operating system.
+CPU_RESERVE <- if (TOTAL_CPUS >= 8) 2 else 1
+CPU_BUDGET <- max(1, TOTAL_CPUS - CPU_RESERVE)
+
+
+# ------------------------------------------------------------
+# 4.6 Determine RAM-Constrained Worker Budget
+# ------------------------------------------------------------
+
+if (is.na(TOTAL_RAM_GB)) {
+
+  # Conservative fallback when physical RAM cannot be detected.
+  RAM_BUDGET_WORKERS <- max(1, min(4, CPU_BUDGET))
+  RAM_HEADROOM_GB <- NA_real_
+
+} else {
+
+  # Reserve at least 20% of total RAM, with a minimum of 1 GB.
+  RAM_HEADROOM_GB <- max(1.0, TOTAL_RAM_GB * 0.20)
+
+  usable_gb <- max(
+    1.0,
+    TOTAL_RAM_GB - RAM_HEADROOM_GB
+  )
+
+  RAM_BUDGET_WORKERS <- max(
+    1,
+    floor(usable_gb / EST_RAM_PER_WORKER_GB)
+  )
+}
+
+
+# ------------------------------------------------------------
+# 4.7 Determine Final Process-Level Worker Count
+# ------------------------------------------------------------
+# Worker count cannot exceed:
+#   1. Number of model-fitting tasks
+#   2. Available CPU budget
+#   3. Estimated RAM budget
+# ------------------------------------------------------------
+
+N_JOBS <- max(
+  1,
+  min(
+    TASKS_PER_DV,
+    CPU_BUDGET,
+    RAM_BUDGET_WORKERS
+  )
+)
+
+
+# ------------------------------------------------------------
+# 4.8 Configure Low-Level Numerical Threads
+# ------------------------------------------------------------
+# Low-level numerical libraries remain restricted to one
+# thread regardless of the number of R-process workers.
+#
+# This preserves the hard thread-cap policy established in
+# Cell 1.2 and prevents nested numerical threading from
+# producing CPU oversubscription.
+#
+# Intentional parallelism therefore occurs only through the
+# process-level future/multisession workers.
+# ------------------------------------------------------------
+
+BLAS_THREADS <- 1
+
+
+Sys.setenv(
+  OMP_NUM_THREADS = "1",
+  OPENBLAS_NUM_THREADS = "1",
+  MKL_NUM_THREADS = "1",
+  VECLIB_MAXIMUM_THREADS = "1",
+  NUMEXPR_NUM_THREADS = "1"
+)
+
+
+# ------------------------------------------------------------
+# 4.9 Resource-Plan Reporting
+# ------------------------------------------------------------
+
+fmt_num <- function(x, nd = 1) {
+  ifelse(
+    is.na(x),
+    "NA",
+    sprintf(paste0("%.", nd, "f"), x)
+  )
+}
+
+est_peak_ram <- if (is.na(TOTAL_RAM_GB)) {
+  NA_real_
+} else {
+  N_JOBS * EST_RAM_PER_WORKER_GB
+}
+
+
+message("\n", strrep("=", 72))
+message("CORRELATED RANDOM-SLOPE RESOURCE PLAN — AFFECTIVE PROVO")
+message(strrep("=", 72))
+
+message(
+  "Full pipeline     : ",
+  TOTAL_PIPELINE_MODELS,
+  " models (",
+  NUM_DVS, " DVs × ",
+  NUM_MODELS, " candidates)"
+)
+
+message(
+  "Current DV run    : ",
+  TASKS_PER_DV,
+  " candidate models"
+)
+
+message("Slope variables   : ", length(SLOPES))
+message("CPUs detected     : ", TOTAL_CPUS)
+message("CPU reserve       : ", CPU_RESERVE, "  → CPU budget=", CPU_BUDGET)
+message("RAM detected GB   : ", fmt_num(TOTAL_RAM_GB))
+message("RAM headroom GB   : ", fmt_num(RAM_HEADROOM_GB))
+message(
+  "RAM/worker GB     : ",
+  sprintf("%.1f", EST_RAM_PER_WORKER_GB),
+  "  → RAM-limited workers=",
+  RAM_BUDGET_WORKERS
+)
+
+message(strrep("-", 72))
+message("N_JOBS (workers)  : ", N_JOBS)
+message("BLAS threads      : ", BLAS_THREADS, " per worker")
+message("Est. peak RAM GB  : ", fmt_num(est_peak_ram))
+message(strrep("=", 72), "\n")
+
+
+
+
+
+
+
+
+
+# ============================================================
+# CELL 5 — HIGH-RELIABILITY RANDOM-SLOPE MODEL FITTING WORKER
+# ============================================================
+# Purpose:
+#   Fit one candidate participant-level random-slope structure
+#   for a single duration DV using a tiered optimization strategy.
+#
+# Inputs:
+#   dv
+#       → current duration dependent variable
+#
+#   fixed_formula
+#       → fixed-effects specification held constant across all
+#         candidate random-slope structures for the current DV
+#
+#   model_df
+#       → DV-specific analysis dataset prepared before this
+#         function is called
+#
+#   re_terms
+#       → candidate participant random-effects specification,
+#         e.g.:
+#
+#             "1"
+#             "1 + Length"
+#             "1 + Length + Frequency"
+#
+#   groups_col
+#       → grouping factor receiving the candidate random slopes
+#         (normally Participant_ID)
+#
+# Random-effects framework:
+#
+#   Correlated slopes:
+#
+#       (1 + candidate_slopes | Participant_ID)
+#
+#   Uncorrelated slopes:
+#
+#       (1 + candidate_slopes || Participant_ID)
+#
+#   Optional crossed random intercept:
+#
+#       + (1 | Word_Unique_ID)
+#
+# Reliability strategy:
+#   1. Construct the complete mixed-effects formula.
+#   2. Fit the candidate using high-precision bobyqa.
+#   3. Rewrite the stored model call so allFit() does not depend
+#      on temporary local symbols created inside this function.
+#   4. Evaluate the actual lme4 convergence messages and the
+#      numerical optimizer convergence code separately.
+#   5. Treat optimizer convergence code 0 as SUCCESS.
+#   6. Retain a clean bobyqa fit immediately.
+#   7. Run allFit() only when bobyqa has an actual convergence
+#      problem.
+#   8. If allFit() produces one or more warning-free solutions,
+#      retain the valid solution with the highest log-likelihood.
+#   9. If allFit() cannot rescue the model, retain the original
+#      bobyqa fit and preserve its original convergence problem.
+#  10. Record convergence, singularity, likelihood criteria,
+#      observation count, runtime, and diagnostic messages.
+#
+# Estimation:
+#   REML = TRUE in the present Step 2 pipeline.
+#
+#   This is appropriate here because candidate random-slope
+#   structures for a given DV:
+#
+#       - use the same fixed-effects specification
+#       - use the same observations
+#       - differ only in their random-effects structure
+#
+# allFit() robustness:
+#   allFit() refits the original merMod object by updating its
+#   stored model call.
+#
+#   A model fitted inside a helper function can otherwise retain
+#   references in its call to temporary local symbols such as:
+#
+#       full_formula
+#       model_df
+#       reml
+#
+#   Those symbols may no longer be resolvable when allFit()
+#   performs an update/refit.
+#
+#   Therefore, immediately after the primary lmer() fit, this
+#   function rewrites the stored call so that:
+#
+#       formula → the actual mixed-effects formula expression
+#       data    → the actual prepared model data
+#       REML    → literal TRUE/FALSE
+#       control → the complete literal lmerControl() call
+#
+#   The resulting merMod object is self-contained for the
+#   allFit() rescue operation.
+#
+# Important:
+#   - Optimizer code 0 means successful optimization.
+#   - A clean optimizer code must NOT be interpreted as a
+#     convergence warning.
+#   - allFit() is a rescue/robustness procedure here, not a
+#     mandatory refit of every successfully converged model.
+#
+#   - maxfun = 1e6 is used for the primary bobyqa fit.
+#
+#   - This function does NOT construct the analysis sample.
+#   - This function does NOT remove missing observations.
+#   - This function does NOT apply DV > 0 filtering.
+#   - This function does NOT log-transform the DV.
+#   - This function does NOT standardize predictors.
+#
+#   Those operations must occur before model_df is supplied.
+#
+# Shared use:
+#   The same fitting logic is used for:
+#
+#       Paper 1 → Affective Provo candidate slopes
+#       Paper 2 → Lexical Provo candidate slopes
+#
+#   The difference between papers is determined upstream by
+#   SLOPES and model_df, not by this fitting function.
+#
+# Output:
+#   A structured list containing:
+#
+#       winner
+#           → statistics from the retained model fit
+#
+#       audit
+#           → model-fit diagnostic record
+#
+#       full_formula
+#           → complete lmer formula used
+# ============================================================
+
+
+fit_single_candidate_tiered <- function(
+    dv,
+    fixed_formula,
+    model_df,
+    re_terms,
+    groups_col,
+    use_additional_intercept = FALSE,
+    additional_intercept_col = NULL,
+    reml = TRUE
+) {
+  
+  
+  # ----------------------------------------------------------
+  # 5.1 Construct Full Mixed-Effects Formula
+  # ----------------------------------------------------------
+  
+  bar <- if (
+    isTRUE(USE_UNCORRELATED_SLOPES)
+  ) {
+    "||"
+  } else {
+    "|"
+  }
+  
+  
+  rand_part <- paste0(
+    "(",
+    re_terms,
+    " ",
+    bar,
+    " ",
+    groups_col,
+    ")"
+  )
+  
+  
+  rand_other <- if (
+    use_additional_intercept &&
+    !is.null(additional_intercept_col)
+  ) {
+    
+    paste0(
+      " + (1 | ",
+      additional_intercept_col,
+      ")"
+    )
+    
+  } else {
+    
+    ""
+  }
+  
+  
+  full_formula <- as.formula(
+    paste(
+      deparse(fixed_formula),
+      "+",
+      rand_part,
+      rand_other
+    )
+  )
+  
+  
+  # ----------------------------------------------------------
+  # 5.2 Primary Model-Fitting Wrapper
+  # ----------------------------------------------------------
+  # The complete lmerControl() specification is written
+  # directly inside lmer().
+  #
+  # maxfun = 1e6 is literal rather than stored in a temporary
+  # control-object symbol.
+  # ----------------------------------------------------------
+  
+  run_fit <- function() {
+    
+    suppressWarnings(
+      lmer(
+        formula = full_formula,
+        data = model_df,
+        REML = reml,
+        control = lmerControl(
+          optimizer = "bobyqa",
+          optCtrl = list(
+            maxfun = 1e6
+          ),
+          calc.derivs = TRUE,
+          check.conv.grad = .makeCC(
+            "warning",
+            tol = 2e-3
+          ),
+          check.conv.singular = .makeCC(
+            "message",
+            tol = 1e-5
+          ),
+          check.nobs.vs.nlev = "ignore",
+          check.nobs.vs.nRE = "ignore"
+        )
+      )
+    )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 5.3 Start Runtime Tracking
+  # ----------------------------------------------------------
+  
+  t0 <- proc.time()[["elapsed"]]
+  
+  
+  # ----------------------------------------------------------
+  # 5.4 Primary High-Precision bobyqa Fit
+  # ----------------------------------------------------------
+  
+  primary_res <- try(
+    run_fit(),
+    silent = TRUE
+  )
+  
+  
+  # ----------------------------------------------------------
+  # 5.5 Determine Whether Primary Model Initialized
+  # ----------------------------------------------------------
+  
+  primary_initialized <- (
+    !inherits(primary_res, "try-error") &&
+      inherits(primary_res, "merMod")
+  )
+  
+  
+  # ----------------------------------------------------------
+  # 5.6 Handle Initial-Fit Failure
+  # ----------------------------------------------------------
+  
+  if (!primary_initialized) {
+    
+    return(
+      list(
+        
+        winner = list(
+          name = paste0(
+            "RE=",
+            re_terms
+          ),
+          re_formula = re_terms,
+          optimizer = "FAILED",
+          selected_via = "FAILED",
+          converged = FALSE,
+          singular = NA,
+          aic = NA_real_,
+          bic = NA_real_,
+          llf = NA_real_,
+          nobs = nrow(model_df),
+          time_s =
+            proc.time()[["elapsed"]] - t0,
+          status_msg = "FAILED",
+          warnings = paste(
+            "Model failed during initial bobyqa fitting;",
+            "allFit requires an initialized merMod model and",
+            "could not provide a fallback.",
+            as.character(primary_res)
+          )
+        ),
+        
+        audit = list(),
+        
+        full_formula = full_formula
+      )
+    )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 5.7 Make Stored Model Call Self-Contained for allFit()
+  # ----------------------------------------------------------
+  # allFit() uses update() on the fitted merMod object.
+  #
+  # The original call generated inside run_fit() contains local
+  # symbols such as:
+  #
+  #       full_formula
+  #       model_df
+  #       reml
+  #
+  # Replace those references with their actual values so the
+  # stored call can be evaluated independently of this helper's
+  # local environment.
+  #
+  # substitute() converts the formula object into its language
+  # representation for the stored call.
+  #
+  # The prepared data frame itself is inserted into the call.
+  # This increases the size of the stored call but makes the
+  # subsequent allFit() update/refit independent of model_df.
+  # ----------------------------------------------------------
+  
+  self_contained_call <- primary_res@call
+  
+  
+  self_contained_call$formula <-
+    substitute(
+      FORMULA_VALUE,
+      list(
+        FORMULA_VALUE = full_formula
+      )
+    )
+  
+  
+  self_contained_call$data <-
+    substitute(
+      DATA_VALUE,
+      list(
+        DATA_VALUE = model_df
+      )
+    )
+  
+  
+  self_contained_call$REML <-
+    isTRUE(reml)
+  
+  
+  self_contained_call$control <- quote(
+    lmerControl(
+      optimizer = "bobyqa",
+      optCtrl = list(
+        maxfun = 1e6
+      ),
+      calc.derivs = TRUE,
+      check.conv.grad = .makeCC(
+        "warning",
+        tol = 2e-3
+      ),
+      check.conv.singular = .makeCC(
+        "message",
+        tol = 1e-5
+      ),
+      check.nobs.vs.nlev = "ignore",
+      check.nobs.vs.nRE = "ignore"
+    )
+  )
+  
+  
+  primary_res@call <-
+    self_contained_call
+  
+  
+  # ----------------------------------------------------------
+  # 5.8 Evaluate Initial bobyqa Convergence
+  # ----------------------------------------------------------
+  # lme4 stores two distinct forms of convergence information:
+  #
+  #   @optinfo$conv$lme4$messages
+  #       → lme4 convergence diagnostics
+  #
+  #   @optinfo$conv$opt
+  #       → numerical optimizer convergence code
+  #
+  # Optimizer code 0 means SUCCESS.
+  # ----------------------------------------------------------
+  
+  primary_msgs_lme4 <-
+    primary_res@optinfo$conv$lme4$messages
+  
+  
+  primary_opt_code <-
+    primary_res@optinfo$conv$opt
+  
+  
+  primary_lme4_msgs <- if (
+    !is.null(primary_msgs_lme4)
+  ) {
+    
+    as.character(
+      unlist(
+        primary_msgs_lme4
+      )
+    )
+    
+  } else {
+    
+    character(0)
+  }
+  
+  
+  primary_opt_failed <- FALSE
+  
+  
+  if (
+    !is.null(primary_opt_code) &&
+    length(primary_opt_code) > 0
+  ) {
+    
+    primary_opt_code_num <- suppressWarnings(
+      as.numeric(
+        unlist(
+          primary_opt_code
+        )
+      )
+    )
+    
+    
+    primary_opt_failed <- any(
+      is.na(primary_opt_code_num) |
+        primary_opt_code_num != 0
+    )
+  }
+  
+  
+  primary_is_good <- (
+    length(primary_lme4_msgs) == 0 &&
+      !primary_opt_failed
+  )
+  
+  
+  # ----------------------------------------------------------
+  # 5.9 Retain Clean bobyqa Fit or Run allFit() Rescue
+  # ----------------------------------------------------------
+  
+  if (primary_is_good) {
+    
+    res <- primary_res
+    
+    selected_via <-
+      "bobyqa"
+    
+    retained_warning <-
+      NA_character_
+    
+    
+  } else {
+    
+    
+    # --------------------------------------------------------
+    # Preserve Original bobyqa Convergence Diagnostics
+    # --------------------------------------------------------
+    
+    primary_diagnostic_msgs <-
+      primary_lme4_msgs
+    
+    
+    if (primary_opt_failed) {
+      
+      primary_diagnostic_msgs <- c(
+        primary_diagnostic_msgs,
+        paste0(
+          "optimizer convergence code: ",
+          paste(
+            unlist(
+              primary_opt_code
+            ),
+            collapse = ", "
+          )
+        )
+      )
+    }
+    
+    
+    primary_warning_txt <- if (
+      length(primary_diagnostic_msgs) > 0
+    ) {
+      
+      paste(
+        primary_diagnostic_msgs,
+        collapse = " | "
+      )
+      
+    } else {
+      
+      NA_character_
+    }
+    
+    
+    # --------------------------------------------------------
+    # Run allFit() as a Rescue Procedure
+    # --------------------------------------------------------
+    
+    message(
+      "   -> bobyqa convergence issue; running allFit() for ",
+      re_terms,
+      "..."
+    )
+    
+    
+    af <- try(
+      suppressWarnings(
+        lme4::allFit(
+          primary_res,
+          verbose = FALSE,
+          parallel = "no"
+        )
+      ),
+      silent = TRUE
+    )
+    
+    
+    # --------------------------------------------------------
+    # 5.9A allFit() Itself Failed
+    # --------------------------------------------------------
+    
+    if (inherits(af, "try-error")) {
+      
+      res <- primary_res
+      
+      selected_via <-
+        "bobyqa (allFit failed)"
+      
+      retained_warning <- paste(
+        primary_warning_txt,
+        "allFit error:",
+        as.character(af),
+        sep = " | "
+      )
+      
+      
+    } else {
+      
+      
+      ss <- summary(
+        af
+      )
+      
+      
+      # ------------------------------------------------------
+      # 5.9B Identify Warning-Free allFit Solutions
+      # ------------------------------------------------------
+      
+      valid_indices <- which(
+        is.finite(
+          ss$logLik
+        ) &
+          vapply(
+            ss$msgs,
+            function(x) {
+              is.null(x) ||
+                length(x) == 0
+            },
+            logical(1)
+          )
+      )
+      
+      
+      # ------------------------------------------------------
+      # 5.9C No Warning-Free allFit Solution
+      # ------------------------------------------------------
+      
+      if (length(valid_indices) == 0) {
+        
+        res <- primary_res
+        
+        selected_via <-
+          "bobyqa (allFit found no warning-free solution)"
+        
+        retained_warning <-
+          primary_warning_txt
+        
+        
+      } else {
+        
+        
+        # ----------------------------------------------------
+        # 5.9D Retain Best Clean allFit Solution
+        # ----------------------------------------------------
+        # allFit() optimizers estimate the same statistical
+        # model. Among warning-free solutions, retain the one
+        # with the highest reported log-likelihood.
+        # ----------------------------------------------------
+        
+        best_idx <- valid_indices[
+          which.max(
+            ss$logLik[
+              valid_indices
+            ]
+          )
+        ]
+        
+        
+        res <- af[[best_idx]]
+        
+        
+        selected_via <- paste0(
+          "allFit: ",
+          names(af)[best_idx]
+        )
+        
+        
+        retained_warning <-
+          NA_character_
+      }
+    }
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 5.10 Extract Final Convergence Diagnostics
+  # ----------------------------------------------------------
+  
+  msgs_lme4 <-
+    res@optinfo$conv$lme4$messages
+  
+  
+  opt_code <-
+    res@optinfo$conv$opt
+  
+  
+  lme4_msgs <- if (
+    !is.null(msgs_lme4)
+  ) {
+    
+    as.character(
+      unlist(
+        msgs_lme4
+      )
+    )
+    
+  } else {
+    
+    character(0)
+  }
+  
+  
+  opt_failed <- FALSE
+  
+  
+  if (
+    !is.null(opt_code) &&
+    length(opt_code) > 0
+  ) {
+    
+    opt_code_num <- suppressWarnings(
+      as.numeric(
+        unlist(
+          opt_code
+        )
+      )
+    )
+    
+    
+    opt_failed <- any(
+      is.na(opt_code_num) |
+        opt_code_num != 0
+    )
+  }
+  
+  
+  final_diagnostic_msgs <-
+    lme4_msgs
+  
+  
+  if (opt_failed) {
+    
+    final_diagnostic_msgs <- c(
+      final_diagnostic_msgs,
+      paste0(
+        "optimizer convergence code: ",
+        paste(
+          unlist(
+            opt_code
+          ),
+          collapse = ", "
+        )
+      )
+    )
+  }
+  
+  
+  final_warning_txt <- if (
+    length(final_diagnostic_msgs) > 0
+  ) {
+    
+    paste(
+      final_diagnostic_msgs,
+      collapse = " | "
+    )
+    
+  } else {
+    
+    NA_character_
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 5.11 Combine Rescue Information and Final Diagnostics
+  # ----------------------------------------------------------
+  
+  warning_parts <- c(
+    
+    if (!is.na(retained_warning)) {
+      retained_warning
+    } else {
+      NULL
+    },
+    
+    if (!is.na(final_warning_txt)) {
+      final_warning_txt
+    } else {
+      NULL
+    }
+  )
+  
+  
+  warning_parts <- unique(
+    warning_parts[
+      nzchar(
+        warning_parts
+      )
+    ]
+  )
+  
+  
+  warn_txt <- if (
+    length(warning_parts) > 0
+  ) {
+    
+    paste(
+      warning_parts,
+      collapse = " | "
+    )
+    
+  } else {
+    
+    NA_character_
+  }
+  
+  
+  converged <-
+    is.na(warn_txt)
+  
+  
+  # ----------------------------------------------------------
+  # 5.12 Extract Final Model Statistics
+  # ----------------------------------------------------------
+  
+  final_stats <- list(
+    
+    name = paste0(
+      "RE=",
+      re_terms
+    ),
+    
+    re_formula =
+      re_terms,
+    
+    optimizer =
+      res@optinfo$optimizer,
+    
+    selected_via =
+      selected_via,
+    
+    converged =
+      converged,
+    
+    singular =
+      isSingular(
+        res,
+        tol = 1e-5
+      ),
+    
+    aic =
+      AIC(res),
+    
+    bic =
+      BIC(res),
+    
+    llf =
+      as.numeric(
+        logLik(res)
+      ),
+    
+    nobs =
+      nobs(res),
+    
+    time_s =
+      proc.time()[["elapsed"]] - t0,
+    
+    status_msg =
+      if (converged) {
+        "OK"
+      } else {
+        "WARN"
+      },
+    
+    warnings =
+      warn_txt
+  )
+  
+  
+  # ----------------------------------------------------------
+  # 5.13 Structured Return
+  # ----------------------------------------------------------
+  
+  list(
+    winner =
+      final_stats,
+    
+    audit =
+      list(
+        final_stats
+      ),
+    
+    full_formula =
+      full_formula
+  )
+}
+
+
+
+
+
+
+
+
+
+# ============================================================
+# CELL 6/7 — DV-SPECIFIC PREPARATION + PARALLEL MODEL RUNNER
+# ============================================================
+# Purpose:
+#   Construct one analysis-ready dataset per duration DV and
+#   compare all candidate correlated random-slope structures
+#   using that identical dataset.
+#
+# Responsibilities:
+#   1. Validate all variables required for the current DV.
+#   2. Construct the DV-specific complete-case sample.
+#   3. Remove non-positive values of the current duration DV.
+#   4. Natural-log transform the current duration DV.
+#   5. Standardize predictors using population SD (DDOF = 0)
+#      AFTER the final DV-specific sample has been established.
+#   6. Convert grouping variables to factors.
+#   7. Fit every candidate random-slope structure using the
+#      exact same prepared dataset.
+#   8. Execute candidate models in parallel.
+#   9. Collect model diagnostics and fit statistics.
+#  10. Evaluate and order candidate structures using
+#      convergence, singularity, and BIC/AIC.
+#  11. Produce a detailed sample-size audit.
+#
+# Paper 1 fixed-effects specification:
+#
+#   Lexical predictors:
+#       - Length
+#       - Predictability
+#       - Frequency
+#
+#   Affective predictors:
+#       - Valence
+#       - Arousal
+#       - Dominance
+#
+# Important:
+#   Filtering is DV-specific.
+#
+#   No global IA_DWELL_TIME > 0 restriction is imposed.
+#   Instead, the CURRENT duration DV must be non-missing and > 0.
+#
+#   Predictor standardization occurs only AFTER this DV-specific
+#   sample has been established. All candidate random-slope
+#   models for the same DV therefore receive:
+#
+#       - identical observations
+#       - identical transformed DV values
+#       - identical standardized predictor values
+#       - identical fixed-effects specification
+#
+#   Only the participant-level random-slope structure changes.
+#
+# This is essential for fair AIC/BIC comparison.
+# ============================================================
+
+
+# ------------------------------------------------------------
+# 6.1 Population-SD Standardization Function (DDOF = 0)
+# ------------------------------------------------------------
+# R's sd() uses sample SD (n - 1). The conversion below yields
+# population SD (n), matching DDOF = 0 standardization used
+# elsewhere in the analysis pipeline.
+# ------------------------------------------------------------
+
+zscore_ddof0 <- function(x) {
+  
+  x <- suppressWarnings(
+    as.numeric(x)
+  )
+  
+  n <- sum(
+    !is.na(x)
+  )
+  
+  if (n <= 1) {
+    return(x)
+  }
+  
+  s1 <- sd(
+    x,
+    na.rm = TRUE
+  )
+  
+  if (
+    !is.finite(s1) ||
+    s1 <= 0
+  ) {
+    return(x)
+  }
+  
+  s0 <- s1 * sqrt(
+    (n - 1) / n
+  )
+  
+  (
+    x - mean(
+      x,
+      na.rm = TRUE
+    )
+  ) / s0
+}
+
+
+# ------------------------------------------------------------
+# 6.2 DV-Specific Analysis-Data Preparation
+# ------------------------------------------------------------
+
+prep_df_complete_cases <- function(
+    df,
+    dv,
+    participant_col,
+    required_cols,
+    use_additional_intercept = FALSE,
+    additional_intercept_col = NULL
+) {
+  
+  needed <- unique(
+    c(
+      dv,
+      participant_col,
+      required_cols,
+      if (use_additional_intercept) {
+        additional_intercept_col
+      } else {
+        NULL
+      }
+    )
+  )
+  
+  
+  # ----------------------------------------------------------
+  # Validate Required Variables
+  # ----------------------------------------------------------
+  
+  missing_required <- setdiff(
+    needed,
+    names(df)
+  )
+  
+  if (length(missing_required) > 0) {
+    
+    stop(
+      "Missing required variable(s) for ",
+      dv,
+      ": ",
+      paste(
+        missing_required,
+        collapse = ", "
+      )
+    )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # Select Required Variables
+  # ----------------------------------------------------------
+  
+  df_clean <- df %>%
+    select(
+      all_of(needed)
+    )
+  
+  n_source <- nrow(
+    df_clean
+  )
+  
+  
+  # ----------------------------------------------------------
+  # Coerce DV and Continuous Predictors to Numeric
+  # ----------------------------------------------------------
+  
+  numeric_cols <- unique(
+    c(
+      dv,
+      required_cols
+    )
+  )
+  
+  df_clean <- df_clean %>%
+    mutate(
+      across(
+        all_of(numeric_cols),
+        ~ suppressWarnings(
+          as.numeric(.x)
+        )
+      )
+    )
+  
+  
+  # ----------------------------------------------------------
+  # Remove Missing Values
+  # ----------------------------------------------------------
+  
+  df_clean <- df_clean %>%
+    drop_na()
+  
+  n_complete <- nrow(
+    df_clean
+  )
+  
+  n_removed_missing <-
+    n_source - n_complete
+  
+  
+  # ----------------------------------------------------------
+  # Retain Positive Values of the Current Duration DV
+  # ----------------------------------------------------------
+  # Zero/non-positive values are excluded because the present
+  # models analyze positive duration observations.
+  #
+  # Do not interpret every zero here as equivalent to IA_SKIP.
+  # ----------------------------------------------------------
+  
+  df_clean <- df_clean %>%
+    filter(
+      .data[[dv]] > 0
+    )
+  
+  n_positive <- nrow(
+    df_clean
+  )
+  
+  n_removed_nonpositive <-
+    n_complete - n_positive
+  
+  
+  # ----------------------------------------------------------
+  # Natural-Log Transform Current DV
+  # ----------------------------------------------------------
+  
+  df_clean[[dv]] <- log(
+    df_clean[[dv]]
+  )
+  
+  
+  # ----------------------------------------------------------
+  # Standardize Predictors Within Final DV-Specific Sample
+  # ----------------------------------------------------------
+  
+  df_clean <- df_clean %>%
+    mutate(
+      across(
+        all_of(required_cols),
+        zscore_ddof0
+      )
+    )
+  
+  
+  # ----------------------------------------------------------
+  # Convert Grouping Variables to Factors
+  # ----------------------------------------------------------
+  
+  df_clean[[participant_col]] <- as.factor(
+    as.character(
+      df_clean[[participant_col]]
+    )
+  )
+  
+  
+  if (
+    use_additional_intercept &&
+    !is.null(additional_intercept_col)
+  ) {
+    
+    df_clean[[additional_intercept_col]] <- as.factor(
+      as.character(
+        df_clean[[additional_intercept_col]]
+      )
+    )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # Attach Filtering Diagnostics
+  # ----------------------------------------------------------
+  
+  attr(
+    df_clean,
+    "filter_summary"
+  ) <- tibble(
+    
+    DV =
+      dv,
+    
+    N_Source =
+      n_source,
+    
+    N_Removed_Missing =
+      n_removed_missing,
+    
+    N_Complete =
+      n_complete,
+    
+    N_Removed_NonPositive =
+      n_removed_nonpositive,
+    
+    N_Final =
+      n_positive,
+    
+    Percent_Retained =
+      if (n_source > 0) {
+        
+        round(
+          100 * n_positive / n_source,
+          2
+        )
+        
+      } else {
+        
+        NA_real_
+      },
+    
+    N_Participants =
+      n_distinct(
+        df_clean[[participant_col]]
+      ),
+    
+    N_Additional_Intercept =
+      if (
+        use_additional_intercept &&
+        !is.null(additional_intercept_col)
+      ) {
+        
+        n_distinct(
+          df_clean[[additional_intercept_col]]
+        )
+        
+      } else {
+        
+        NA_integer_
+      }
+  )
+  
+  
+  message(
+    "   Source observations       : ",
+    format(
+      n_source,
+      big.mark = ","
+    )
+  )
+  
+  message(
+    "   Removed for missingness   : ",
+    format(
+      n_removed_missing,
+      big.mark = ","
+    )
+  )
+  
+  message(
+    "   Removed DV <= 0           : ",
+    format(
+      n_removed_nonpositive,
+      big.mark = ","
+    )
+  )
+  
+  message(
+    "   Final modeling N          : ",
+    format(
+      n_positive,
+      big.mark = ","
+    )
+  )
+  
+  message(
+    "   DV log transformation     : APPLIED"
+  )
+  
+  message(
+    "   Predictor standardization : APPLIED (DDOF = 0)"
+  )
+  
+  
+  df_clean
+}
+
+
+# ------------------------------------------------------------
+# 6.3 Dynamic Correlated Random-Slope Selection Engine
+# ------------------------------------------------------------
+
+select_re_structure_dynamic <- function(
+    df,
+    dv,
+    re_candidates,
+    participant_col = "Participant_ID",
+    additional_intercept_col = NULL,
+    use_additional_intercept = FALSE,
+    controls = c(
+      "Length",
+      "Predictability",
+      "Frequency"
+    ),
+    emotions = c(
+      "Valence",
+      "Arousal",
+      "Dominance"
+    ),
+    rank_by = c(
+      "BIC",
+      "AIC"
+    ),
+    n_jobs = 1
+) {
+  
+  
+  # ----------------------------------------------------------
+  # 6.3.1 Configuration
+  # ----------------------------------------------------------
+  
+  rank_by <- match.arg(
+    toupper(rank_by),
+    c(
+      "BIC",
+      "AIC"
+    )
+  )
+  
+  n_jobs <- max(
+    1L,
+    as.integer(n_jobs)
+  )
+  
+  
+  required_cols <- unique(
+    c(
+      controls,
+      emotions
+    )
+  )
+  
+  
+  # ----------------------------------------------------------
+  # Validate Fixed-Effect Variables
+  # ----------------------------------------------------------
+  
+  missing_fixed <- setdiff(
+    required_cols,
+    names(df)
+  )
+  
+  if (length(missing_fixed) > 0) {
+    
+    stop(
+      "Missing fixed-effect variable(s) for ",
+      dv,
+      ": ",
+      paste(
+        missing_fixed,
+        collapse = ", "
+      )
+    )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # Construct Fixed-Effects Formula
+  # ----------------------------------------------------------
+  
+  fixed_formula <- as.formula(
+    paste0(
+      dv,
+      " ~ ",
+      paste(
+        required_cols,
+        collapse = " + "
+      )
+    )
+  )
+  
+  
+  # ----------------------------------------------------------
+  # 6.3.2 Prepare ONE Modeling Dataset for Current DV
+  # ----------------------------------------------------------
+  
+  model_df <- prep_df_complete_cases(
+    df = df,
+    dv = dv,
+    participant_col = participant_col,
+    required_cols = required_cols,
+    use_additional_intercept =
+      use_additional_intercept,
+    additional_intercept_col =
+      additional_intercept_col
+  )
+  
+  
+  filter_summary <- attr(
+    model_df,
+    "filter_summary"
+  )
+  
+  
+  # ----------------------------------------------------------
+  # Safety Check: Final Modeling Dataset Must Be Nonempty
+  # ----------------------------------------------------------
+  
+  if (nrow(model_df) == 0) {
+    
+    stop(
+      "No eligible observations remain for ",
+      dv,
+      " after DV-specific preparation."
+    )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 6.3.3 Row-Count Audit
+  # ----------------------------------------------------------
+  
+  rowcounts <- dv_rowcount_summary(
+    df = df,
+    dv = dv,
+    required_cols = c(
+      required_cols,
+      participant_col,
+      if (use_additional_intercept) {
+        additional_intercept_col
+      } else {
+        NULL
+      }
+    ),
+    label = paste0(
+      dv,
+      "_AIC_BIC_rows"
+    )
+  ) %>%
+    mutate(
+      
+      rows_after_complete_case =
+        filter_summary$N_Complete,
+      
+      rows_removed_DV_nonpositive =
+        filter_summary$N_Removed_NonPositive,
+      
+      final_rows_used_for_AIC_BIC =
+        filter_summary$N_Final,
+      
+      pct_final_rows_retained =
+        filter_summary$Percent_Retained
+    )
+  
+  
+  # ----------------------------------------------------------
+  # 6.3.4 Candidate Execution Ordering
+  # ----------------------------------------------------------
+  
+  cand_list <- rev(
+    re_candidates
+  )
+  
+  
+  indexed <- tibble(
+    idx = seq_along(
+      cand_list
+    ),
+    candidate = cand_list
+  )
+  
+  
+  # ----------------------------------------------------------
+  # 6.3.5 Parallel Execution Setup
+  # ----------------------------------------------------------
+  
+  future::plan(
+    future::multisession,
+    workers = n_jobs
+  )
+  
+  
+  progressr::handlers(
+    global = TRUE
+  )
+  
+  
+  # ----------------------------------------------------------
+  # 6.3.6 Parallel Candidate-Model Execution
+  # ----------------------------------------------------------
+  
+  results_payload <- progressr::with_progress({
+    
+    progressor_obj <- progressr::progressor(
+      steps = nrow(indexed)
+    )
+    
+    
+    future.apply::future_lapply(
+      
+      seq_len(
+        nrow(indexed)
+      ),
+      
+      function(i) {
+        
+        idx <- indexed$idx[i]
+        cand <- indexed$candidate[i]
+        
+        
+        t0 <- proc.time()[["elapsed"]]
+        
+        
+        fit <- fit_single_candidate_tiered(
+          dv = dv,
+          fixed_formula = fixed_formula,
+          model_df = model_df,
+          re_terms = cand,
+          groups_col = participant_col,
+          use_additional_intercept =
+            use_additional_intercept,
+          additional_intercept_col =
+            additional_intercept_col,
+          reml = TRUE
+        )
+        
+        
+        progressor_obj(
+          message = paste0(
+            "[",
+            idx,
+            "/",
+            nrow(indexed),
+            "] ",
+            cand
+          )
+        )
+        
+        
+        list(
+          idx = idx,
+          candidate = cand,
+          winner = fit$winner,
+          audit = fit$audit,
+          task_wall_s =
+            proc.time()[["elapsed"]] - t0
+        )
+      },
+      
+      future.seed = TRUE,
+      
+      future.globals = list(
+        
+        indexed =
+          indexed,
+        
+        dv =
+          dv,
+        
+        fixed_formula =
+          fixed_formula,
+        
+        model_df =
+          model_df,
+        
+        participant_col =
+          participant_col,
+        
+        additional_intercept_col =
+          additional_intercept_col,
+        
+        use_additional_intercept =
+          use_additional_intercept,
+        
+        fit_single_candidate_tiered =
+          fit_single_candidate_tiered,
+        
+        USE_UNCORRELATED_SLOPES =
+          USE_UNCORRELATED_SLOPES
+      ),
+      
+      future.packages = c(
+        "lme4"
+      )
+    )
+  })
+  
+  
+  # ----------------------------------------------------------
+  # 6.3.7 Restore Deterministic Execution Order
+  # ----------------------------------------------------------
+  
+  results_payload <- results_payload[
+    order(
+      vapply(
+        results_payload,
+        `[[`,
+        numeric(1),
+        "idx"
+      )
+    )
+  ]
+  
+  
+  # ----------------------------------------------------------
+  # 6.3.8 Collect Model Results and Audit Records
+  # ----------------------------------------------------------
+  
+  winner_rows <- list()
+  audit_rows <- list()
+  
+  
+  for (payload in results_payload) {
+    
+    w <- payload$winner
+    
+    
+    if (
+      is.finite(w$aic) &&
+      is.finite(w$bic)
+    ) {
+      
+      winner_rows <- append(
+        winner_rows,
+        list(
+          tibble(
+            
+            idx =
+              payload$idx,
+            
+            candidate =
+              payload$candidate,
+            
+            re_formula =
+              w$re_formula,
+            
+            optimizer =
+              w$optimizer,
+            
+            selected_via =
+              w$selected_via,
+            
+            converged =
+              w$converged,
+            
+            singular =
+              w$singular,
+            
+            aic =
+              w$aic,
+            
+            bic =
+              w$bic,
+            
+            llf =
+              w$llf,
+            
+            nobs =
+              as.integer(
+                w$nobs
+              ),
+            
+            winner_fit_time_s =
+              as.numeric(
+                w$time_s
+              ),
+            
+            candidate_task_time_s =
+              as.numeric(
+                payload$task_wall_s
+              ),
+            
+            warnings =
+              w$warnings,
+            
+            status =
+              w$status_msg
+          )
+        )
+      )
+    }
+    
+    
+    for (a in payload$audit) {
+      
+      audit_rows <- append(
+        audit_rows,
+        list(
+          tibble(
+            
+            idx =
+              payload$idx,
+            
+            candidate =
+              payload$candidate,
+            
+            re_formula =
+              a$re_formula,
+            
+            optimizer =
+              a$optimizer,
+            
+            selected_via =
+              a$selected_via,
+            
+            status =
+              a$status_msg,
+            
+            converged =
+              a$converged,
+            
+            singular =
+              a$singular,
+            
+            aic =
+              a$aic,
+            
+            bic =
+              a$bic,
+            
+            llf =
+              a$llf,
+            
+            nobs =
+              as.integer(
+                a$nobs
+              ),
+            
+            time_s =
+              as.numeric(
+                a$time_s
+              ),
+            
+            warnings =
+              a$warnings
+          )
+        )
+      )
+    }
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 6.3.9 Final Candidate Evaluation and Selection Ordering
+  # ----------------------------------------------------------
+  
+  df_results <- if (
+    length(winner_rows) > 0
+  ) {
+    
+    bind_rows(
+      winner_rows
+    )
+    
+  } else {
+    
+    tibble()
+  }
+  
+  
+  df_audit <- if (
+    length(audit_rows) > 0
+  ) {
+    
+    bind_rows(
+      audit_rows
+    )
+    
+  } else {
+    
+    tibble()
+  }
+  
+  
+  if (nrow(df_results) > 0) {
+    
+    sort_col <- if (
+      rank_by == "BIC"
+    ) {
+      
+      "bic"
+      
+    } else {
+      
+      "aic"
+    }
+    
+    
+    # --------------------------------------------------------
+    # Identify Models Eligible for Primary Structure Selection
+    # --------------------------------------------------------
+    
+    df_results <- df_results %>%
+      mutate(
+        selection_eligible =
+          converged %in% TRUE &
+          singular %in% FALSE
+      )
+    
+    
+    # --------------------------------------------------------
+    # Compute Raw Information-Criterion Differences
+    # --------------------------------------------------------
+    
+    df_results <- df_results %>%
+      mutate(
+        
+        delta_aic =
+          aic - min(
+            aic,
+            na.rm = TRUE
+          ),
+        
+        delta_bic =
+          bic - min(
+            bic,
+            na.rm = TRUE
+          )
+      )
+    
+    
+    # --------------------------------------------------------
+    # Rank Eligible Models First
+    # --------------------------------------------------------
+    
+    df_results <- df_results %>%
+      arrange(
+        desc(
+          selection_eligible
+        ),
+        .data[[sort_col]]
+      )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 6.3.10 Verify Equal Observation Counts Across Candidates
+  # ----------------------------------------------------------
+  
+  if (nrow(df_results) > 0) {
+    
+    unique_nobs <- unique(
+      df_results$nobs
+    )
+    
+    
+    if (length(unique_nobs) != 1) {
+      
+      warning(
+        "Candidate models for ",
+        dv,
+        " were fitted with different observation counts."
+      )
+    }
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 6.3.11 Return Results
+  # ----------------------------------------------------------
+  
+  list(
+    
+    df_results =
+      df_results,
+    
+    df_audit =
+      df_audit,
+    
+    rowcounts =
+      rowcounts,
+    
+    filter_summary =
+      filter_summary
+  )
+}
+
+
+
+
+
+
+
+
+
+# ============================================================
+# CELL 8/9 — MANUAL DV-BY-DV CORRELATED-SLOPE EXECUTION
+# ============================================================
+# Purpose:
+#   Run the correlated random-slope selection procedure
+#   independently for each duration-based dependent variable.
+#
+# Execution strategy:
+#   Each DV is defined in a separate execution block rather
+#   than inside a single loop.
+#
+#   When the full script is executed, the four DV blocks run
+#   sequentially. Individual DV blocks can also be executed
+#   independently when rerunning or recovering an analysis.
+#
+# Advantages:
+#   - Limits the consequences of a long-running model failure.
+#   - Allows each DV to be restarted independently.
+#   - Simplifies monitoring of CPU/RAM use.
+#   - Allows results to be inspected before proceeding.
+#   - Produces a separate Excel workbook for each DV.
+#
+# For each DV:
+#   1. Construct the DV-specific analysis sample.
+#   2. Remove missing/non-positive duration observations.
+#   3. Log-transform the current duration DV.
+#   4. Standardize LFP + VAD predictors within that sample.
+#   5. Fit all candidate correlated random-slope structures.
+#   6. Evaluate candidates using BIC, convergence, and
+#      singularity diagnostics.
+#   7. Order selection-eligible candidates first, ranked by BIC
+#      within eligibility class.
+#
+# Paper 1:
+#   Source dataset:
+#       Affective Provo
+#
+#   Fixed effects / candidate slopes:
+#       Length
+#       Predictability
+#       Frequency
+#       Valence
+#       Arousal
+#       Dominance
+#
+#   Random-effects framework:
+#       (1 + candidate slopes | Participant_ID)
+#       + (1 | Word_Unique_ID)
+#
+# Important:
+#   - Candidate models within a DV use exactly the same
+#     DV-specific analysis sample.
+#   - Filtering and standardization are performed once per DV,
+#     before candidate-model fitting.
+#   - BIC is the primary ranking criterion.
+#   - Convergence and singularity diagnostics must also be
+#     considered when selecting the final random-slope structure.
+#
+# Output:
+#   One Step 2 Excel workbook per duration DV containing:
+#       - candidate ranking
+#       - model-fit audit
+#       - sample-size / row-count audit
+#
+# Runtime:
+#   Runtime depends on sample size, candidate complexity,
+#   optimizer behavior, hardware, and number of workers.
+#   Previous runtime estimates should therefore not be assumed
+#   for the revised pipeline.
+# ============================================================
+
+
+# ------------------------------------------------------------
+# 8.1 DV Registry
+# ------------------------------------------------------------
+
+DV_INFO <- list(
+  IA_FIRST_FIXATION_DURATION  = list(serial = 1, suffix = "FFD"),
+  IA_FIRST_RUN_DWELL_TIME     = list(serial = 2, suffix = "GD"),
+  IA_REGRESSION_PATH_DURATION = list(serial = 3, suffix = "GPT"),
+  IA_DWELL_TIME               = list(serial = 4, suffix = "TDT")
+)
+
+
+
+# ============================================================
+# DV 1 — FIRST FIXATION DURATION (FFD)
+# ============================================================
+
+DV_TO_RUN <- "IA_FIRST_FIXATION_DURATION"
+
+if (is.null(DV_INFO[[DV_TO_RUN]])) {
+  stop("Unknown DV_TO_RUN: ", DV_TO_RUN)
+}
+
+DV_SERIAL <- DV_INFO[[DV_TO_RUN]]$serial
+DV_SUFFIX <- DV_INFO[[DV_TO_RUN]]$suffix
+
+message("\n", strrep("=", 80))
+message("STARTING CORRELATED-SLOPE ANALYSIS")
+message("DV: ", DV_TO_RUN, " | Stage=", DV_SERIAL, " | Measure=", DV_SUFFIX)
+message("Dataset: Affective Provo")
+message(strrep("=", 80))
+
+t0 <- proc.time()[["elapsed"]]
+
+res <- select_re_structure_dynamic(
+  df = df,
+  dv = DV_TO_RUN,
+  re_candidates = CANDIDATES,
+  rank_by = "BIC",
+  n_jobs = N_JOBS,
+  participant_col = "Participant_ID",
+  additional_intercept_col = ADDITIONAL_INTERCEPT,
+  use_additional_intercept = USE_ADDITIONAL_INTERCEPT
+)
+
+out_path <- file.path(
+  OUTPUT_DATA_DIR,
+  paste0(
+    "Step-2-",
+    DV_SERIAL, "_",
+    DV_SUFFIX,
+    "_CorrelatedSlopes_Affective_Provo.xlsx"
+  )
+)
+
+save_re_outputs_to_excel(
+  excel_path = out_path,
+  dv = DV_TO_RUN,
+  df_results = res$df_results,
+  df_audit = res$df_audit,
+  rowcount_summary = res$rowcounts
+)
+
+elapsed_total <- proc.time()[["elapsed"]] - t0
+
+message("\nDV-SPECIFIC SAMPLE:")
+print(res$filter_summary)
+
+message("\nCOMPLETED DV: ", DV_TO_RUN)
+message("Saved to: ", out_path)
+message("Elapsed time: ", fmt_secs(elapsed_total))
+
+
+
+# ============================================================
+# DV 2 — FIRST-RUN DWELL TIME / GAZE DURATION (GD)
+# ============================================================
+
+DV_TO_RUN <- "IA_FIRST_RUN_DWELL_TIME"
+
+if (is.null(DV_INFO[[DV_TO_RUN]])) {
+  stop("Unknown DV_TO_RUN: ", DV_TO_RUN)
+}
+
+DV_SERIAL <- DV_INFO[[DV_TO_RUN]]$serial
+DV_SUFFIX <- DV_INFO[[DV_TO_RUN]]$suffix
+
+message("\n", strrep("=", 80))
+message("STARTING CORRELATED-SLOPE ANALYSIS")
+message("DV: ", DV_TO_RUN, " | Stage=", DV_SERIAL, " | Measure=", DV_SUFFIX)
+message("Dataset: Affective Provo")
+message(strrep("=", 80))
+
+t0 <- proc.time()[["elapsed"]]
+
+res <- select_re_structure_dynamic(
+  df = df,
+  dv = DV_TO_RUN,
+  re_candidates = CANDIDATES,
+  rank_by = "BIC",
+  n_jobs = N_JOBS,
+  participant_col = "Participant_ID",
+  additional_intercept_col = ADDITIONAL_INTERCEPT,
+  use_additional_intercept = USE_ADDITIONAL_INTERCEPT
+)
+
+out_path <- file.path(
+  OUTPUT_DATA_DIR,
+  paste0(
+    "Step-2-",
+    DV_SERIAL, "_",
+    DV_SUFFIX,
+    "_CorrelatedSlopes_Affective_Provo.xlsx"
+  )
+)
+
+save_re_outputs_to_excel(
+  excel_path = out_path,
+  dv = DV_TO_RUN,
+  df_results = res$df_results,
+  df_audit = res$df_audit,
+  rowcount_summary = res$rowcounts
+)
+
+elapsed_total <- proc.time()[["elapsed"]] - t0
+
+message("\nDV-SPECIFIC SAMPLE:")
+print(res$filter_summary)
+
+message("\nCOMPLETED DV: ", DV_TO_RUN)
+message("Saved to: ", out_path)
+message("Elapsed time: ", fmt_secs(elapsed_total))
+
+
+
+# ============================================================
+# DV 3 — REGRESSION PATH DURATION / GO-PAST TIME (GPT)
+# ============================================================
+
+DV_TO_RUN <- "IA_REGRESSION_PATH_DURATION"
+
+if (is.null(DV_INFO[[DV_TO_RUN]])) {
+  stop("Unknown DV_TO_RUN: ", DV_TO_RUN)
+}
+
+DV_SERIAL <- DV_INFO[[DV_TO_RUN]]$serial
+DV_SUFFIX <- DV_INFO[[DV_TO_RUN]]$suffix
+
+message("\n", strrep("=", 80))
+message("STARTING CORRELATED-SLOPE ANALYSIS")
+message("DV: ", DV_TO_RUN, " | Stage=", DV_SERIAL, " | Measure=", DV_SUFFIX)
+message("Dataset: Affective Provo")
+message(strrep("=", 80))
+
+t0 <- proc.time()[["elapsed"]]
+
+res <- select_re_structure_dynamic(
+  df = df,
+  dv = DV_TO_RUN,
+  re_candidates = CANDIDATES,
+  rank_by = "BIC",
+  n_jobs = N_JOBS,
+  participant_col = "Participant_ID",
+  additional_intercept_col = ADDITIONAL_INTERCEPT,
+  use_additional_intercept = USE_ADDITIONAL_INTERCEPT
+)
+
+out_path <- file.path(
+  OUTPUT_DATA_DIR,
+  paste0(
+    "Step-2-",
+    DV_SERIAL, "_",
+    DV_SUFFIX,
+    "_CorrelatedSlopes_Affective_Provo.xlsx"
+  )
+)
+
+save_re_outputs_to_excel(
+  excel_path = out_path,
+  dv = DV_TO_RUN,
+  df_results = res$df_results,
+  df_audit = res$df_audit,
+  rowcount_summary = res$rowcounts
+)
+
+elapsed_total <- proc.time()[["elapsed"]] - t0
+
+message("\nDV-SPECIFIC SAMPLE:")
+print(res$filter_summary)
+
+message("\nCOMPLETED DV: ", DV_TO_RUN)
+message("Saved to: ", out_path)
+message("Elapsed time: ", fmt_secs(elapsed_total))
+
+
+
+# ============================================================
+# DV 4 — TOTAL DWELL TIME / TOTAL READING TIME (TDT)
+# ============================================================
+
+DV_TO_RUN <- "IA_DWELL_TIME"
+
+if (is.null(DV_INFO[[DV_TO_RUN]])) {
+  stop("Unknown DV_TO_RUN: ", DV_TO_RUN)
+}
+
+DV_SERIAL <- DV_INFO[[DV_TO_RUN]]$serial
+DV_SUFFIX <- DV_INFO[[DV_TO_RUN]]$suffix
+
+message("\n", strrep("=", 80))
+message("STARTING CORRELATED-SLOPE ANALYSIS")
+message("DV: ", DV_TO_RUN, " | Stage=", DV_SERIAL, " | Measure=", DV_SUFFIX)
+message("Dataset: Affective Provo")
+message(strrep("=", 80))
+
+t0 <- proc.time()[["elapsed"]]
+
+res <- select_re_structure_dynamic(
+  df = df,
+  dv = DV_TO_RUN,
+  re_candidates = CANDIDATES,
+  rank_by = "BIC",
+  n_jobs = N_JOBS,
+  participant_col = "Participant_ID",
+  additional_intercept_col = ADDITIONAL_INTERCEPT,
+  use_additional_intercept = USE_ADDITIONAL_INTERCEPT
+)
+
+out_path <- file.path(
+  OUTPUT_DATA_DIR,
+  paste0(
+    "Step-2-",
+    DV_SERIAL, "_",
+    DV_SUFFIX,
+    "_CorrelatedSlopes_Affective_Provo.xlsx"
+  )
+)
+
+save_re_outputs_to_excel(
+  excel_path = out_path,
+  dv = DV_TO_RUN,
+  df_results = res$df_results,
+  df_audit = res$df_audit,
+  rowcount_summary = res$rowcounts
+)
+
+elapsed_total <- proc.time()[["elapsed"]] - t0
+
+message("\nDV-SPECIFIC SAMPLE:")
+print(res$filter_summary)
+
+message("\nCOMPLETED DV: ", DV_TO_RUN)
+message("Saved to: ", out_path)
+message("Elapsed time: ", fmt_secs(elapsed_total))
+
+
+
+
+
+# ============================================================
+# RUNTIME LOG — END
+# ============================================================
+# Purpose:
+#   Finalize the Step 2 runtime log after all requested
+#   correlated random-slope analyses have completed.
+#
+# Records:
+#   - Analysis completion timestamp
+#   - R session information
+#
+# Cleanup:
+#   - Close the message sink
+#   - Close the standard-output sink
+#   - Close the runtime-log file connection
+#
+# Safety:
+#   Sink and connection states are checked before closing so
+#   this cell can be rerun without unnecessarily attempting
+#   to close inactive sinks or an already-closed connection.
+# ============================================================
+
+
+# ------------------------------------------------------------
+# 1. Record Analysis Completion
+# ------------------------------------------------------------
+
+cat(
+  paste0(
+    "\n",
+    strrep("=", 80), "\n",
+    "STEP 2 — CORRELATED RANDOM-SLOPE ANALYSIS COMPLETED\n",
+    "Dataset: Affective Provo\n",
+    "Finished: ", format(Sys.time(), "%Y-%m-%d %H:%M:%S"), "\n",
+    strrep("=", 80), "\n\n"
+  )
+)
+
+
+# ------------------------------------------------------------
+# 2. Record R Session Information
+# ------------------------------------------------------------
+
+cat("SESSION INFORMATION\n")
+cat(strrep("-", 80), "\n")
+
+print(sessionInfo())
+
+cat(
+  "\n",
+  strrep("=", 80), "\n",
+  "END OF RUNTIME LOG\n",
+  strrep("=", 80), "\n"
+)
+
+
+# ------------------------------------------------------------
+# 3. Flush Runtime-Log Connection
+# ------------------------------------------------------------
+# Push any buffered output to disk before sinks are closed.
+# ------------------------------------------------------------
+
+if (exists("log_con") && isOpen(log_con)) {
+  flush(log_con)
+}
+
+
+# ------------------------------------------------------------
+# 4. Close Message Sink
+# ------------------------------------------------------------
+# Message output was redirected separately using:
+#   sink(log_con, type = "message")
+# ------------------------------------------------------------
+
+if (sink.number(type = "message") > 0) {
+  sink(type = "message")
+}
+
+
+# ------------------------------------------------------------
+# 5. Close Standard-Output Sink
+# ------------------------------------------------------------
+# Standard output was redirected using:
+#   sink(log_con, split = TRUE)
+# ------------------------------------------------------------
+
+if (sink.number(type = "output") > 0) {
+  sink(type = "output")
+}
+
+
+# ------------------------------------------------------------
+# 6. Close Runtime-Log Connection
+# ------------------------------------------------------------
+
+if (exists("log_con") && isOpen(log_con)) {
+  close(log_con)
+}
+
+
+# ------------------------------------------------------------
+# 7. Confirm Successful Log Export
+# ------------------------------------------------------------
+# This message is intentionally emitted AFTER the sinks have
+# been closed, so it appears only in the active R console.
+# ------------------------------------------------------------
+
+message(
+  "Runtime log saved successfully: ",
+  LOG_PATH
+)

05-Research_Program-Affective_Provo/01-Fixation_Duration_Research/01-LME_Model_Structure/01-Scripts/Step-3-Testing_Best_UncorrelatedSlopes_for_Selected_Random_Intercept.R

@@ -0,0 +1,3925 @@
+# ============================================================
+# COPYRIGHT, LICENSING, AND SCHOLARLY CITATION
+# ============================================================
+# Copyright (c) 2026 Mohit Gupta
+# License: MIT
+# SPDX-License-Identifier: MIT
+#
+# This script contains original computational software
+# developed by Mohit Gupta for the AffLex-Provo
+# Research Program.
+#
+# Citation:
+# Researchers using this software in published research
+# are strongly requested to cite the AffLex-Provo repository:
+# https://huggingface.co/datasets/mohitg2/AffLex-Provo
+#
+# Third-party datasets and externally sourced materials
+# remain subject to their respective original licenses.
+#
+# See the applicable repository LICENSE file for the
+# complete MIT License terms.
+# ============================================================
+
+# ============================================================
+# CELL 1.1 — PACKAGE INSTALLATION AND INITIALIZATION (Affective Provo)
+# ============================================================
+#
+#
+# REQUIRED R VERSION: R version 4.5.2 (2025-10-31)
+#
+#
+# Purpose:
+#   Ensure that all R packages required by the Step 3 analysis
+#   pipeline are installed and loaded.
+#
+# Required packages:
+#   readr        → CSV import
+#   readxl       → Excel import
+#   openxlsx     → Excel export and formatting
+#   dplyr        → data manipulation
+#   tidyr        → missing-data handling
+#   stringr      → string utilities
+#   purrr        → functional/list operations
+#   lme4         → linear mixed-effects models
+#   optimx       → additional optimizers used by lme4::allFit()
+#   dfoptim      → additional optimizers used by lme4::allFit()
+#   future       → parallel-processing infrastructure
+#   future.apply → future-based apply functions
+#   progressr    → progress-handling utilities
+#   here         → portable project-root paths
+#
+# Procedure:
+#   1. Define the complete set of required packages.
+#   2. Identify packages that are not currently installed.
+#   3. Install only the missing packages from CRAN.
+#   4. Load all required packages.
+#
+# Notes:
+#   - Existing package installations are left unchanged.
+#   - Packages are installed only when absent.
+#   - suppressPackageStartupMessages() keeps notebook output clean.
+#   - Package versions are recorded later by sessionInfo() in
+#     the runtime log.
+# ============================================================
+
+
+# ------------------------------------------------------------
+# 1. Define Required Packages
+# ------------------------------------------------------------
+
+REQUIRED_PACKAGES <- c(
+  "readr",
+  "readxl",
+  "openxlsx",
+  "dplyr",
+  "tidyr",
+  "stringr",
+  "purrr",
+  "lme4",
+  "optimx",
+  "dfoptim",
+  "future",
+  "future.apply",
+  "progressr",
+  "here"
+)
+
+
+# ------------------------------------------------------------
+# 2. Identify Missing Packages
+# ------------------------------------------------------------
+
+MISSING_PACKAGES <- REQUIRED_PACKAGES[
+  !vapply(
+    REQUIRED_PACKAGES,
+    requireNamespace,
+    quietly = TRUE,
+    FUN.VALUE = logical(1)
+  )
+]
+
+
+# ------------------------------------------------------------
+# 3. Install Missing Packages
+# ------------------------------------------------------------
+
+if (length(MISSING_PACKAGES) > 0) {
+
+  message(
+    "Installing missing package(s): ",
+    paste(MISSING_PACKAGES, collapse = ", ")
+  )
+
+  install.packages(
+    MISSING_PACKAGES,
+    repos = "https://cloud.r-project.org",
+    dependencies = TRUE
+  )
+
+} else {
+
+  message("All required packages are already installed.")
+}
+
+
+# ------------------------------------------------------------
+# 4. Load Required Packages
+# ------------------------------------------------------------
+
+suppressPackageStartupMessages({
+
+  library(readr)
+  library(readxl)
+  library(openxlsx)
+
+  library(dplyr)
+  library(tidyr)
+  library(stringr)
+  library(purrr)
+
+  library(lme4)
+  library(optimx)
+  library(dfoptim)
+
+  library(future)
+  library(future.apply)
+
+  library(progressr)
+
+  library(here)
+})
+
+
+# ------------------------------------------------------------
+# 5. Confirm Package Initialization
+# ------------------------------------------------------------
+
+message(
+  "Package initialization complete: ",
+  length(REQUIRED_PACKAGES),
+  " required packages available."
+)
+
+
+
+
+
+
+
+
+
+
+# ============================================================
+# CELL 1.2 — HARD THREAD CAPS
+# ============================================================
+# Purpose:
+#   Restrict low-level numerical libraries to a single thread.
+#
+# Rationale:
+#   Mixed-effects models and allFit() may perform substantial
+#   numerical computation. If process-level parallelism is used
+#   later, unrestricted BLAS/OpenMP threading inside individual
+#   workers can cause:
+#
+#     - CPU oversubscription
+#     - memory contention
+#     - reduced performance
+#     - computational instability
+#
+# Strategy:
+#   Restrict low-level numerical libraries to one thread.
+#   Any intentional parallelism should occur at the R-process
+#   level rather than within each numerical operation.
+#
+# Controlled libraries:
+#   - VECLIB / macOS Accelerate
+#   - OpenMP
+#   - OpenBLAS
+#   - Intel MKL
+#   - NumExpr
+#
+# Notes:
+#   - This does NOT change the statistical model.
+#   - This does NOT change the analysis sample.
+#   - This should be configured before heavy model fitting.
+# ============================================================
+
+Sys.setenv(
+  VECLIB_MAXIMUM_THREADS = "1",
+  OMP_NUM_THREADS = "1",
+  OPENBLAS_NUM_THREADS = "1",
+  MKL_NUM_THREADS = "1",
+  NUMEXPR_NUM_THREADS = "1"
+)
+
+
+
+
+
+
+# ============================================================
+# CELL 1.3 — UNCORRELATED RANDOM-SLOPE CONFIGURATION
+# ============================================================
+# Purpose:
+#   Define the random-effects configuration used during Step 3,
+#   which evaluates candidate participant-level random slopes
+#   without estimating correlations among the participant
+#   random intercept and random slopes.
+#
+# Step 1 established the random-intercept structure.
+#
+# Step 2 evaluated correlated participant-level random slopes.
+#
+# Step 3 evaluates the corresponding candidate random-slope
+# structures using an UNCORRELATED parameterization.
+#
+# Lexical and affective fixed-effect predictors are therefore
+# evaluated as potential participant-level random slopes while
+# covariance parameters among those participant random effects
+# are omitted.
+#
+# ------------------------------------------------------------
+# Additional Random Intercept
+# ------------------------------------------------------------
+# ADDITIONAL_INTERCEPT:
+#   Specifies the crossed random-intercept grouping factor
+#   retained alongside Participant_ID.
+#
+# USE_ADDITIONAL_INTERCEPT:
+#   TRUE  → include the additional crossed random intercept
+#   FALSE → use participant grouping only
+#
+# With the current configuration:
+#
+#   (1 + candidate slopes || Participant_ID)
+#   + (1 | Word_Unique_ID)
+#
+# Thus, Step 3 retains the same crossed random-intercept
+# structure used in Step 2 while changing only the participant
+# random-slope correlation structure.
+# ------------------------------------------------------------
+
+ADDITIONAL_INTERCEPT <- "Word_Unique_ID"
+USE_ADDITIONAL_INTERCEPT <- TRUE
+
+
+# ------------------------------------------------------------
+# Random-Slope Correlation Structure
+# ------------------------------------------------------------
+# USE_UNCORRELATED_SLOPES:
+#
+#   FALSE:
+#       (1 + slopes | Participant_ID)
+#
+#       Participant intercepts and random slopes are allowed
+#       to correlate.
+#
+#   TRUE:
+#       (1 + slopes || Participant_ID)
+#
+#       Participant random-effect covariance parameters are
+#       omitted, producing the uncorrelated parameterization
+#       evaluated in this Step 3 analysis.
+#
+# This Step 3 script evaluates UNCORRELATED random slopes, so
+# the setting must remain TRUE.
+# ------------------------------------------------------------
+
+USE_UNCORRELATED_SLOPES <- TRUE
+
+
+# ------------------------------------------------------------
+# Candidate-Slope Complexity Limit
+# ------------------------------------------------------------
+# MAX_SLOPES_PER_CANDIDATE controls the maximum number of
+# participant-level random slopes allowed in a candidate model.
+#
+# Inf:
+#   Do not impose an artificial maximum.
+#
+# The same candidate-slope search space used in Step 2 is
+# retained so that correlated and uncorrelated structures are
+# evaluated using equivalent sets of candidate slopes.
+#
+# A smaller value should be used only in a separately defined
+# sensitivity or stability analysis.
+# ------------------------------------------------------------
+
+MAX_SLOPES_PER_CANDIDATE <- Inf
+
+
+# ------------------------------------------------------------
+# Console Confirmation
+# ------------------------------------------------------------
+
+if (USE_ADDITIONAL_INTERCEPT) {
+  message(
+    "Random-intercept structure: Participant_ID + ",
+    ADDITIONAL_INTERCEPT
+  )
+} else {
+  message("Random-intercept structure: Participant_ID only")
+}
+
+message(
+  "Participant random slopes: ",
+  if (USE_UNCORRELATED_SLOPES) "UNCORRELATED" else "CORRELATED"
+)
+
+message(
+  "Maximum slopes per candidate: ",
+  MAX_SLOPES_PER_CANDIDATE
+)
+
+
+
+
+
+# ============================================================
+# CELL 1.4 — ROOT-ANCHORED PROJECT PATHS
+# ============================================================
+# Purpose:
+#   Define portable input and output paths using the 'here'
+#   package.
+#
+# Input:
+#   02-Data/
+#     03-Analysis_Ready/
+#       03_Affective_Provo.csv
+#
+# Dataset:
+#   Affective Provo guarantees complete mandatory:
+#
+#   Lexical predictors:
+#       - Word_Length
+#       - Response_Proportion
+#       - Lg10WF
+#
+#   Affective predictors:
+#       - V.Mean.Y
+#       - A.Mean.Y
+#       - D.Mean.Y
+#
+# Important:
+#   Eye-tracking outcomes have NOT been used to determine
+#   inclusion in the exported Affective Provo dataset.
+#
+#   DV-specific duration filtering therefore occurs later in
+#   this Step 3 analysis pipeline, using the same preparation
+#   principles as Step 2.
+#
+# Output:
+#   05-Research_Program-Affective_Provo/
+#     01-LME_Model_Structure/
+#       02-Results/
+#
+# Steps 1, 2, and 3 intentionally use the same results
+# directory. Step-specific filenames distinguish their outputs.
+#
+# This ensures that the correlated and uncorrelated random-
+# slope analyses use the same source dataset and repository
+# location while remaining distinguishable by output filename.
+# ============================================================
+
+PROJECT_ROOT <- here()
+
+RAW_DATA_PATH <- here(
+  "02-Data",
+  "03-Analysis_Ready",
+  "03_Affective_Provo.csv"
+)
+
+OUTPUT_DATA_DIR <- here(
+  "05-Research_Program-Affective_Provo",
+  "01-Fixation_Duration_Research",
+  "01-LME_Model_Structure",
+  "02-Results"
+)
+
+
+# ------------------------------------------------------------
+# Create Output Directory if Necessary
+# ------------------------------------------------------------
+
+dir.create(
+  OUTPUT_DATA_DIR,
+  recursive = TRUE,
+  showWarnings = FALSE
+)
+
+
+# ------------------------------------------------------------
+# Verify Input Dataset
+# ------------------------------------------------------------
+
+stopifnot(
+  file.exists(RAW_DATA_PATH)
+)
+
+
+# ------------------------------------------------------------
+# Report Resolved Project Paths
+# ------------------------------------------------------------
+
+message("PROJECT_ROOT: ", PROJECT_ROOT)
+message("RAW_DATA_PATH: ", RAW_DATA_PATH)
+message("OUTPUT_DATA_DIR: ", OUTPUT_DATA_DIR)
+
+
+
+
+
+
+
+
+
+# ============================================================
+# CELL 1.5 — RUNTIME LOG — START
+# ============================================================
+# Purpose:
+#   Initialize the runtime log for the Step 3 uncorrelated
+#   random-slope analysis.
+#
+# Records:
+#   - Analysis identity
+#   - Dataset identity
+#   - Analysis start timestamp
+#   - R version
+#
+# Output:
+#   Step-3_Runtime_Log_Affective_Provo_Uncorrelated_Slopes.txt
+#
+# Important:
+#   Step 2 and Step 3 use the same results directory, but
+#   distinct runtime-log filenames prevent the correlated and
+#   uncorrelated analyses from overwriting one another.
+# ============================================================
+
+LOG_PATH <- file.path(
+  OUTPUT_DATA_DIR,
+  "Step-3_Runtime_Log_Affective_Provo_Uncorrelated_Slopes.txt"
+)
+
+log_con <- file(
+  LOG_PATH,
+  open = "wt"
+)
+
+sink(log_con, split = TRUE)
+sink(log_con, type = "message")
+
+cat(
+  paste0(
+    "\n",
+    strrep("=", 80), "\n",
+    "STEP 3 — UNCORRELATED RANDOM-SLOPE ANALYSIS\n",
+    "Dataset: Affective Provo\n",
+    "Started: ", format(Sys.time(), "%Y-%m-%d %H:%M:%S"), "\n",
+    "R version: ", R.version.string, "\n",
+    strrep("=", 80), "\n\n"
+  )
+)
+
+
+
+
+
+
+
+
+
+
+# ============================================================
+# CELL 2 — SHARED HELPER FUNCTIONS
+# ============================================================
+# Purpose:
+#   Define reusable utility functions used throughout the
+#   uncorrelated random-slope model-selection pipeline.
+#
+# Includes:
+#   - Random-slope candidate generation
+#   - Runtime formatting
+#   - Excel sheet-name sanitization
+#   - Row-count auditing for fair AIC/BIC comparison
+#   - Structured Excel export with safe sheet replacement
+#
+# Design principles:
+#   - Functions are reusable across DVs.
+#   - Functions are shared by Paper 1 (Affective Provo) and
+#     Paper 2 (Lexical Provo).
+#   - Candidate generation is independent of whether slopes are
+#     correlated or uncorrelated; the correlation structure is
+#     imposed later when the lmer formula is constructed.
+#   - No model fitting occurs in this cell.
+#   - No analysis-specific row filtering occurs in this cell.
+#   - File-writing side effects occur only in the explicitly
+#     defined Excel-export function.
+# ============================================================
+
+
+# ------------------------------------------------------------
+# 2.1 Random-Slope Candidate Generator
+# ------------------------------------------------------------
+# Purpose:
+#   Generate all candidate participant-level random-slope
+#   structures from a supplied set of slope variables.
+#
+# Behavior:
+#   - Always includes the random-intercept-only candidate:
+#
+#         "1"
+#
+#   - Generates every combination of the supplied slopes.
+#
+#   - max_slopes can optionally restrict the maximum number
+#     of slopes included in any candidate structure.
+#
+# Example for the Affective Provo Step 3 analysis:
+#
+#   slope_vars = c(
+#       "Length",
+#       "Predictability",
+#       "Frequency",
+#       "Valence",
+#       "Arousal",
+#       "Dominance"
+#   )
+#
+# Candidate structures include:
+#
+#   "1"
+#   "1 + Length"
+#   "1 + Predictability"
+#   "1 + Frequency"
+#   "1 + Valence"
+#   ...
+#   "1 + Length + Predictability + Frequency + Valence + Arousal + Dominance"
+#
+# The generated strings contain only the random-intercept /
+# random-slope portion of the participant random-effects term.
+#
+# The correlation structure is imposed later:
+#
+#   Correlated:
+#       (1 + slopes | Participant_ID)
+#
+#   Uncorrelated:
+#       (1 + slopes || Participant_ID)
+#
+# Step 3 uses the latter parameterization.
+# ------------------------------------------------------------
+
+generate_re_candidates <- function(slope_vars, max_slopes = Inf) {
+  
+  candidates <- c("1")
+  
+  if (length(slope_vars) == 0) return(candidates)
+  
+  for (r in seq_along(slope_vars)) {
+    
+    if (is.finite(max_slopes) && r > max_slopes) next
+    
+    combos <- combn(
+      slope_vars,
+      r,
+      simplify = FALSE
+    )
+    
+    candidates <- c(
+      candidates,
+      vapply(
+        combos,
+        function(x) {
+          paste(
+            "1 +",
+            paste(x, collapse = " + ")
+          )
+        },
+        character(1)
+      )
+    )
+  }
+  
+  unique(candidates)
+}
+
+
+# ------------------------------------------------------------
+# 2.2 Runtime Formatter
+# ------------------------------------------------------------
+# Purpose:
+#   Convert elapsed execution time in seconds into a compact
+#   human-readable representation.
+#
+# Output examples:
+#   12.5 seconds → "12.5s"
+#   492 seconds  → "8.2m"
+#   4860 seconds → "1.35h"
+# ------------------------------------------------------------
+
+fmt_secs <- function(s) {
+
+  if (is.null(s) || !is.finite(s)) return("NA")
+
+  s <- as.numeric(s)
+
+  if (s < 60) {
+    return(sprintf("%.1fs", s))
+  }
+
+  if (s < 3600) {
+    return(sprintf("%.1fm", s / 60))
+  }
+
+  sprintf("%.2fh", s / 3600)
+}
+
+
+# ------------------------------------------------------------
+# 2.3 Excel Sheet-Name Sanitizer
+# ------------------------------------------------------------
+# Purpose:
+#   Ensure dynamically generated worksheet names comply with
+#   Microsoft Excel naming restrictions.
+#
+# Excel restrictions handled:
+#   - Maximum worksheet-name length = 31 characters
+#   - Prohibited characters:
+#
+#         \ / * [ ] : ?
+#
+# This prevents worksheet-creation errors during repeated
+# automated exports.
+# ------------------------------------------------------------
+
+safe_sheet_name <- function(name) {
+
+  name <- str_replace_all(
+    name,
+    "[\\\\/*\\[\\]:?]",
+    "_"
+  )
+
+  str_sub(
+    name,
+    1,
+    31
+  )
+}
+
+
+# ------------------------------------------------------------
+# 2.4 Row-Count Audit for Fair Model Comparison
+# ------------------------------------------------------------
+# Purpose:
+#   Audit the analysis sample used for AIC/BIC comparison.
+#
+# Why this matters:
+#   Candidate random-slope models for the SAME DV must be
+#   compared on exactly the same observations. Otherwise,
+#   differences in AIC/BIC could reflect differences in sample
+#   composition rather than differences in model structure.
+#
+# Reports:
+#   original_rows
+#       → rows supplied to the audit function
+#
+#   dv_nonmissing_rows
+#       → rows with a non-missing value for the current DV
+#
+#   complete_case_rows_used_for_AIC_BIC
+#       → rows complete across the current DV and all variables
+#         specified in required_cols
+#
+#   rows_dropped_for_complete_case
+#       → rows removed because at least one required value
+#         was missing
+#
+#   pct_dropped
+#       → percentage of supplied rows removed by complete-case
+#         filtering
+#
+# Important:
+#   This helper audits MISSINGNESS only.
+#
+#   It does NOT automatically impose DV > 0.
+#
+#   For duration-based analyses, the positive-duration
+#   restriction must be applied during the analysis-data
+#   preparation stage before candidate models are compared.
+#
+# Safety:
+#   Required columns are validated explicitly. Missing required
+#   variables cause the pipeline to stop rather than being
+#   silently omitted from the audit.
+#
+#   This behavior is intentionally retained from Step 2 so that
+#   Step 2 and Step 3 use identical sample-validation rules.
+# ------------------------------------------------------------
+
+dv_rowcount_summary <- function(
+  df,
+  dv,
+  required_cols,
+  label = ""
+) {
+
+  cols_needed <- unique(
+    c(
+      dv,
+      required_cols
+    )
+  )
+
+  missing_required <- setdiff(
+    cols_needed,
+    names(df)
+  )
+
+  if (length(missing_required) > 0) {
+
+    stop(
+      "Row-count audit cannot proceed. Missing required variable(s): ",
+      paste(
+        missing_required,
+        collapse = ", "
+      )
+    )
+  }
+
+
+  # ----------------------------------------------------------
+  # Source-Data Row Counts
+  # ----------------------------------------------------------
+
+  original_n <- nrow(df)
+
+  dv_nonmissing <- sum(
+    !is.na(df[[dv]])
+  )
+
+
+  # ----------------------------------------------------------
+  # Complete-Case Count
+  # ----------------------------------------------------------
+
+  complete_n <- df %>%
+    select(
+      all_of(cols_needed)
+    ) %>%
+    drop_na() %>%
+    nrow()
+
+
+  # ----------------------------------------------------------
+  # Removal Diagnostics
+  # ----------------------------------------------------------
+
+  dropped <- original_n - complete_n
+
+
+  # ----------------------------------------------------------
+  # Return Audit Record
+  # ----------------------------------------------------------
+
+  tibble(
+    label = ifelse(
+      nchar(label) > 0,
+      label,
+      dv
+    ),
+    dv = dv,
+    original_rows = original_n,
+    dv_nonmissing_rows = dv_nonmissing,
+    complete_case_rows_used_for_AIC_BIC = complete_n,
+    rows_dropped_for_complete_case = dropped,
+    pct_dropped = if (original_n > 0) {
+      dropped / original_n * 100
+    } else {
+      NA_real_
+    },
+    required_cols_used = paste(
+      required_cols,
+      collapse = ", "
+    )
+  )
+}
+
+
+# ------------------------------------------------------------
+# 2.5 Structured Excel Export
+# ------------------------------------------------------------
+# Purpose:
+#   Save uncorrelated random-slope model-selection outputs to a
+#   structured multi-sheet Excel workbook.
+#
+# Sheets created for each DV:
+#
+#   <DV>_ranking
+#       → candidate random-slope model ranking
+#
+#   <DV>_audit
+#       → model-fitting / convergence audit information
+#
+#   <DV>_rowcounts
+#       → sample-size and complete-case diagnostics
+#
+# Repeated-execution behavior:
+#   - Creates the workbook if it does not already exist.
+#   - Loads the existing workbook when rerunning the analysis.
+#   - Removes only the sheets corresponding to the current DV.
+#   - Recreates those sheets with the updated results.
+#   - Preserves any other sheets already present in the workbook.
+#
+# Safety:
+#   - Normalizes the output path.
+#   - Creates the parent directory when necessary.
+#   - Sanitizes dynamically generated worksheet names.
+#   - Saves with overwrite = TRUE after the workbook has been
+#     updated in memory.
+#
+# Important:
+#   The export mechanism itself is identical to Step 2.
+#   Step 3 output filenames defined later distinguish the
+#   uncorrelated results from the correlated Step 2 results.
+# ------------------------------------------------------------
+
+save_re_outputs_to_excel <- function(
+  excel_path,
+  dv,
+  df_results,
+  df_audit,
+  rowcount_summary
+) {
+
+  excel_path <- normalizePath(
+    excel_path,
+    winslash = "/",
+    mustWork = FALSE
+  )
+
+  dir.create(
+    dirname(excel_path),
+    recursive = TRUE,
+    showWarnings = FALSE
+  )
+
+
+  # ----------------------------------------------------------
+  # Construct Excel-Safe Worksheet Names
+  # ----------------------------------------------------------
+
+  rank_sheet <- safe_sheet_name(
+    paste0(dv, "_ranking")
+  )
+
+  audit_sheet <- safe_sheet_name(
+    paste0(dv, "_audit")
+  )
+
+  rows_sheet <- safe_sheet_name(
+    paste0(dv, "_rowcounts")
+  )
+
+
+  # ----------------------------------------------------------
+  # Create or Load Workbook
+  # ----------------------------------------------------------
+
+  if (file.exists(excel_path)) {
+
+    wb <- loadWorkbook(
+      excel_path
+    )
+
+    if (rank_sheet %in% names(wb)) {
+      removeWorksheet(
+        wb,
+        rank_sheet
+      )
+    }
+
+    if (audit_sheet %in% names(wb)) {
+      removeWorksheet(
+        wb,
+        audit_sheet
+      )
+    }
+
+    if (rows_sheet %in% names(wb)) {
+      removeWorksheet(
+        wb,
+        rows_sheet
+      )
+    }
+
+  } else {
+
+    wb <- createWorkbook()
+  }
+
+
+  # ----------------------------------------------------------
+  # Write Candidate Ranking
+  # ----------------------------------------------------------
+
+  addWorksheet(
+    wb,
+    rank_sheet
+  )
+
+  writeData(
+    wb,
+    rank_sheet,
+    df_results
+  )
+
+
+  # ----------------------------------------------------------
+  # Write Model-Fit Audit
+  # ----------------------------------------------------------
+
+  addWorksheet(
+    wb,
+    audit_sheet
+  )
+
+  writeData(
+    wb,
+    audit_sheet,
+    df_audit
+  )
+
+
+  # ----------------------------------------------------------
+  # Write Row-Count Audit
+  # ----------------------------------------------------------
+
+  addWorksheet(
+    wb,
+    rows_sheet
+  )
+
+  writeData(
+    wb,
+    rows_sheet,
+    rowcount_summary
+  )
+
+
+  # ----------------------------------------------------------
+  # Save Workbook
+  # ----------------------------------------------------------
+
+  saveWorkbook(
+    wb,
+    excel_path,
+    overwrite = TRUE
+  )
+
+
+  # ----------------------------------------------------------
+  # Confirm Export
+  # ----------------------------------------------------------
+
+  message(
+    "Saved uncorrelated random-slope results: ",
+    excel_path
+  )
+}
+
+
+
+
+
+
+
+
+
+# ============================================================
+# CELL 3 — LOAD AND VALIDATE AFFECTIVE PROVO
+# ============================================================
+# Purpose:
+#   Load the analysis-ready Affective Provo dataset and prepare
+#   variable names for the uncorrelated random-slope pipeline.
+#
+# Input:
+#   03_Affective_Provo.csv
+#
+# Dataset guarantees:
+#   Every observation has complete mandatory:
+#
+#   Lexical predictors:
+#       - Word_Length
+#       - Response_Proportion
+#       - Lg10WF
+#
+#   Affective predictors:
+#       - V.Mean.Y
+#       - A.Mean.Y
+#       - D.Mean.Y
+#
+# Procedure:
+#   1. Load the Affective Provo dataset.
+#   2. Preserve the loaded dataset in df_main.
+#   3. Create df as the working modeling copy.
+#   4. Rename VAD variables for model readability.
+#   5. Validate mandatory predictors.
+#
+# IMPORTANT:
+#   No eye-tracking filtering occurs here.
+#
+#   No DV > 0 filtering occurs here.
+#
+#   No predictor standardization occurs here.
+#
+#   Predictors will be standardized AFTER the DV-specific
+#   analysis sample has been constructed. This ensures that
+#   scaling is based on the observations actually entering
+#   each duration-DV model comparison.
+#
+#   Consequently, FFD, GD, GPT, and TDT may be standardized
+#   using slightly different means/SDs if their eligible
+#   analysis samples differ.
+#
+#   This preparation procedure is intentionally identical to
+#   Step 2. The distinction between Step 2 and Step 3 concerns
+#   the participant-level random-slope correlation structure,
+#   not data preprocessing.
+# ============================================================
+
+
+# ------------------------------------------------------------
+# 3.1 Load Affective Provo
+# ------------------------------------------------------------
+
+df_main <- read_csv(
+  RAW_DATA_PATH,
+  show_col_types = FALSE
+)
+
+message(
+  "Affective Provo rows loaded: ",
+  format(nrow(df_main), big.mark = ",")
+)
+
+
+# ------------------------------------------------------------
+# 3.2 Create Modeling Copy
+# ------------------------------------------------------------
+# df_main preserves the loaded analysis-ready dataset.
+# Subsequent preparation occurs on df.
+# ------------------------------------------------------------
+
+df <- df_main
+
+
+# ------------------------------------------------------------
+# 3.3 Rename Affective Predictors
+# ------------------------------------------------------------
+# Rename the original VAD columns to concise names used in
+# subsequent model formulas:
+#
+#   V.Mean.Y → Valence
+#   A.Mean.Y → Arousal
+#   D.Mean.Y → Dominance
+# ------------------------------------------------------------
+
+rename_map <- c(
+  "V.Mean.Y" = "Valence",
+  "A.Mean.Y" = "Arousal",
+  "D.Mean.Y" = "Dominance",
+  "Word_Length" = "Length",
+  "Response_Proportion" = "Predictability",
+  "Lg10WF" = "Frequency"
+)
+
+for (k in names(rename_map)) {
+
+  if (k %in% names(df)) {
+
+    names(df)[
+      names(df) == k
+    ] <- rename_map[[k]]
+  }
+}
+
+
+# ------------------------------------------------------------
+# 3.4 Validate Mandatory LFP + VAD Predictors
+# ------------------------------------------------------------
+# Affective Provo should contain complete LFP + VAD predictors
+# by construction. Missing columns or missing values therefore
+# indicate an incorrect/incomplete input dataset and should
+# stop the analysis rather than being silently filtered.
+# ------------------------------------------------------------
+
+REQUIRED_PREDICTORS <- c(
+  "Length",
+  "Predictability",
+  "Frequency",
+  "Valence",
+  "Arousal",
+  "Dominance"
+)
+
+missing_columns <- setdiff(
+  REQUIRED_PREDICTORS,
+  names(df)
+)
+
+if (length(missing_columns) > 0) {
+
+  stop(
+    "Missing mandatory Affective Provo predictor(s): ",
+    paste(
+      missing_columns,
+      collapse = ", "
+    )
+  )
+}
+
+if (anyNA(df[REQUIRED_PREDICTORS])) {
+
+  stop(
+    "Affective Provo contains missing values in one or more ",
+    "mandatory LFP + VAD predictors."
+  )
+}
+
+
+# ------------------------------------------------------------
+# 3.5 Confirm Dataset Readiness
+# ------------------------------------------------------------
+
+message(
+  "Mandatory LFP + VAD predictors: complete."
+)
+
+message(
+  "Predictors remain UNSCALED at this stage."
+)
+
+message(
+  "DV-specific filtering and standardization will occur later."
+)
+
+
+
+
+
+
+
+
+# ============================================================
+# CELL 4 — DVs, UNCORRELATED-SLOPE CANDIDATES, AND RESOURCE PLAN
+# ============================================================
+# Purpose:
+#   Define the duration-based dependent variables, generate all
+#   candidate participant-level uncorrelated random-slope
+#   structures, and determine a conservative computational
+#   execution plan.
+#
+# Paper 1 candidate slopes:
+#
+#   Lexical predictors:
+#       - Length
+#       - Predictability
+#       - Frequency
+#
+#   Affective predictors:
+#       - Valence
+#       - Arousal
+#       - Dominance
+#
+# Random-slope framework:
+#
+#   Candidate slopes are added at the Participant_ID level:
+#
+#       (1 + candidate_slopes || Participant_ID)
+#
+#   Because USE_UNCORRELATED_SLOPES = TRUE in Cell 1.3,
+#   participant intercepts and random slopes are modeled
+#   without correlation parameters.
+#
+#   The additional crossed random intercept configured in
+#   Cell 1.3 is retained separately:
+#
+#       + (1 | Word_Unique_ID)
+#
+# Candidate generation:
+#   With 6 possible slopes and no complexity cap:
+#
+#       2^6 = 64 candidate structures
+#
+#   including the participant random-intercept-only candidate.
+#
+# Computational planning:
+#   - Detect available logical CPUs.
+#   - Estimate available system RAM.
+#   - Reserve CPU and RAM headroom for system stability.
+#   - Limit process-level workers according to:
+#         TASKS_PER_DV
+#         CPU_BUDGET
+#         RAM_BUDGET_WORKERS
+#   - Restrict low-level numerical threading to prevent
+#     oversubscription.
+#
+# Important:
+#   - This cell defines candidate structures only.
+#   - No model fitting occurs here.
+#   - No DV-specific filtering occurs here.
+#   - No predictor standardization occurs here.
+#   - Standardization will occur after construction of each
+#     DV-specific analysis sample.
+#
+#   The candidate slope combinations are intentionally identical
+#   to Step 2. The difference is that Step 3 estimates these
+#   candidate slopes without participant intercept-slope or
+#   slope-slope correlation parameters.
+# ============================================================
+
+
+# ------------------------------------------------------------
+# 4.1 Define Duration-Based Dependent Variables
+# ------------------------------------------------------------
+
+DVS <- c(
+  "IA_FIRST_FIXATION_DURATION",   # Stage 1: FFD
+  "IA_FIRST_RUN_DWELL_TIME",      # Stage 2: GD
+  "IA_REGRESSION_PATH_DURATION",  # Stage 3: GPT
+  "IA_DWELL_TIME"                 # Stage 4: TDT
+)
+
+
+# ------------------------------------------------------------
+# 4.2 Define Candidate Participant-Level Random Slopes
+# ------------------------------------------------------------
+# Paper 1 evaluates whether lexical and/or affective predictor
+# effects vary across participants.
+#
+# Step 3 uses the same candidate slope variables as Step 2.
+# The distinction is the uncorrelated random-effects
+# parameterization configured in Cell 1.3.
+# ------------------------------------------------------------
+
+SLOPES <- c(
+  "Length",
+  "Predictability",
+  "Frequency",
+  "Valence",
+  "Arousal",
+  "Dominance"
+)
+
+
+# Validate candidate-slope variables before generating models
+
+missing_slopes <- setdiff(
+  SLOPES,
+  names(df)
+)
+
+if (length(missing_slopes) > 0) {
+  
+  stop(
+    "Missing candidate random-slope variable(s): ",
+    paste(
+      missing_slopes,
+      collapse = ", "
+    )
+  )
+}
+
+
+# ------------------------------------------------------------
+# 4.3 Generate Candidate Random-Slope Structures
+# ------------------------------------------------------------
+
+CANDIDATES <- generate_re_candidates(
+  SLOPES,
+  max_slopes = MAX_SLOPES_PER_CANDIDATE
+)
+
+NUM_MODELS <- length(CANDIDATES)
+NUM_DVS <- length(DVS)
+
+# Full pipeline = all four DVs combined
+
+TOTAL_PIPELINE_MODELS <- NUM_DVS * NUM_MODELS
+
+# Each DV is executed manually, one at a time
+
+TASKS_PER_DV <- NUM_MODELS
+
+
+message(
+  "Candidate slope variables : ",
+  length(SLOPES)
+)
+
+message(
+  "Candidate structures / DV : ",
+  NUM_MODELS
+)
+
+message(
+  "Duration DVs              : ",
+  NUM_DVS
+)
+
+message(
+  "Full pipeline models      : ",
+  TOTAL_PIPELINE_MODELS
+)
+
+message(
+  "Tasks per manual DV run   : ",
+  TASKS_PER_DV
+)
+
+
+# ------------------------------------------------------------
+# 4.4 System RAM Detection Helper
+# ------------------------------------------------------------
+# Detect total physical RAM in GB.
+#
+# Supported:
+#   - macOS
+#   - Linux
+#
+# Returns NA if RAM detection fails, in which case a conservative
+# fallback worker limit is used below.
+# ------------------------------------------------------------
+
+get_total_ram_gb <- function() {
+  
+  out <- NA_real_
+  os <- Sys.info()[["sysname"]]
+  
+  suppressWarnings({
+    
+    if (os == "Darwin") {
+      
+      mem <- as.numeric(
+        system(
+          "sysctl -n hw.memsize",
+          intern = TRUE
+        )
+      )
+      
+      if (is.finite(mem)) {
+        out <- mem / (1024^3)
+      }
+      
+    } else if (os == "Linux") {
+      
+      memline <- system(
+        "grep MemTotal /proc/meminfo",
+        intern = TRUE
+      )
+      
+      memkb <- as.numeric(
+        str_extract(
+          memline,
+          "\\d+"
+        )
+      )
+      
+      if (is.finite(memkb)) {
+        out <- memkb / (1024^2)
+      }
+    }
+  })
+  
+  if (length(out) == 0) {
+    out <- NA_real_
+  }
+  
+  out
+}
+
+
+# ------------------------------------------------------------
+# 4.5 Initialize Hardware and Resource Assumptions
+# ------------------------------------------------------------
+
+TOTAL_RAM_GB <- get_total_ram_gb()
+
+
+# Approximate memory allowance per concurrent lmer task.
+# This is a planning heuristic rather than a measured guarantee.
+
+EST_RAM_PER_WORKER_GB <- 2.5
+
+
+# Reserve RAM for the operating system and other processes.
+
+RAM_HEADROOM_GB <- NA_real_
+
+
+# Conservative fallback if RAM detection fails.
+
+RAM_BUDGET_WORKERS <- 1
+
+
+# Detect logical CPUs
+
+TOTAL_CPUS <- parallel::detectCores(
+  logical = TRUE
+)
+
+if (is.na(TOTAL_CPUS)) {
+  TOTAL_CPUS <- 1
+}
+
+
+# Reserve CPU capacity for the operating system.
+
+CPU_RESERVE <- if (TOTAL_CPUS >= 8) {
+  2
+} else {
+  1
+}
+
+CPU_BUDGET <- max(
+  1,
+  TOTAL_CPUS - CPU_RESERVE
+)
+
+
+# ------------------------------------------------------------
+# 4.6 Determine RAM-Constrained Worker Budget
+# ------------------------------------------------------------
+
+if (is.na(TOTAL_RAM_GB)) {
+  
+  # Conservative fallback when physical RAM cannot be detected.
+  
+  RAM_BUDGET_WORKERS <- max(
+    1,
+    min(
+      4,
+      CPU_BUDGET
+    )
+  )
+  
+  RAM_HEADROOM_GB <- NA_real_
+  
+} else {
+  
+  # Reserve at least 20% of total RAM, with a minimum of 1 GB.
+  
+  RAM_HEADROOM_GB <- max(
+    1.0,
+    TOTAL_RAM_GB * 0.20
+  )
+  
+  usable_gb <- max(
+    1.0,
+    TOTAL_RAM_GB - RAM_HEADROOM_GB
+  )
+  
+  RAM_BUDGET_WORKERS <- max(
+    1,
+    floor(
+      usable_gb / EST_RAM_PER_WORKER_GB
+    )
+  )
+}
+
+
+# ------------------------------------------------------------
+# 4.7 Determine Final Process-Level Worker Count
+# ------------------------------------------------------------
+# Worker count cannot exceed:
+#
+#   1. Number of candidate models in the current DV run
+#   2. Available CPU budget
+#   3. Estimated RAM budget
+#
+# The current analysis executes one DV at a time, so the
+# relevant task count is TASKS_PER_DV rather than the total
+# number of models across all four DVs.
+# ------------------------------------------------------------
+
+N_JOBS <- max(
+  1,
+  min(
+    TASKS_PER_DV,
+    CPU_BUDGET,
+    RAM_BUDGET_WORKERS
+  )
+)
+
+
+# ------------------------------------------------------------
+# 4.8 Configure Low-Level Numerical Threads
+# ------------------------------------------------------------
+# Low-level numerical libraries remain restricted to one
+# thread regardless of the number of R-process workers.
+#
+# This preserves the hard thread-cap policy established in
+# Cell 1.2 and prevents nested numerical threading from
+# producing CPU oversubscription.
+#
+# Intentional parallelism therefore occurs only through the
+# process-level future/multisession workers.
+# ------------------------------------------------------------
+
+BLAS_THREADS <- 1
+
+
+Sys.setenv(
+  OMP_NUM_THREADS = "1",
+  OPENBLAS_NUM_THREADS = "1",
+  MKL_NUM_THREADS = "1",
+  VECLIB_MAXIMUM_THREADS = "1",
+  NUMEXPR_NUM_THREADS = "1"
+)
+
+
+# ------------------------------------------------------------
+# 4.9 Resource-Plan Reporting
+# ------------------------------------------------------------
+
+fmt_num <- function(x, nd = 1) {
+  
+  ifelse(
+    is.na(x),
+    "NA",
+    sprintf(
+      paste0(
+        "%.",
+        nd,
+        "f"
+      ),
+      x
+    )
+  )
+}
+
+
+est_peak_ram <- if (is.na(TOTAL_RAM_GB)) {
+  
+  NA_real_
+  
+} else {
+  
+  N_JOBS * EST_RAM_PER_WORKER_GB
+}
+
+
+message(
+  "\n",
+  strrep("=", 72)
+)
+
+message(
+  "UNCORRELATED RANDOM-SLOPE RESOURCE PLAN — AFFECTIVE PROVO"
+)
+
+message(
+  strrep("=", 72)
+)
+
+
+message(
+  "Full pipeline     : ",
+  TOTAL_PIPELINE_MODELS,
+  " models (",
+  NUM_DVS,
+  " DVs × ",
+  NUM_MODELS,
+  " candidates)"
+)
+
+
+message(
+  "Current DV run    : ",
+  TASKS_PER_DV,
+  " candidate models"
+)
+
+
+message(
+  "Slope variables   : ",
+  length(SLOPES)
+)
+
+message(
+  "CPUs detected     : ",
+  TOTAL_CPUS
+)
+
+message(
+  "CPU reserve       : ",
+  CPU_RESERVE,
+  "  → CPU budget=",
+  CPU_BUDGET
+)
+
+message(
+  "RAM detected GB   : ",
+  fmt_num(TOTAL_RAM_GB)
+)
+
+message(
+  "RAM headroom GB   : ",
+  fmt_num(RAM_HEADROOM_GB)
+)
+
+message(
+  "RAM/worker GB     : ",
+  sprintf(
+    "%.1f",
+    EST_RAM_PER_WORKER_GB
+  ),
+  "  → RAM-limited workers=",
+  RAM_BUDGET_WORKERS
+)
+
+
+message(
+  strrep("-", 72)
+)
+
+message(
+  "N_JOBS (workers)  : ",
+  N_JOBS
+)
+
+message(
+  "BLAS threads      : ",
+  BLAS_THREADS,
+  " per worker"
+)
+
+message(
+  "Est. peak RAM GB  : ",
+  fmt_num(est_peak_ram)
+)
+
+message(
+  strrep("=", 72),
+  "\n"
+)
+
+
+
+
+
+
+
+
+
+# ============================================================
+# CELL 5 — HIGH-RELIABILITY UNCORRELATED RANDOM-SLOPE
+#          MODEL FITTING WORKER
+# ============================================================
+# Purpose:
+#   Fit one candidate participant-level uncorrelated random-
+#   slope structure for a single duration DV using a tiered
+#   optimization strategy.
+#
+# Inputs:
+#   dv
+#       → current duration dependent variable
+#
+#   fixed_formula
+#       → fixed-effects specification held constant across all
+#         candidate random-slope structures for the current DV
+#
+#   model_df
+#       → DV-specific analysis dataset prepared before this
+#         function is called
+#
+#   re_terms
+#       → candidate participant random-effects specification,
+#         e.g.:
+#
+#             "1"
+#             "1 + Length"
+#             "1 + Length + Frequency"
+#
+#   groups_col
+#       → grouping factor receiving the candidate random slopes
+#         (normally Participant_ID)
+#
+# Random-effects framework:
+#
+#   Step 3 uses UNCORRELATED participant-level random slopes:
+#
+#       (1 + candidate_slopes || Participant_ID)
+#
+#   This removes participant intercept-slope and slope-slope
+#   correlation parameters from the candidate structures.
+#
+#   The optional crossed random intercept is retained:
+#
+#       + (1 | Word_Unique_ID)
+#
+#   USE_UNCORRELATED_SLOPES is configured globally in Cell 1.3
+#   and must remain TRUE for this Step 3 analysis.
+#
+# Reliability strategy:
+#   1. Construct the complete mixed-effects formula.
+#   2. Fit the candidate using high-precision bobyqa.
+#   3. Rewrite the stored model call so allFit() does not depend
+#      on temporary local symbols created inside this function.
+#   4. Evaluate the actual lme4 convergence messages and the
+#      numerical optimizer convergence code separately.
+#   5. Treat optimizer convergence code 0 as SUCCESS.
+#   6. Retain a clean bobyqa fit immediately.
+#   7. Run allFit() only when bobyqa has an actual convergence
+#      problem.
+#   8. If allFit() produces one or more warning-free solutions,
+#      retain the valid solution with the highest log-likelihood.
+#   9. If allFit() cannot rescue the model, retain the original
+#      bobyqa fit and preserve its original convergence problem.
+#  10. Re-evaluate convergence diagnostics for the retained fit.
+#  11. Record convergence, singularity, likelihood criteria,
+#      observation count, runtime, and diagnostic messages.
+#
+# Estimation:
+#   REML = TRUE in the present Step 3 pipeline.
+#
+#   REML-based information-criterion comparisons are used here
+#   because candidate models for a given DV:
+#
+#       - have identical fixed-effects specifications
+#       - use identical observations
+#       - differ only in random-effects structure
+#
+#   REML-based AIC/BIC should not be used to compare models
+#   having different fixed-effects specifications.
+#
+# allFit() robustness:
+#   allFit() refits the original merMod object by updating its
+#   stored model call.
+#
+#   A model fitted inside a helper function can otherwise retain
+#   references in its call to temporary local symbols such as:
+#
+#       full_formula
+#       model_df
+#       reml
+#
+#   Those symbols may no longer be resolvable when allFit()
+#   performs an update/refit.
+#
+#   Therefore, immediately after the primary lmer() fit, this
+#   function rewrites the stored call so that:
+#
+#       formula → the actual mixed-effects formula expression
+#       data    → the actual prepared model data
+#       REML    → literal TRUE/FALSE
+#       control → the complete literal lmerControl() call
+#
+#   The resulting merMod object is self-contained for the
+#   allFit() rescue operation.
+#
+# Important:
+#   - Optimizer convergence code 0 means successful
+#     optimization and must NOT be treated as a warning.
+#
+#   - allFit() is used as a rescue/robustness procedure rather
+#     than automatically refitting every clean bobyqa model.
+#
+#   - maxfun = 1e6 is used for the primary bobyqa fit.
+#
+#   - This function does NOT construct the analysis sample.
+#   - This function does NOT remove missing observations.
+#   - This function does NOT apply DV > 0 filtering.
+#   - This function does NOT log-transform the DV.
+#   - This function does NOT standardize predictors.
+#
+#   Those operations occur before model_df is supplied.
+#
+# Output:
+#   A structured list containing:
+#
+#       winner
+#           → statistics from the retained model fit
+#
+#       audit
+#           → model-fit diagnostic record
+#
+#       full_formula
+#           → complete lmer formula used
+# ============================================================
+
+
+fit_single_candidate_tiered <- function(
+    dv,
+    fixed_formula,
+    model_df,
+    re_terms,
+    groups_col,
+    use_additional_intercept = FALSE,
+    additional_intercept_col = NULL,
+    reml = TRUE
+) {
+  
+  
+  # ----------------------------------------------------------
+  # 5.1 Construct Full Mixed-Effects Formula
+  # ----------------------------------------------------------
+  
+  bar <- if (
+    isTRUE(USE_UNCORRELATED_SLOPES)
+  ) {
+    "||"
+  } else {
+    "|"
+  }
+  
+  
+  rand_part <- paste0(
+    "(",
+    re_terms,
+    " ",
+    bar,
+    " ",
+    groups_col,
+    ")"
+  )
+  
+  
+  rand_other <- if (
+    use_additional_intercept &&
+    !is.null(additional_intercept_col)
+  ) {
+    
+    paste0(
+      " + (1 | ",
+      additional_intercept_col,
+      ")"
+    )
+    
+  } else {
+    
+    ""
+  }
+  
+  
+  full_formula <- as.formula(
+    paste(
+      deparse(fixed_formula),
+      "+",
+      rand_part,
+      rand_other
+    )
+  )
+  
+  
+  # ----------------------------------------------------------
+  # 5.2 Primary Model-Fitting Wrapper
+  # ----------------------------------------------------------
+  
+  run_fit <- function() {
+    
+    suppressWarnings(
+      lmer(
+        formula = full_formula,
+        data = model_df,
+        REML = reml,
+        control = lmerControl(
+          optimizer = "bobyqa",
+          optCtrl = list(
+            maxfun = 1e6
+          ),
+          calc.derivs = TRUE,
+          check.conv.grad = .makeCC(
+            "warning",
+            tol = 2e-3
+          ),
+          check.conv.singular = .makeCC(
+            "message",
+            tol = 1e-5
+          ),
+          check.nobs.vs.nlev = "ignore",
+          check.nobs.vs.nRE = "ignore"
+        )
+      )
+    )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 5.3 Start Runtime Tracking
+  # ----------------------------------------------------------
+  
+  t0 <- proc.time()[["elapsed"]]
+  
+  
+  # ----------------------------------------------------------
+  # 5.4 Primary High-Precision bobyqa Fit
+  # ----------------------------------------------------------
+  
+  primary_res <- try(
+    run_fit(),
+    silent = TRUE
+  )
+  
+  
+  # ----------------------------------------------------------
+  # 5.5 Determine Whether Primary Model Initialized
+  # ----------------------------------------------------------
+  
+  primary_initialized <- (
+    !inherits(primary_res, "try-error") &&
+      inherits(primary_res, "merMod")
+  )
+  
+  
+  # ----------------------------------------------------------
+  # 5.6 Handle Initial-Fit Failure
+  # ----------------------------------------------------------
+  # allFit() requires an initialized merMod object.
+  #
+  # Therefore, if bobyqa fails before model initialization,
+  # there is no fitted model available for allFit() to rescue.
+  #
+  # The failed candidate is retained explicitly in the audit
+  # output so that catastrophic fitting failures remain visible
+  # in the exported model-fit diagnostics.
+  #
+  # Because AIC and BIC are NA for a failed candidate, it will
+  # not enter the successful-candidate ranking in Cell 6/7.
+  # ----------------------------------------------------------
+  
+  if (!primary_initialized) {
+    
+    failed_stats <- list(
+      
+      name = paste0(
+        "RE=",
+        re_terms
+      ),
+      
+      re_formula =
+        re_terms,
+      
+      optimizer =
+        "FAILED",
+      
+      selected_via =
+        "FAILED",
+      
+      converged =
+        FALSE,
+      
+      singular =
+        NA,
+      
+      aic =
+        NA_real_,
+      
+      bic =
+        NA_real_,
+      
+      llf =
+        NA_real_,
+      
+      nobs =
+        nrow(model_df),
+      
+      time_s =
+        proc.time()[["elapsed"]] - t0,
+      
+      status_msg =
+        "FAILED",
+      
+      warnings = paste(
+        "Model failed during initial bobyqa fitting;",
+        "allFit requires an initialized merMod model and",
+        "could not provide a fallback.",
+        as.character(primary_res)
+      )
+    )
+    
+    
+    return(
+      list(
+        
+        winner =
+          failed_stats,
+        
+        audit =
+          list(
+            failed_stats
+          ),
+        
+        full_formula =
+          full_formula
+      )
+    )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 5.7 Make Stored Model Call Self-Contained for allFit()
+  # ----------------------------------------------------------
+  
+  self_contained_call <- primary_res@call
+  
+  
+  self_contained_call$formula <-
+    substitute(
+      FORMULA_VALUE,
+      list(
+        FORMULA_VALUE = full_formula
+      )
+    )
+  
+  
+  self_contained_call$data <-
+    substitute(
+      DATA_VALUE,
+      list(
+        DATA_VALUE = model_df
+      )
+    )
+  
+  
+  self_contained_call$REML <-
+    isTRUE(reml)
+  
+  
+  self_contained_call$control <- quote(
+    lmerControl(
+      optimizer = "bobyqa",
+      optCtrl = list(
+        maxfun = 1e6
+      ),
+      calc.derivs = TRUE,
+      check.conv.grad = .makeCC(
+        "warning",
+        tol = 2e-3
+      ),
+      check.conv.singular = .makeCC(
+        "message",
+        tol = 1e-5
+      ),
+      check.nobs.vs.nlev = "ignore",
+      check.nobs.vs.nRE = "ignore"
+    )
+  )
+  
+  
+  primary_res@call <-
+    self_contained_call
+  
+  
+  # ----------------------------------------------------------
+  # 5.8 Evaluate Initial bobyqa Convergence
+  # ----------------------------------------------------------
+  
+  primary_msgs_lme4 <-
+    primary_res@optinfo$conv$lme4$messages
+  
+  
+  primary_opt_code <-
+    primary_res@optinfo$conv$opt
+  
+  
+  primary_lme4_msgs <- if (
+    !is.null(primary_msgs_lme4)
+  ) {
+    
+    as.character(
+      unlist(
+        primary_msgs_lme4
+      )
+    )
+    
+  } else {
+    
+    character(0)
+  }
+  
+  
+  primary_opt_failed <- FALSE
+  
+  
+  if (
+    !is.null(primary_opt_code) &&
+    length(primary_opt_code) > 0
+  ) {
+    
+    primary_opt_code_num <- suppressWarnings(
+      as.numeric(
+        unlist(
+          primary_opt_code
+        )
+      )
+    )
+    
+    
+    primary_opt_failed <- any(
+      is.na(primary_opt_code_num) |
+        primary_opt_code_num != 0
+    )
+  }
+  
+  
+  primary_is_good <- (
+    length(primary_lme4_msgs) == 0 &&
+      !primary_opt_failed
+  )
+  
+  
+  # ----------------------------------------------------------
+  # 5.9 Retain Clean bobyqa Fit or Run allFit() Rescue
+  # ----------------------------------------------------------
+  
+  if (primary_is_good) {
+    
+    res <- primary_res
+    
+    selected_via <-
+      "bobyqa"
+    
+    retained_warning <-
+      NA_character_
+    
+    
+  } else {
+    
+    
+    # --------------------------------------------------------
+    # Preserve Original bobyqa Convergence Diagnostics
+    # --------------------------------------------------------
+    
+    primary_diagnostic_msgs <-
+      primary_lme4_msgs
+    
+    
+    if (primary_opt_failed) {
+      
+      primary_diagnostic_msgs <- c(
+        primary_diagnostic_msgs,
+        paste0(
+          "optimizer convergence code: ",
+          paste(
+            unlist(
+              primary_opt_code
+            ),
+            collapse = ", "
+          )
+        )
+      )
+    }
+    
+    
+    primary_warning_txt <- if (
+      length(primary_diagnostic_msgs) > 0
+    ) {
+      
+      paste(
+        primary_diagnostic_msgs,
+        collapse = " | "
+      )
+      
+    } else {
+      
+      NA_character_
+    }
+    
+    
+    # --------------------------------------------------------
+    # Run allFit() as Multi-Optimizer Rescue
+    # --------------------------------------------------------
+    
+    message(
+      "   -> bobyqa convergence issue; running allFit() for ",
+      re_terms,
+      "..."
+    )
+    
+    
+    af <- try(
+      suppressWarnings(
+        lme4::allFit(
+          primary_res,
+          verbose = FALSE,
+          parallel = "no"
+        )
+      ),
+      silent = TRUE
+    )
+    
+    
+    # --------------------------------------------------------
+    # 5.9A allFit() Itself Failed
+    # --------------------------------------------------------
+    
+    if (inherits(af, "try-error")) {
+      
+      res <- primary_res
+      
+      selected_via <-
+        "bobyqa (allFit failed)"
+      
+      retained_warning <- paste(
+        primary_warning_txt,
+        "allFit error:",
+        as.character(af),
+        sep = " | "
+      )
+      
+      
+    } else {
+      
+      
+      ss <- summary(
+        af
+      )
+      
+      
+      # ------------------------------------------------------
+      # 5.9B Identify Warning-Free allFit Solutions
+      # ------------------------------------------------------
+      
+      valid_indices <- which(
+        is.finite(
+          ss$logLik
+        ) &
+          vapply(
+            ss$msgs,
+            function(x) {
+              is.null(x) ||
+                length(x) == 0
+            },
+            logical(1)
+          )
+      )
+      
+      
+      # ------------------------------------------------------
+      # 5.9C No Warning-Free allFit Solution
+      # ------------------------------------------------------
+      
+      if (length(valid_indices) == 0) {
+        
+        res <- primary_res
+        
+        selected_via <-
+          "bobyqa (allFit found no warning-free solution)"
+        
+        retained_warning <-
+          primary_warning_txt
+        
+        
+      } else {
+        
+        
+        # ----------------------------------------------------
+        # 5.9D Retain Best Clean allFit Solution
+        # ----------------------------------------------------
+        
+        best_idx <- valid_indices[
+          which.max(
+            ss$logLik[
+              valid_indices
+            ]
+          )
+        ]
+        
+        
+        res <- af[[best_idx]]
+        
+        
+        selected_via <- paste0(
+          "allFit: ",
+          names(af)[best_idx]
+        )
+        
+        
+        retained_warning <-
+          NA_character_
+      }
+    }
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 5.10 Extract Final Convergence Diagnostics
+  # ----------------------------------------------------------
+  
+  msgs_lme4 <-
+    res@optinfo$conv$lme4$messages
+  
+  
+  opt_code <-
+    res@optinfo$conv$opt
+  
+  
+  lme4_msgs <- if (
+    !is.null(msgs_lme4)
+  ) {
+    
+    as.character(
+      unlist(
+        msgs_lme4
+      )
+    )
+    
+  } else {
+    
+    character(0)
+  }
+  
+  
+  opt_failed <- FALSE
+  
+  
+  if (
+    !is.null(opt_code) &&
+    length(opt_code) > 0
+  ) {
+    
+    opt_code_num <- suppressWarnings(
+      as.numeric(
+        unlist(
+          opt_code
+        )
+      )
+    )
+    
+    
+    opt_failed <- any(
+      is.na(opt_code_num) |
+        opt_code_num != 0
+    )
+  }
+  
+  
+  final_diagnostic_msgs <-
+    lme4_msgs
+  
+  
+  if (opt_failed) {
+    
+    final_diagnostic_msgs <- c(
+      final_diagnostic_msgs,
+      paste0(
+        "optimizer convergence code: ",
+        paste(
+          unlist(
+            opt_code
+          ),
+          collapse = ", "
+        )
+      )
+    )
+  }
+  
+  
+  final_warning_txt <- if (
+    length(final_diagnostic_msgs) > 0
+  ) {
+    
+    paste(
+      final_diagnostic_msgs,
+      collapse = " | "
+    )
+    
+  } else {
+    
+    NA_character_
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 5.11 Combine Rescue Information and Final Diagnostics
+  # ----------------------------------------------------------
+  
+  warning_parts <- c(
+    
+    if (!is.na(retained_warning)) {
+      retained_warning
+    } else {
+      NULL
+    },
+    
+    if (!is.na(final_warning_txt)) {
+      final_warning_txt
+    } else {
+      NULL
+    }
+  )
+  
+  
+  warning_parts <- unique(
+    warning_parts[
+      nzchar(
+        warning_parts
+      )
+    ]
+  )
+  
+  
+  warn_txt <- if (
+    length(warning_parts) > 0
+  ) {
+    
+    paste(
+      warning_parts,
+      collapse = " | "
+    )
+    
+  } else {
+    
+    NA_character_
+  }
+  
+  
+  converged <-
+    is.na(warn_txt)
+  
+  
+  # ----------------------------------------------------------
+  # 5.12 Extract Final Model Statistics
+  # ----------------------------------------------------------
+  
+  final_stats <- list(
+    
+    name = paste0(
+      "RE=",
+      re_terms
+    ),
+    
+    re_formula =
+      re_terms,
+    
+    optimizer =
+      res@optinfo$optimizer,
+    
+    selected_via =
+      selected_via,
+    
+    converged =
+      converged,
+    
+    singular =
+      isSingular(
+        res,
+        tol = 1e-5
+      ),
+    
+    aic =
+      AIC(res),
+    
+    bic =
+      BIC(res),
+    
+    llf =
+      as.numeric(
+        logLik(res)
+      ),
+    
+    nobs =
+      nobs(res),
+    
+    time_s =
+      proc.time()[["elapsed"]] - t0,
+    
+    status_msg =
+      if (converged) {
+        "OK"
+      } else {
+        "WARN"
+      },
+    
+    warnings =
+      warn_txt
+  )
+  
+  
+  # ----------------------------------------------------------
+  # 5.13 Structured Return
+  # ----------------------------------------------------------
+  
+  list(
+    
+    winner =
+      final_stats,
+    
+    audit =
+      list(
+        final_stats
+      ),
+    
+    full_formula =
+      full_formula
+  )
+}
+
+
+
+
+
+
+
+
+
+# ============================================================
+# CELL 6/7 — DV-SPECIFIC PREPARATION + PARALLEL MODEL RUNNER
+#             FOR UNCORRELATED RANDOM SLOPES
+# ============================================================
+# Purpose:
+#   Construct one analysis-ready dataset per duration DV and
+#   compare all candidate uncorrelated random-slope structures
+#   using that identical dataset.
+#
+# Responsibilities:
+#   1. Validate all variables required for the current DV.
+#   2. Construct the DV-specific complete-case sample.
+#   3. Remove non-positive values of the current duration DV.
+#   4. Natural-log transform the current duration DV.
+#   5. Standardize predictors using population SD (DDOF = 0)
+#      AFTER the final DV-specific sample has been established.
+#   6. Convert grouping variables to factors.
+#   7. Fit every candidate uncorrelated random-slope structure
+#      using the exact same prepared dataset.
+#   8. Execute candidate models in parallel.
+#   9. Collect model diagnostics and fit statistics.
+#  10. Evaluate and order candidate structures using
+#      convergence, singularity, and BIC/AIC.
+#  11. Produce a detailed sample-size audit.
+#
+# Paper 1 fixed-effects specification:
+#
+#   Lexical predictors:
+#       - Length
+#       - Predictability
+#       - Frequency
+#
+#   Affective predictors:
+#       - Valence
+#       - Arousal
+#       - Dominance
+#
+# Random-effects framework:
+#
+#   Step 3 evaluates participant-level UNCORRELATED random
+#   slopes:
+#
+#       (1 + candidate slopes || Participant_ID)
+#
+#   while retaining the crossed random intercept:
+#
+#       + (1 | Word_Unique_ID)
+#
+#   The use of || rather than | is controlled globally by:
+#
+#       USE_UNCORRELATED_SLOPES <- TRUE
+#
+# Important:
+#   Filtering is DV-specific.
+#
+#   No global IA_DWELL_TIME > 0 restriction is imposed.
+#   Instead, the CURRENT duration DV must be non-missing and > 0.
+#
+#   Predictor standardization occurs only AFTER this DV-specific
+#   sample has been established. All candidate random-slope
+#   models for the same DV therefore receive:
+#
+#       - identical observations
+#       - identical transformed DV values
+#       - identical standardized predictor values
+#       - identical fixed-effects specification
+#
+#   Only the participant-level uncorrelated random-slope
+#   structure changes across candidates.
+#
+# This is essential for fair AIC/BIC comparison.
+# ============================================================
+
+
+# ------------------------------------------------------------
+# 6.1 Population-SD Standardization Function (DDOF = 0)
+# ------------------------------------------------------------
+
+zscore_ddof0 <- function(x) {
+  
+  x <- suppressWarnings(
+    as.numeric(x)
+  )
+  
+  n <- sum(
+    !is.na(x)
+  )
+  
+  if (n <= 1) {
+    return(x)
+  }
+  
+  s1 <- sd(
+    x,
+    na.rm = TRUE
+  )
+  
+  if (
+    !is.finite(s1) ||
+    s1 <= 0
+  ) {
+    return(x)
+  }
+  
+  s0 <- s1 * sqrt(
+    (n - 1) / n
+  )
+  
+  (
+    x - mean(
+      x,
+      na.rm = TRUE
+    )
+  ) / s0
+}
+
+
+# ------------------------------------------------------------
+# 6.2 DV-Specific Analysis-Data Preparation
+# ------------------------------------------------------------
+
+prep_df_complete_cases <- function(
+    df,
+    dv,
+    participant_col,
+    required_cols,
+    use_additional_intercept = FALSE,
+    additional_intercept_col = NULL
+) {
+  
+  needed <- unique(
+    c(
+      dv,
+      participant_col,
+      required_cols,
+      if (use_additional_intercept) {
+        additional_intercept_col
+      } else {
+        NULL
+      }
+    )
+  )
+  
+  
+  # ----------------------------------------------------------
+  # Validate Required Variables
+  # ----------------------------------------------------------
+  
+  missing_required <- setdiff(
+    needed,
+    names(df)
+  )
+  
+  if (length(missing_required) > 0) {
+    
+    stop(
+      "Missing required variable(s) for ",
+      dv,
+      ": ",
+      paste(
+        missing_required,
+        collapse = ", "
+      )
+    )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # Select Required Variables
+  # ----------------------------------------------------------
+  
+  df_clean <- df %>%
+    select(
+      all_of(needed)
+    )
+  
+  n_source <- nrow(
+    df_clean
+  )
+  
+  
+  # ----------------------------------------------------------
+  # Coerce DV and Continuous Predictors to Numeric
+  # ----------------------------------------------------------
+  
+  numeric_cols <- unique(
+    c(
+      dv,
+      required_cols
+    )
+  )
+  
+  df_clean <- df_clean %>%
+    mutate(
+      across(
+        all_of(numeric_cols),
+        ~ suppressWarnings(
+          as.numeric(.x)
+        )
+      )
+    )
+  
+  
+  # ----------------------------------------------------------
+  # Remove Missing Values
+  # ----------------------------------------------------------
+  
+  df_clean <- df_clean %>%
+    drop_na()
+  
+  n_complete <- nrow(
+    df_clean
+  )
+  
+  n_removed_missing <- (
+    n_source -
+      n_complete
+  )
+  
+  
+  # ----------------------------------------------------------
+  # Retain Positive Values of the Current Duration DV
+  # ----------------------------------------------------------
+  
+  df_clean <- df_clean %>%
+    filter(
+      .data[[dv]] > 0
+    )
+  
+  n_positive <- nrow(
+    df_clean
+  )
+  
+  n_removed_nonpositive <- (
+    n_complete -
+      n_positive
+  )
+  
+  
+  # ----------------------------------------------------------
+  # Natural-Log Transform Current DV
+  # ----------------------------------------------------------
+  
+  df_clean[[dv]] <- log(
+    df_clean[[dv]]
+  )
+  
+  
+  # ----------------------------------------------------------
+  # Standardize Predictors Within Final DV-Specific Sample
+  # ----------------------------------------------------------
+  
+  df_clean <- df_clean %>%
+    mutate(
+      across(
+        all_of(required_cols),
+        zscore_ddof0
+      )
+    )
+  
+  
+  # ----------------------------------------------------------
+  # Convert Grouping Variables to Factors
+  # ----------------------------------------------------------
+  
+  df_clean[[participant_col]] <- as.factor(
+    as.character(
+      df_clean[[participant_col]]
+    )
+  )
+  
+  if (
+    use_additional_intercept &&
+    !is.null(additional_intercept_col)
+  ) {
+    
+    df_clean[[additional_intercept_col]] <- as.factor(
+      as.character(
+        df_clean[[additional_intercept_col]]
+      )
+    )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # Attach Filtering Diagnostics
+  # ----------------------------------------------------------
+  
+  attr(
+    df_clean,
+    "filter_summary"
+  ) <- tibble(
+    
+    DV = dv,
+    
+    N_Source = n_source,
+    
+    N_Removed_Missing =
+      n_removed_missing,
+    
+    N_Complete =
+      n_complete,
+    
+    N_Removed_NonPositive =
+      n_removed_nonpositive,
+    
+    N_Final =
+      n_positive,
+    
+    Percent_Retained =
+      if (n_source > 0) {
+        round(
+          100 * n_positive / n_source,
+          2
+        )
+      } else {
+        NA_real_
+      },
+    
+    N_Participants =
+      n_distinct(
+        df_clean[[participant_col]]
+      ),
+    
+    N_Additional_Intercept =
+      if (
+        use_additional_intercept &&
+        !is.null(additional_intercept_col)
+      ) {
+        
+        n_distinct(
+          df_clean[[additional_intercept_col]]
+        )
+        
+      } else {
+        
+        NA_integer_
+      }
+  )
+  
+  
+  # ----------------------------------------------------------
+  # Report Preparation Summary
+  # ----------------------------------------------------------
+  
+  message(
+    "   Source observations       : ",
+    format(
+      n_source,
+      big.mark = ","
+    )
+  )
+  
+  message(
+    "   Removed for missingness   : ",
+    format(
+      n_removed_missing,
+      big.mark = ","
+    )
+  )
+  
+  message(
+    "   Removed DV <= 0           : ",
+    format(
+      n_removed_nonpositive,
+      big.mark = ","
+    )
+  )
+  
+  message(
+    "   Final modeling N          : ",
+    format(
+      n_positive,
+      big.mark = ","
+    )
+  )
+  
+  message(
+    "   DV log transformation     : APPLIED"
+  )
+  
+  message(
+    "   Predictor standardization : APPLIED (DDOF = 0)"
+  )
+  
+  
+  df_clean
+}
+
+
+# ------------------------------------------------------------
+# 6.3 Dynamic Uncorrelated Random-Slope Selection Engine
+# ------------------------------------------------------------
+
+select_re_structure_dynamic <- function(
+    df,
+    dv,
+    re_candidates,
+    participant_col = "Participant_ID",
+    additional_intercept_col = NULL,
+    use_additional_intercept = FALSE,
+    controls = c(
+      "Length",
+      "Predictability",
+      "Frequency"
+    ),
+    emotions = c(
+      "Valence",
+      "Arousal",
+      "Dominance"
+    ),
+    rank_by = c(
+      "BIC",
+      "AIC"
+    ),
+    n_jobs = 1
+) {
+  
+  
+  # ----------------------------------------------------------
+  # 6.3.1 Configuration
+  # ----------------------------------------------------------
+  
+  rank_by <- match.arg(
+    toupper(rank_by),
+    c(
+      "BIC",
+      "AIC"
+    )
+  )
+  
+  n_jobs <- max(
+    1L,
+    as.integer(n_jobs)
+  )
+  
+  required_cols <- unique(
+    c(
+      controls,
+      emotions
+    )
+  )
+  
+  
+  # ----------------------------------------------------------
+  # Validate Fixed-Effect Variables
+  # ----------------------------------------------------------
+  
+  missing_fixed <- setdiff(
+    required_cols,
+    names(df)
+  )
+  
+  if (length(missing_fixed) > 0) {
+    
+    stop(
+      "Missing fixed-effect variable(s) for ",
+      dv,
+      ": ",
+      paste(
+        missing_fixed,
+        collapse = ", "
+      )
+    )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # Construct Fixed-Effects Formula
+  # ----------------------------------------------------------
+  
+  fixed_formula <- as.formula(
+    paste0(
+      dv,
+      " ~ ",
+      paste(
+        required_cols,
+        collapse = " + "
+      )
+    )
+  )
+  
+  
+  # ----------------------------------------------------------
+  # 6.3.2 Prepare ONE Modeling Dataset for Current DV
+  # ----------------------------------------------------------
+  
+  model_df <- prep_df_complete_cases(
+    df = df,
+    dv = dv,
+    participant_col = participant_col,
+    required_cols = required_cols,
+    use_additional_intercept =
+      use_additional_intercept,
+    additional_intercept_col =
+      additional_intercept_col
+  )
+  
+  filter_summary <- attr(
+    model_df,
+    "filter_summary"
+  )
+  
+  
+  # ----------------------------------------------------------
+  # Safety Check: Final Modeling Dataset Must Be Nonempty
+  # ----------------------------------------------------------
+  
+  if (nrow(model_df) == 0) {
+    
+    stop(
+      "No eligible observations remain for ",
+      dv,
+      " after DV-specific preparation."
+    )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 6.3.3 Row-Count Audit
+  # ----------------------------------------------------------
+  
+  rowcounts <- dv_rowcount_summary(
+    df = df,
+    dv = dv,
+    required_cols = c(
+      required_cols,
+      participant_col,
+      if (use_additional_intercept) {
+        additional_intercept_col
+      } else {
+        NULL
+      }
+    ),
+    label = paste0(
+      dv,
+      "_AIC_BIC_rows"
+    )
+  ) %>%
+    mutate(
+      rows_after_complete_case =
+        filter_summary$N_Complete,
+      
+      rows_removed_DV_nonpositive =
+        filter_summary$N_Removed_NonPositive,
+      
+      final_rows_used_for_AIC_BIC =
+        filter_summary$N_Final,
+      
+      pct_final_rows_retained =
+        filter_summary$Percent_Retained
+    )
+  
+  
+  # ----------------------------------------------------------
+  # 6.3.4 Candidate Execution Ordering
+  # ----------------------------------------------------------
+  
+  cand_list <- rev(
+    re_candidates
+  )
+  
+  indexed <- tibble(
+    idx = seq_along(
+      cand_list
+    ),
+    candidate = cand_list
+  )
+  
+  
+  # ----------------------------------------------------------
+  # 6.3.5 Parallel Execution Setup
+  # ----------------------------------------------------------
+  # Preserve the future strategy that was active before this
+  # function was called.
+  #
+  # The current DV is evaluated using a multisession plan with
+  # the resource-constrained worker count determined earlier.
+  #
+  # on.exit() guarantees restoration of the previous future
+  # strategy when this function terminates, including after an
+  # error. This prevents the DV-specific multisession plan from
+  # leaking into subsequent analysis code.
+  # ----------------------------------------------------------
+  
+  old_plan <- future::plan()
+  
+  
+  on.exit(
+    {
+      future::plan(
+        old_plan
+      )
+    },
+    add = TRUE
+  )
+  
+  
+  future::plan(
+    future::multisession,
+    workers = n_jobs
+  )
+  
+  
+  progressr::handlers(
+    global = TRUE
+  )
+  
+  
+  # ----------------------------------------------------------
+  # 6.3.6 Parallel Candidate-Model Execution
+  # ----------------------------------------------------------
+  
+  results_payload <- progressr::with_progress({
+    
+    progressor_obj <- progressr::progressor(
+      steps = nrow(indexed)
+    )
+    
+    future.apply::future_lapply(
+      seq_len(
+        nrow(indexed)
+      ),
+      function(i) {
+        
+        idx <- indexed$idx[i]
+        cand <- indexed$candidate[i]
+        
+        t0 <- proc.time()[["elapsed"]]
+        
+        fit <- fit_single_candidate_tiered(
+          dv = dv,
+          fixed_formula = fixed_formula,
+          model_df = model_df,
+          re_terms = cand,
+          groups_col = participant_col,
+          use_additional_intercept =
+            use_additional_intercept,
+          additional_intercept_col =
+            additional_intercept_col,
+          reml = TRUE
+        )
+        
+        progressor_obj(
+          message = paste0(
+            "[",
+            idx,
+            "/",
+            nrow(indexed),
+            "] ",
+            cand
+          )
+        )
+        
+        list(
+          idx = idx,
+          candidate = cand,
+          winner = fit$winner,
+          audit = fit$audit,
+          task_wall_s =
+            proc.time()[["elapsed"]] - t0
+        )
+      },
+      
+      future.seed = TRUE,
+      
+      future.globals = list(
+        indexed = indexed,
+        dv = dv,
+        fixed_formula = fixed_formula,
+        model_df = model_df,
+        participant_col = participant_col,
+        additional_intercept_col =
+          additional_intercept_col,
+        use_additional_intercept =
+          use_additional_intercept,
+        fit_single_candidate_tiered =
+          fit_single_candidate_tiered,
+        USE_UNCORRELATED_SLOPES =
+          USE_UNCORRELATED_SLOPES
+      ),
+      
+      future.packages = c(
+        "lme4"
+      )
+    )
+  })
+  
+  
+  # ----------------------------------------------------------
+  # 6.3.7 Restore Deterministic Execution Order
+  # ----------------------------------------------------------
+  
+  results_payload <- results_payload[
+    order(
+      vapply(
+        results_payload,
+        `[[`,
+        numeric(1),
+        "idx"
+      )
+    )
+  ]
+  
+  
+  # ----------------------------------------------------------
+  # 6.3.8 Collect Model Results and Audit Records
+  # ----------------------------------------------------------
+  
+  winner_rows <- list()
+  audit_rows <- list()
+  
+  
+  for (payload in results_payload) {
+    
+    w <- payload$winner
+    
+    if (
+      is.finite(w$aic) &&
+      is.finite(w$bic)
+    ) {
+      
+      winner_rows <- append(
+        winner_rows,
+        list(
+          tibble(
+            idx = payload$idx,
+            candidate = payload$candidate,
+            re_formula = w$re_formula,
+            optimizer = w$optimizer,
+            selected_via = w$selected_via,
+            converged = w$converged,
+            singular = w$singular,
+            aic = w$aic,
+            bic = w$bic,
+            llf = w$llf,
+            nobs = as.integer(
+              w$nobs
+            ),
+            winner_fit_time_s = as.numeric(
+              w$time_s
+            ),
+            candidate_task_time_s = as.numeric(
+              payload$task_wall_s
+            ),
+            warnings = w$warnings,
+            status = w$status_msg
+          )
+        )
+      )
+    }
+    
+    
+    for (a in payload$audit) {
+      
+      audit_rows <- append(
+        audit_rows,
+        list(
+          tibble(
+            idx = payload$idx,
+            candidate = payload$candidate,
+            re_formula = a$re_formula,
+            optimizer = a$optimizer,
+            selected_via = a$selected_via,
+            status = a$status_msg,
+            converged = a$converged,
+            singular = a$singular,
+            aic = a$aic,
+            bic = a$bic,
+            llf = a$llf,
+            nobs = as.integer(
+              a$nobs
+            ),
+            time_s = as.numeric(
+              a$time_s
+            ),
+            warnings = a$warnings
+          )
+        )
+      )
+    }
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 6.3.9 Final Candidate Evaluation and Selection Ordering
+  # ----------------------------------------------------------
+  
+  df_results <- if (
+    length(winner_rows) > 0
+  ) {
+    
+    bind_rows(
+      winner_rows
+    )
+    
+  } else {
+    
+    tibble()
+  }
+  
+  
+  df_audit <- if (
+    length(audit_rows) > 0
+  ) {
+    
+    bind_rows(
+      audit_rows
+    )
+    
+  } else {
+    
+    tibble()
+  }
+  
+  
+  if (nrow(df_results) > 0) {
+    
+    sort_col <- if (
+      rank_by == "BIC"
+    ) {
+      
+      "bic"
+      
+    } else {
+      
+      "aic"
+    }
+    
+    
+    # --------------------------------------------------------
+    # Identify Models Eligible for Primary Structure Selection
+    # --------------------------------------------------------
+    
+    df_results <- df_results %>%
+      mutate(
+        selection_eligible =
+          converged %in% TRUE &
+          singular %in% FALSE
+      )
+    
+    
+    # --------------------------------------------------------
+    # Compute Raw Information-Criterion Differences
+    # --------------------------------------------------------
+    
+    df_results <- df_results %>%
+      mutate(
+        delta_aic =
+          aic - min(
+            aic,
+            na.rm = TRUE
+          ),
+        
+        delta_bic =
+          bic - min(
+            bic,
+            na.rm = TRUE
+          )
+      )
+    
+    
+    # --------------------------------------------------------
+    # Rank Eligible Models First
+    # --------------------------------------------------------
+    
+    df_results <- df_results %>%
+      arrange(
+        desc(
+          selection_eligible
+        ),
+        .data[[sort_col]]
+      )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 6.3.10 Verify Equal Observation Counts Across Candidates
+  # ----------------------------------------------------------
+  
+  if (nrow(df_results) > 0) {
+    
+    unique_nobs <- unique(
+      df_results$nobs
+    )
+    
+    if (length(unique_nobs) != 1) {
+      
+      warning(
+        "Candidate models for ",
+        dv,
+        " were fitted with different observation counts."
+      )
+    }
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 6.3.11 Return Results
+  # ----------------------------------------------------------
+  
+  list(
+    df_results = df_results,
+    df_audit = df_audit,
+    rowcounts = rowcounts,
+    filter_summary = filter_summary
+  )
+}
+
+
+
+
+
+
+
+
+
+# ============================================================
+# CELL 8/9 — MANUAL DV-BY-DV UNCORRELATED-SLOPE EXECUTION
+# ============================================================
+# Purpose:
+#   Run the uncorrelated random-slope selection procedure
+#   independently for each duration-based dependent variable.
+#
+# Execution strategy:
+#   Each DV is defined in a separate execution block rather
+#   than inside a single loop.
+#
+#   When the full script is executed, the four DV blocks run
+#   sequentially. Individual DV blocks can also be executed
+#   independently when rerunning or recovering an analysis.
+#
+# Advantages:
+#   - Limits the consequences of a long-running model failure.
+#   - Allows each DV to be restarted independently.
+#   - Simplifies monitoring of CPU/RAM use.
+#   - Allows results to be inspected before proceeding.
+#   - Produces a separate Excel workbook for each DV.
+#
+# For each DV:
+#   1. Construct the DV-specific analysis sample.
+#   2. Remove missing/non-positive duration observations.
+#   3. Log-transform the current duration DV.
+#   4. Standardize LFP + VAD predictors within that sample.
+#   5. Fit all candidate uncorrelated random-slope structures.
+#   6. Evaluate candidates using BIC, convergence, and
+#      singularity diagnostics.
+#   7. Order selection-eligible candidates first, ranked by BIC
+#      within eligibility class.
+#
+# Paper 1:
+#   Source dataset:
+#       Affective Provo
+#
+#   Fixed effects / candidate slopes:
+#       Length
+#       Predictability
+#       Frequency
+#       Valence
+#       Arousal
+#       Dominance
+#
+#   Random-effects framework:
+#       (1 + candidate slopes || Participant_ID)
+#       + (1 | Word_Unique_ID)
+#
+# Important:
+#   - Candidate models within a DV use exactly the same
+#     DV-specific analysis sample.
+#   - Filtering and standardization are performed once per DV,
+#     before candidate-model fitting.
+#   - BIC is the primary ranking criterion.
+#   - Convergence and singularity diagnostics must also be
+#     considered when selecting the final random-slope structure.
+#   - The distinction from Step 2 is the participant-level
+#     covariance structure:
+#
+#         Step 2: (1 + slopes | Participant_ID)
+#         Step 3: (1 + slopes || Participant_ID)
+#
+# Output:
+#   One Step 3 Excel workbook per duration DV containing:
+#       - candidate ranking
+#       - model-fit audit
+#       - sample-size / row-count audit
+#
+# Runtime:
+#   Runtime depends on sample size, candidate complexity,
+#   optimizer behavior, hardware, and number of workers.
+#   Runtime estimates from earlier versions should therefore
+#   not be assumed for the revised pipeline.
+# ============================================================
+
+
+# ------------------------------------------------------------
+# 8.1 DV Registry
+# ------------------------------------------------------------
+
+DV_INFO <- list(
+  IA_FIRST_FIXATION_DURATION  = list(serial = 1, suffix = "FFD"),
+  IA_FIRST_RUN_DWELL_TIME     = list(serial = 2, suffix = "GD"),
+  IA_REGRESSION_PATH_DURATION = list(serial = 3, suffix = "GPT"),
+  IA_DWELL_TIME               = list(serial = 4, suffix = "TDT")
+)
+
+
+
+# ============================================================
+# DV 1 — FIRST FIXATION DURATION (FFD)
+# ============================================================
+
+DV_TO_RUN <- "IA_FIRST_FIXATION_DURATION"
+
+if (is.null(DV_INFO[[DV_TO_RUN]])) {
+  stop("Unknown DV_TO_RUN: ", DV_TO_RUN)
+}
+
+DV_SERIAL <- DV_INFO[[DV_TO_RUN]]$serial
+DV_SUFFIX <- DV_INFO[[DV_TO_RUN]]$suffix
+
+message("\n", strrep("=", 80))
+message("STARTING UNCORRELATED-SLOPE ANALYSIS")
+message(
+  "DV: ",
+  DV_TO_RUN,
+  " | Stage=",
+  DV_SERIAL,
+  " | Measure=",
+  DV_SUFFIX
+)
+message("Dataset: Affective Provo")
+message(strrep("=", 80))
+
+t0 <- proc.time()[["elapsed"]]
+
+res <- select_re_structure_dynamic(
+  df = df,
+  dv = DV_TO_RUN,
+  re_candidates = CANDIDATES,
+  rank_by = "BIC",
+  n_jobs = N_JOBS,
+  participant_col = "Participant_ID",
+  additional_intercept_col = ADDITIONAL_INTERCEPT,
+  use_additional_intercept = USE_ADDITIONAL_INTERCEPT
+)
+
+out_path <- file.path(
+  OUTPUT_DATA_DIR,
+  paste0(
+    "Step-3-",
+    DV_SERIAL, "_",
+    DV_SUFFIX,
+    "_UncorrelatedSlopes_Affective_Provo.xlsx"
+  )
+)
+
+save_re_outputs_to_excel(
+  excel_path = out_path,
+  dv = DV_TO_RUN,
+  df_results = res$df_results,
+  df_audit = res$df_audit,
+  rowcount_summary = res$rowcounts
+)
+
+elapsed_total <- proc.time()[["elapsed"]] - t0
+
+message("\nDV-SPECIFIC SAMPLE:")
+print(res$filter_summary)
+
+message("\nCOMPLETED DV: ", DV_TO_RUN)
+message("Saved to: ", out_path)
+message("Elapsed time: ", fmt_secs(elapsed_total))
+
+
+
+# ============================================================
+# DV 2 — FIRST-RUN DWELL TIME / GAZE DURATION (GD)
+# ============================================================
+
+DV_TO_RUN <- "IA_FIRST_RUN_DWELL_TIME"
+
+if (is.null(DV_INFO[[DV_TO_RUN]])) {
+  stop("Unknown DV_TO_RUN: ", DV_TO_RUN)
+}
+
+DV_SERIAL <- DV_INFO[[DV_TO_RUN]]$serial
+DV_SUFFIX <- DV_INFO[[DV_TO_RUN]]$suffix
+
+message("\n", strrep("=", 80))
+message("STARTING UNCORRELATED-SLOPE ANALYSIS")
+message(
+  "DV: ",
+  DV_TO_RUN,
+  " | Stage=",
+  DV_SERIAL,
+  " | Measure=",
+  DV_SUFFIX
+)
+message("Dataset: Affective Provo")
+message(strrep("=", 80))
+
+t0 <- proc.time()[["elapsed"]]
+
+res <- select_re_structure_dynamic(
+  df = df,
+  dv = DV_TO_RUN,
+  re_candidates = CANDIDATES,
+  rank_by = "BIC",
+  n_jobs = N_JOBS,
+  participant_col = "Participant_ID",
+  additional_intercept_col = ADDITIONAL_INTERCEPT,
+  use_additional_intercept = USE_ADDITIONAL_INTERCEPT
+)
+
+out_path <- file.path(
+  OUTPUT_DATA_DIR,
+  paste0(
+    "Step-3-",
+    DV_SERIAL, "_",
+    DV_SUFFIX,
+    "_UncorrelatedSlopes_Affective_Provo.xlsx"
+  )
+)
+
+save_re_outputs_to_excel(
+  excel_path = out_path,
+  dv = DV_TO_RUN,
+  df_results = res$df_results,
+  df_audit = res$df_audit,
+  rowcount_summary = res$rowcounts
+)
+
+elapsed_total <- proc.time()[["elapsed"]] - t0
+
+message("\nDV-SPECIFIC SAMPLE:")
+print(res$filter_summary)
+
+message("\nCOMPLETED DV: ", DV_TO_RUN)
+message("Saved to: ", out_path)
+message("Elapsed time: ", fmt_secs(elapsed_total))
+
+
+
+# ============================================================
+# DV 3 — REGRESSION PATH DURATION / GO-PAST TIME (GPT)
+# ============================================================
+
+DV_TO_RUN <- "IA_REGRESSION_PATH_DURATION"
+
+if (is.null(DV_INFO[[DV_TO_RUN]])) {
+  stop("Unknown DV_TO_RUN: ", DV_TO_RUN)
+}
+
+DV_SERIAL <- DV_INFO[[DV_TO_RUN]]$serial
+DV_SUFFIX <- DV_INFO[[DV_TO_RUN]]$suffix
+
+message("\n", strrep("=", 80))
+message("STARTING UNCORRELATED-SLOPE ANALYSIS")
+message(
+  "DV: ",
+  DV_TO_RUN,
+  " | Stage=",
+  DV_SERIAL,
+  " | Measure=",
+  DV_SUFFIX
+)
+message("Dataset: Affective Provo")
+message(strrep("=", 80))
+
+t0 <- proc.time()[["elapsed"]]
+
+res <- select_re_structure_dynamic(
+  df = df,
+  dv = DV_TO_RUN,
+  re_candidates = CANDIDATES,
+  rank_by = "BIC",
+  n_jobs = N_JOBS,
+  participant_col = "Participant_ID",
+  additional_intercept_col = ADDITIONAL_INTERCEPT,
+  use_additional_intercept = USE_ADDITIONAL_INTERCEPT
+)
+
+out_path <- file.path(
+  OUTPUT_DATA_DIR,
+  paste0(
+    "Step-3-",
+    DV_SERIAL, "_",
+    DV_SUFFIX,
+    "_UncorrelatedSlopes_Affective_Provo.xlsx"
+  )
+)
+
+save_re_outputs_to_excel(
+  excel_path = out_path,
+  dv = DV_TO_RUN,
+  df_results = res$df_results,
+  df_audit = res$df_audit,
+  rowcount_summary = res$rowcounts
+)
+
+elapsed_total <- proc.time()[["elapsed"]] - t0
+
+message("\nDV-SPECIFIC SAMPLE:")
+print(res$filter_summary)
+
+message("\nCOMPLETED DV: ", DV_TO_RUN)
+message("Saved to: ", out_path)
+message("Elapsed time: ", fmt_secs(elapsed_total))
+
+
+
+# ============================================================
+# DV 4 — TOTAL DWELL TIME / TOTAL READING TIME (TDT)
+# ============================================================
+
+DV_TO_RUN <- "IA_DWELL_TIME"
+
+if (is.null(DV_INFO[[DV_TO_RUN]])) {
+  stop("Unknown DV_TO_RUN: ", DV_TO_RUN)
+}
+
+DV_SERIAL <- DV_INFO[[DV_TO_RUN]]$serial
+DV_SUFFIX <- DV_INFO[[DV_TO_RUN]]$suffix
+
+message("\n", strrep("=", 80))
+message("STARTING UNCORRELATED-SLOPE ANALYSIS")
+message(
+  "DV: ",
+  DV_TO_RUN,
+  " | Stage=",
+  DV_SERIAL,
+  " | Measure=",
+  DV_SUFFIX
+)
+message("Dataset: Affective Provo")
+message(strrep("=", 80))
+
+t0 <- proc.time()[["elapsed"]]
+
+res <- select_re_structure_dynamic(
+  df = df,
+  dv = DV_TO_RUN,
+  re_candidates = CANDIDATES,
+  rank_by = "BIC",
+  n_jobs = N_JOBS,
+  participant_col = "Participant_ID",
+  additional_intercept_col = ADDITIONAL_INTERCEPT,
+  use_additional_intercept = USE_ADDITIONAL_INTERCEPT
+)
+
+out_path <- file.path(
+  OUTPUT_DATA_DIR,
+  paste0(
+    "Step-3-",
+    DV_SERIAL, "_",
+    DV_SUFFIX,
+    "_UncorrelatedSlopes_Affective_Provo.xlsx"
+  )
+)
+
+save_re_outputs_to_excel(
+  excel_path = out_path,
+  dv = DV_TO_RUN,
+  df_results = res$df_results,
+  df_audit = res$df_audit,
+  rowcount_summary = res$rowcounts
+)
+
+elapsed_total <- proc.time()[["elapsed"]] - t0
+
+message("\nDV-SPECIFIC SAMPLE:")
+print(res$filter_summary)
+
+message("\nCOMPLETED DV: ", DV_TO_RUN)
+message("Saved to: ", out_path)
+message("Elapsed time: ", fmt_secs(elapsed_total))
+
+
+
+
+
+# ============================================================
+# RUNTIME LOG — END
+# ============================================================
+# Purpose:
+#   Finalize the Step 3 runtime log after all requested
+#   uncorrelated random-slope analyses have completed.
+#
+# Records:
+#   - Analysis completion timestamp
+#   - R session information
+#
+# Cleanup:
+#   - Close the message sink
+#   - Close the standard-output sink
+#   - Close the runtime-log file connection
+#
+# Safety:
+#   Sink and connection states are checked before closing so
+#   this cell can be rerun without unnecessarily attempting
+#   to close inactive sinks or an already-closed connection.
+# ============================================================
+
+
+# ------------------------------------------------------------
+# 1. Record Analysis Completion
+# ------------------------------------------------------------
+
+cat(
+  paste0(
+    "\n",
+    strrep("=", 80), "\n",
+    "STEP 3 — UNCORRELATED RANDOM-SLOPE ANALYSIS COMPLETED\n",
+    "Dataset: Affective Provo\n",
+    "Finished: ",
+    format(
+      Sys.time(),
+      "%Y-%m-%d %H:%M:%S"
+    ),
+    "\n",
+    strrep("=", 80), "\n\n"
+  )
+)
+
+
+# ------------------------------------------------------------
+# 2. Record R Session Information
+# ------------------------------------------------------------
+
+cat("SESSION INFORMATION\n")
+cat(strrep("-", 80), "\n")
+
+print(sessionInfo())
+
+cat(
+  "\n",
+  strrep("=", 80), "\n",
+  "END OF RUNTIME LOG\n",
+  strrep("=", 80), "\n"
+)
+
+
+# ------------------------------------------------------------
+# 3. Flush Runtime-Log Connection
+# ------------------------------------------------------------
+# Push any buffered output to disk before sinks are closed.
+# ------------------------------------------------------------
+
+if (exists("log_con") && isOpen(log_con)) {
+  flush(log_con)
+}
+
+
+# ------------------------------------------------------------
+# 4. Close Message Sink
+# ------------------------------------------------------------
+# Message output was redirected separately using:
+#   sink(log_con, type = "message")
+# ------------------------------------------------------------
+
+if (sink.number(type = "message") > 0) {
+  sink(type = "message")
+}
+
+
+# ------------------------------------------------------------
+# 5. Close Standard-Output Sink
+# ------------------------------------------------------------
+# Standard output was redirected using:
+#   sink(log_con, split = TRUE)
+# ------------------------------------------------------------
+
+if (sink.number(type = "output") > 0) {
+  sink(type = "output")
+}
+
+
+# ------------------------------------------------------------
+# 6. Close Runtime-Log Connection
+# ------------------------------------------------------------
+
+if (exists("log_con") && isOpen(log_con)) {
+  close(log_con)
+}
+
+
+# ------------------------------------------------------------
+# 7. Confirm Successful Log Export
+# ------------------------------------------------------------
+# This message is intentionally emitted AFTER the sinks have
+# been closed, so it appears only in the active R console.
+# ------------------------------------------------------------
+
+message(
+  "Runtime log saved successfully: ",
+  LOG_PATH
+)

05-Research_Program-Affective_Provo/01-Fixation_Duration_Research/01-LME_Model_Structure/01-Scripts/Step-4-Merging_Results_of_Correlated+Uncorrelated_Slopes.R

@@ -0,0 +1,2336 @@
+# ============================================================
+# COPYRIGHT, LICENSING, AND SCHOLARLY CITATION
+# ============================================================
+# Copyright (c) 2026 Mohit Gupta
+# License: MIT
+# SPDX-License-Identifier: MIT
+#
+# This script contains original computational software
+# developed by Mohit Gupta for the AffLex-Provo
+# Research Program.
+#
+# Citation:
+# Researchers using this software in published research
+# are strongly requested to cite the AffLex-Provo repository:
+# https://huggingface.co/datasets/mohitg2/AffLex-Provo
+#
+# Third-party datasets and externally sourced materials
+# remain subject to their respective original licenses.
+#
+# See the applicable repository LICENSE file for the
+# complete MIT License terms.
+# ============================================================
+
+# ============================================================
+# STEP 4 — MERGE, COMPARE, SORT, REORDER, AND FORMAT (Affective Provo)
+# ============================================================
+#
+#
+# REQUIRED R VERSION: R version 4.5.2 (2025-10-31)
+#
+#
+# Purpose:
+#   Merge the Step 2 correlated and Step 3 uncorrelated
+#   random-slope results across all four duration-based reading
+#   measures into one consolidated result table.
+#
+# Inputs:
+#   Step 2:
+#       Correlated random-slope candidate rankings
+#
+#   Step 3:
+#       Uncorrelated random-slope candidate rankings
+#
+# Reading measures:
+#       1. First Fixation Duration (FFD)
+#       2. Gaze Duration / First-Run Dwell Time (GD)
+#       3. Regression Path Duration / Go-Past Time (GPT)
+#       4. Total Dwell Time / Total Reading Time (TDT)
+#
+# Workflow:
+#   1. Locate Step 2 and Step 3 result workbooks.
+#   2. Read the ranking sheet from each workbook.
+#   3. Tag each result with:
+#        - Stage of Reading
+#        - Reading Measure
+#        - Dependent Variable Name
+#        - Random-Slope Structure
+#   4. Combine correlated and uncorrelated candidate models.
+#   5. Recalculate AIC/BIC differences across the combined
+#      candidate set within each DV.
+#   6. Preserve convergence/singularity-based selection
+#      eligibility from Steps 2 and 3.
+#   7. Order selection-eligible models first and then by BIC.
+#   8. Export the consolidated results to Excel.
+#
+# Dataset:
+#   Affective Provo
+#
+# Input / Output Directory:
+#
+#   05-Research_Program-Affective_Provo/
+#     01-Fixation_Duration_Research/
+#       01-LME_Model_Structure/
+#         02-Results/
+#
+# Important:
+#   Step 2 and Step 3 intentionally use the same results
+#   directory. Their files are distinguished by:
+#
+#       Step-2-* → correlated random slopes
+#       Step-3-* → uncorrelated random slopes
+#
+#   Step 4 reads both model families from the same directory
+#   and compares them within each duration DV.
+#
+#   Information criteria are comparable within each DV because
+#   the corresponding Step 2 and Step 3 models use:
+#
+#       - the same source dataset
+#       - the same DV-specific filtering
+#       - the same predictor standardization procedure
+#       - the same fixed-effects specification
+#       - the same observations
+#       - REML estimation
+#
+#   The random-intercept-only candidate is shared across the
+#   parameterization families and is represented once. Models
+#   containing participant-level random slopes are compared under
+#   correlated and uncorrelated parameterizations.
+# ============================================================
+
+
+
+# ============================================================
+# CELL 1 — PACKAGE INSTALLATION AND INITIALIZATION
+# ============================================================
+
+REQUIRED_PACKAGES <- c(
+  "readxl",
+  "openxlsx",
+  "dplyr",
+  "stringr",
+  "here"
+)
+
+
+# ------------------------------------------------------------
+# 1.1 Identify Missing Packages
+# ------------------------------------------------------------
+
+MISSING_PACKAGES <- REQUIRED_PACKAGES[
+  !vapply(
+    REQUIRED_PACKAGES,
+    requireNamespace,
+    quietly = TRUE,
+    FUN.VALUE = logical(1)
+  )
+]
+
+
+# ------------------------------------------------------------
+# 1.2 Install Missing Packages
+# ------------------------------------------------------------
+
+if (length(MISSING_PACKAGES) > 0) {
+
+  message(
+    "Installing missing package(s): ",
+    paste(MISSING_PACKAGES, collapse = ", ")
+  )
+
+  install.packages(
+    MISSING_PACKAGES,
+    repos = "https://cloud.r-project.org",
+    dependencies = TRUE
+  )
+
+} else {
+
+  message("All required packages are already installed.")
+}
+
+
+# ------------------------------------------------------------
+# 1.3 Load Required Packages
+# ------------------------------------------------------------
+
+suppressPackageStartupMessages({
+
+  library(readxl)
+  library(openxlsx)
+
+  library(dplyr)
+  library(stringr)
+
+  library(here)
+})
+
+
+message(
+  "Package initialization complete: ",
+  length(REQUIRED_PACKAGES),
+  " required packages available."
+)
+
+
+
+
+
+# ============================================================
+# CELL 2 — PROJECT PATHS
+# ============================================================
+# Purpose:
+#   Define the shared Step 2 / Step 3 results directory and
+#   the Step 4 merged-result output path.
+# ============================================================
+
+PROJECT_ROOT <- here()
+
+
+RESULTS_DIR <- here(
+  "05-Research_Program-Affective_Provo",
+  "01-Fixation_Duration_Research",
+  "01-LME_Model_Structure",
+  "02-Results"
+)
+
+
+# ------------------------------------------------------------
+# 2.1 Validate Results Directory
+# ------------------------------------------------------------
+
+if (!dir.exists(RESULTS_DIR)) {
+
+  stop(
+    "Results directory not found: ",
+    RESULTS_DIR
+  )
+}
+
+
+# ------------------------------------------------------------
+# 2.2 Define Step 4 Output File
+# ------------------------------------------------------------
+
+MERGED_OUTPUT_PATH <- file.path(
+  RESULTS_DIR,
+  "Step-4_Merged_Correlated-Uncorrelated_Slopes_Affective_Provo.xlsx"
+)
+
+
+# ------------------------------------------------------------
+# 2.3 Report Resolved Paths
+# ------------------------------------------------------------
+
+message("PROJECT_ROOT: ", PROJECT_ROOT)
+message("RESULTS_DIR: ", RESULTS_DIR)
+message("MERGED_OUTPUT_PATH: ", MERGED_OUTPUT_PATH)
+
+
+
+
+
+# ============================================================
+# CELL 3 — DV REGISTRY
+# ============================================================
+# Purpose:
+#   Define the four duration DVs and the metadata required to
+#   construct Step 2 and Step 3 filenames deterministically.
+# ============================================================
+
+DV_INFO <- list(
+
+  IA_FIRST_FIXATION_DURATION = list(
+    serial = 1,
+    suffix = "FFD",
+    measure = "First Fixation Duration"
+  ),
+
+  IA_FIRST_RUN_DWELL_TIME = list(
+    serial = 2,
+    suffix = "GD",
+    measure = "Gaze Duration"
+  ),
+
+  IA_REGRESSION_PATH_DURATION = list(
+    serial = 3,
+    suffix = "GPT",
+    measure = "Regression Path Duration"
+  ),
+
+  IA_DWELL_TIME = list(
+    serial = 4,
+    suffix = "TDT",
+    measure = "Total Dwell Time"
+  )
+)
+
+
+
+
+
+# ============================================================
+# CELL 4 — RESULT-WORKBOOK READER
+# ============================================================
+# Purpose:
+#   Read one Step 2 or Step 3 ranking workbook, validate its
+#   required columns, normalize model diagnostics, verify
+#   selection eligibility, and attach Step 4 comparison
+#   metadata.
+#
+# Required ranking columns:
+#       candidate
+#       aic
+#       bic
+#       converged
+#       singular
+#       nobs
+#
+# Expected selection column:
+#       selection_eligible
+#
+# If selection_eligible is absent, it is reconstructed using:
+#
+#       converged = TRUE
+#       singular  = FALSE
+#
+# Important:
+#   Steps 2 and 3 construct worksheet names using:
+#
+#       safe_sheet_name(paste0(dv, "_ranking"))
+#
+#   Because Excel limits worksheet names to 31 characters,
+#   long DV names may truncate part or all of the "_ranking"
+#   suffix. Step 4 therefore reconstructs the exact expected
+#   worksheet name rather than searching for the literal word
+#   "ranking".
+#
+# Safety:
+#   - Missing files cause an explicit failure.
+#   - Invalid structure-type arguments cause an explicit failure.
+#   - Missing expected ranking sheets cause an explicit failure.
+#   - Empty ranking sheets cause an explicit failure.
+#   - Missing required ranking columns cause an explicit failure.
+#   - Invalid or non-finite AIC/BIC values cause an explicit
+#     failure.
+#   - Missing convergence/singularity diagnostics cause an
+#     explicit failure.
+#   - Invalid logical diagnostic values cause an explicit
+#     failure.
+#   - Exported selection eligibility is independently checked
+#     against convergence and singularity.
+# ============================================================
+
+
+# ------------------------------------------------------------
+# 4.0 Excel Sheet-Name Sanitizer
+# ------------------------------------------------------------
+# Must match the naming rule used by Steps 2 and 3.
+# ------------------------------------------------------------
+
+safe_sheet_name <- function(name) {
+  
+  name <- str_replace_all(
+    name,
+    "[\\\\/*\\[\\]:?]",
+    "_"
+  )
+  
+  str_sub(
+    name,
+    1,
+    31
+  )
+}
+
+
+# ------------------------------------------------------------
+# 4.1 Logical-Value Normalization Helper
+# ------------------------------------------------------------
+
+normalize_logical <- function(x) {
+  
+  if (is.logical(x)) {
+    return(x)
+  }
+  
+  x_chr <- toupper(
+    trimws(
+      as.character(x)
+    )
+  )
+  
+  out <- rep(
+    NA,
+    length(x_chr)
+  )
+  
+  out[
+    x_chr %in% c(
+      "TRUE",
+      "T",
+      "1"
+    )
+  ] <- TRUE
+  
+  out[
+    x_chr %in% c(
+      "FALSE",
+      "F",
+      "0"
+    )
+  ] <- FALSE
+  
+  out
+}
+
+
+# ------------------------------------------------------------
+# 4.2 Result-Workbook Reader
+# ------------------------------------------------------------
+
+read_and_tag <- function(
+    path,
+    structure_type,
+    serial,
+    suffix,
+    measure,
+    dv_name
+) {
+  
+  
+  # ----------------------------------------------------------
+  # 4.2.1 Validate Input File
+  # ----------------------------------------------------------
+  
+  if (!file.exists(path)) {
+    
+    stop(
+      "Required Step 4 input file not found: ",
+      path
+    )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 4.2.2 Validate Structure-Type Argument
+  # ----------------------------------------------------------
+  
+  if (
+    !structure_type %in% c(
+      "Correlated",
+      "Uncorrelated"
+    )
+  ) {
+    
+    stop(
+      "Invalid structure_type supplied to read_and_tag(): ",
+      structure_type
+    )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 4.2.3 Locate Exact Ranking Sheet
+  # ----------------------------------------------------------
+  
+  sheet_names <- getSheetNames(
+    path
+  )
+  
+  expected_ranking_sheet <- safe_sheet_name(
+    paste0(
+      dv_name,
+      "_ranking"
+    )
+  )
+  
+  if (
+    !expected_ranking_sheet %in%
+    sheet_names
+  ) {
+    
+    stop(
+      "Expected ranking sheet not found in ",
+      basename(path),
+      ".\n",
+      "Expected sheet: ",
+      expected_ranking_sheet,
+      "\n",
+      "Available sheets: ",
+      paste(
+        sheet_names,
+        collapse = ", "
+      )
+    )
+  }
+  
+  sheet_name <- expected_ranking_sheet
+  
+  
+  # ----------------------------------------------------------
+  # 4.2.4 Read Ranking Results
+  # ----------------------------------------------------------
+  
+  result_df <- read_excel(
+    path,
+    sheet = sheet_name
+  )
+  
+  if (nrow(result_df) == 0) {
+    
+    stop(
+      "Ranking sheet contains no candidate models: ",
+      basename(path)
+    )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 4.2.5 Validate Required Ranking Columns
+  # ----------------------------------------------------------
+  
+  required_result_cols <- c(
+    "candidate",
+    "aic",
+    "bic",
+    "converged",
+    "singular",
+    "nobs"
+  )
+  
+  missing_result_cols <- setdiff(
+    required_result_cols,
+    names(result_df)
+  )
+  
+  if (length(missing_result_cols) > 0) {
+    
+    stop(
+      "Missing required ranking column(s) in ",
+      basename(path),
+      ": ",
+      paste(
+        missing_result_cols,
+        collapse = ", "
+      )
+    )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 4.2.6 Validate Candidate Identifiers
+  # ----------------------------------------------------------
+  
+  result_df$candidate <- trimws(
+    as.character(
+      result_df$candidate
+    )
+  )
+  
+  if (
+    anyNA(result_df$candidate) ||
+    any(result_df$candidate == "")
+  ) {
+    
+    stop(
+      "Missing or empty candidate identifier(s) detected in ",
+      basename(path),
+      "."
+    )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 4.2.7 Coerce Information Criteria to Numeric
+  # ----------------------------------------------------------
+  
+  result_df <- result_df %>%
+    mutate(
+      aic = suppressWarnings(
+        as.numeric(aic)
+      ),
+      bic = suppressWarnings(
+        as.numeric(bic)
+      )
+    )
+  
+  
+  # ----------------------------------------------------------
+  # 4.2.8 Validate Information Criteria
+  # ----------------------------------------------------------
+  
+  if (
+    any(!is.finite(result_df$aic)) ||
+    any(!is.finite(result_df$bic))
+  ) {
+    
+    stop(
+      "Missing, invalid, or non-finite AIC/BIC values detected ",
+      "in ranking sheet: ",
+      basename(path)
+    )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 4.2.9 Normalize Core Diagnostic Columns
+  # ----------------------------------------------------------
+  
+  result_df$converged <- normalize_logical(
+    result_df$converged
+  )
+  
+  result_df$singular <- normalize_logical(
+    result_df$singular
+  )
+  
+  
+  # ----------------------------------------------------------
+  # 4.2.10 Reject Missing / Invalid Core Diagnostics
+  # ----------------------------------------------------------
+  
+  if (anyNA(result_df$converged)) {
+    
+    stop(
+      "Missing or invalid logical value(s) detected in ",
+      "'converged' in ",
+      basename(path),
+      ". Accepted values are TRUE/FALSE, T/F, or 1/0."
+    )
+  }
+  
+  if (anyNA(result_df$singular)) {
+    
+    stop(
+      "Missing or invalid logical value(s) detected in ",
+      "'singular' in ",
+      basename(path),
+      ". Accepted values are TRUE/FALSE, T/F, or 1/0."
+    )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 4.2.11 Normalize or Reconstruct Selection Eligibility
+  # ----------------------------------------------------------
+  
+  if ("selection_eligible" %in% names(result_df)) {
+    
+    result_df$selection_eligible <- normalize_logical(
+      result_df$selection_eligible
+    )
+    
+    if (anyNA(result_df$selection_eligible)) {
+      
+      stop(
+        "Missing or invalid logical value(s) detected in ",
+        "'selection_eligible' in ",
+        basename(path),
+        ". Accepted values are TRUE/FALSE, T/F, or 1/0."
+      )
+    }
+    
+  } else {
+    
+    warning(
+      "selection_eligible missing from ",
+      basename(path),
+      "; reconstructing it from converged and singular."
+    )
+    
+    result_df <- result_df %>%
+      mutate(
+        selection_eligible =
+          converged %in% TRUE &
+          singular %in% FALSE
+      )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 4.2.12 Independently Verify Selection Eligibility
+  # ----------------------------------------------------------
+  
+  expected_eligibility <- (
+    result_df$converged %in% TRUE &
+      result_df$singular %in% FALSE
+  )
+  
+  eligibility_mismatch <- which(
+    is.na(result_df$selection_eligible) |
+      result_df$selection_eligible !=
+      expected_eligibility
+  )
+  
+  if (length(eligibility_mismatch) > 0) {
+    
+    stop(
+      "selection_eligible is inconsistent with converged / ",
+      "singular for ",
+      length(eligibility_mismatch),
+      " candidate(s) in ",
+      basename(path),
+      ". Step 4 comparison stopped."
+    )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 4.2.13 Add Step 4 Metadata
+  # ----------------------------------------------------------
+  
+  result_df <- result_df %>%
+    mutate(
+      `Stage of Reading` = serial,
+      `Reading Measure` = measure,
+      `Measure Abbreviation` = suffix,
+      `Dependent Variable Name` = dv_name,
+      `Random-Slope Structure` = structure_type,
+      `Source Step` = ifelse(
+        structure_type == "Correlated",
+        "Step 2",
+        "Step 3"
+      ),
+      `Source Workbook` = basename(path)
+    )
+  
+  
+  # ----------------------------------------------------------
+  # 4.2.14 Return Validated Ranking Table
+  # ----------------------------------------------------------
+  
+  result_df
+}
+
+
+
+
+# ============================================================
+# CELL 5 — READ STEP 2 AND STEP 3 RESULTS
+# ============================================================
+# Purpose:
+#   Read the correlated and uncorrelated ranking workbook for
+#   each duration DV and combine all available model candidates
+#   into one master container.
+#
+# Expected filenames:
+#
+#   Step 2:
+#       Step-2-1_FFD_CorrelatedSlopes_Affective_Provo.xlsx
+#       Step-2-2_GD_CorrelatedSlopes_Affective_Provo.xlsx
+#       Step-2-3_GPT_CorrelatedSlopes_Affective_Provo.xlsx
+#       Step-2-4_TDT_CorrelatedSlopes_Affective_Provo.xlsx
+#
+#   Step 3:
+#       Step-3-1_FFD_UncorrelatedSlopes_Affective_Provo.xlsx
+#       Step-3-2_GD_UncorrelatedSlopes_Affective_Provo.xlsx
+#       Step-3-3_GPT_UncorrelatedSlopes_Affective_Provo.xlsx
+#       Step-3-4_TDT_UncorrelatedSlopes_Affective_Provo.xlsx
+# ============================================================
+
+master_df <- list()
+
+
+message(
+  "\n",
+  strrep("=", 80)
+)
+
+message(
+  "STARTING STEP 4 — MERGING CORRELATED AND UNCORRELATED RESULTS"
+)
+
+message(
+  "Dataset: Affective Provo"
+)
+
+message(
+  strrep("=", 80)
+)
+
+
+for (dv_name in names(DV_INFO)) {
+
+
+  # ----------------------------------------------------------
+  # 5.1 Retrieve DV Metadata
+  # ----------------------------------------------------------
+
+  serial <- DV_INFO[[dv_name]]$serial
+  suffix <- DV_INFO[[dv_name]]$suffix
+  measure <- DV_INFO[[dv_name]]$measure
+
+
+  # ----------------------------------------------------------
+  # 5.2 Construct Step 2 Filename
+  # ----------------------------------------------------------
+
+  f_corr <- paste0(
+    "Step-2-",
+    serial,
+    "_",
+    suffix,
+    "_CorrelatedSlopes_Affective_Provo.xlsx"
+  )
+
+
+  # ----------------------------------------------------------
+  # 5.3 Construct Step 3 Filename
+  # ----------------------------------------------------------
+
+  f_uncorr <- paste0(
+    "Step-3-",
+    serial,
+    "_",
+    suffix,
+    "_UncorrelatedSlopes_Affective_Provo.xlsx"
+  )
+
+
+  path_corr <- file.path(
+    RESULTS_DIR,
+    f_corr
+  )
+
+  path_uncorr <- file.path(
+    RESULTS_DIR,
+    f_uncorr
+  )
+
+
+  # ----------------------------------------------------------
+  # 5.4 Read Correlated Results
+  # ----------------------------------------------------------
+
+  df_corr <- read_and_tag(
+    path = path_corr,
+    structure_type = "Correlated",
+    serial = serial,
+    suffix = suffix,
+    measure = measure,
+    dv_name = dv_name
+  )
+
+
+  # ----------------------------------------------------------
+  # 5.5 Read Uncorrelated Results
+  # ----------------------------------------------------------
+
+  df_uncorr <- read_and_tag(
+    path = path_uncorr,
+    structure_type = "Uncorrelated",
+    serial = serial,
+    suffix = suffix,
+    measure = measure,
+    dv_name = dv_name
+  )
+
+
+  # ----------------------------------------------------------
+  # 5.6 Store Results
+  # ----------------------------------------------------------
+  
+  master_df[[paste0(
+    dv_name,
+    "_Correlated"
+  )]] <- df_corr
+  
+  master_df[[paste0(
+    dv_name,
+    "_Uncorrelated"
+  )]] <- df_uncorr
+  
+  
+  message(
+    "Processed Stage ",
+    serial,
+    " — ",
+    suffix,
+    " — ",
+    dv_name
+  )
+}
+
+
+
+
+
+# ============================================================
+# CELL 6 — MERGE AND RECALCULATE COMBINED MODEL COMPARISONS
+# ============================================================
+# Purpose:
+#   Combine the Step 2 and Step 3 candidate rankings and
+#   calculate information-criterion differences across both
+#   participant-level random-slope parameterizations within
+#   each DV.
+#
+# Affective Provo candidate space:
+#
+#   Six possible participant-level random slopes:
+#
+#       Length
+#       Predictability
+#       Frequency
+#       Valence
+#       Arousal
+#       Dominance
+#
+# Correlated family:
+#
+#       2^6 = 64 candidate structures
+#
+#   This includes the random-intercept-only structure:
+#
+#       1
+#
+# Uncorrelated family:
+#
+#       2^6 - 1 = 63 candidate structures
+#
+#   The random-intercept-only structure is not duplicated in
+#   the uncorrelated family because, in the absence of random
+#   slopes, there are no intercept-slope or slope-slope
+#   correlation parameters to remove.
+#
+# Therefore, each DV contains:
+#
+#       64 correlated-family candidates
+#       63 uncorrelated-family candidates
+#      127 unique combined candidates
+#
+# Across four duration DVs:
+#
+#       4 × 127 = 508 combined candidate rows
+#
+# Important distinction:
+#
+#   delta_aic / delta_bic
+#       → source Step 2 / Step 3 within-family differences.
+#
+#   combined_delta_aic / combined_delta_bic
+#       → differences across the complete unique Step 4
+#         candidate set for the current DV.
+#
+#   eligible_delta_aic / eligible_delta_bic
+#       → differences relative to the best selection-eligible
+#         candidate for the current DV.
+#
+# Primary selection rule:
+#
+#   1. Candidate must satisfy:
+#
+#          converged = TRUE
+#          singular  = FALSE
+#
+#   2. Among eligible candidates, lower BIC is preferred.
+# ============================================================
+
+message(
+  "\nMerging candidate tables and recalculating combined deltas..."
+)
+
+
+# ------------------------------------------------------------
+# 6.1 Safety Check
+# ------------------------------------------------------------
+
+if (length(master_df) == 0) {
+  
+  stop(
+    "No Step 2 or Step 3 ranking results were loaded."
+  )
+}
+
+
+# ------------------------------------------------------------
+# 6.2 Combine All Candidate Tables
+# ------------------------------------------------------------
+
+final_df <- bind_rows(
+  master_df
+)
+
+
+# ------------------------------------------------------------
+# 6.3 Verify Both Structure Families Exist for Every DV
+# ------------------------------------------------------------
+
+structure_check <- final_df %>%
+  distinct(
+    `Dependent Variable Name`,
+    `Random-Slope Structure`
+  ) %>%
+  count(
+    `Dependent Variable Name`,
+    name = "N_Structure_Types"
+  )
+
+
+if (
+  any(
+    structure_check$N_Structure_Types != 2
+  )
+) {
+  
+  print(
+    structure_check
+  )
+  
+  stop(
+    "At least one DV does not contain both correlated and ",
+    "uncorrelated random-slope results. Step 4 requires both ",
+    "model families before combined comparison can proceed."
+  )
+}
+
+
+message(
+  "Structure-family validation passed: correlated and ",
+  "uncorrelated results are present for every DV."
+)
+
+
+# ------------------------------------------------------------
+# 6.3A Define Expected Affective Provo Candidate Structures
+# ------------------------------------------------------------
+
+AFFECTIVE_SLOPES <- c(
+  "Length",
+  "Predictability",
+  "Frequency",
+  "Valence",
+  "Arousal",
+  "Dominance"
+)
+
+
+generate_expected_candidates <- function(
+    slope_vars
+) {
+  
+  candidates <- "1"
+  
+  if (length(slope_vars) == 0) {
+    return(candidates)
+  }
+  
+  for (r in seq_along(slope_vars)) {
+    
+    combinations <- combn(
+      slope_vars,
+      r,
+      simplify = FALSE
+    )
+    
+    candidates <- c(
+      candidates,
+      vapply(
+        combinations,
+        function(x) {
+          paste(
+            "1 +",
+            paste(
+              x,
+              collapse = " + "
+            )
+          )
+        },
+        character(1)
+      )
+    )
+  }
+  
+  unique(
+    candidates
+  )
+}
+
+
+EXPECTED_CORRELATED_STRUCTURES <- (
+  generate_expected_candidates(
+    AFFECTIVE_SLOPES
+  )
+)
+
+
+EXPECTED_UNCORRELATED_STRUCTURES <- setdiff(
+  EXPECTED_CORRELATED_STRUCTURES,
+  "1"
+)
+
+
+EXPECTED_CORRELATED_CANDIDATES <- length(
+  EXPECTED_CORRELATED_STRUCTURES
+)
+
+
+EXPECTED_UNCORRELATED_CANDIDATES <- length(
+  EXPECTED_UNCORRELATED_STRUCTURES
+)
+
+
+EXPECTED_CANDIDATES_PER_DV <- (
+  EXPECTED_CORRELATED_CANDIDATES +
+    EXPECTED_UNCORRELATED_CANDIDATES
+)
+
+
+EXPECTED_TOTAL_CANDIDATES <- (
+  length(DV_INFO) *
+    EXPECTED_CANDIDATES_PER_DV
+)
+
+
+# ------------------------------------------------------------
+# Validate Theoretical Candidate Counts
+# ------------------------------------------------------------
+
+if (EXPECTED_CORRELATED_CANDIDATES != 64) {
+  
+  stop(
+    "Internal candidate-generation error: expected 64 ",
+    "correlated Affective Provo structures but generated ",
+    EXPECTED_CORRELATED_CANDIDATES,
+    "."
+  )
+}
+
+
+if (EXPECTED_UNCORRELATED_CANDIDATES != 63) {
+  
+  stop(
+    "Internal candidate-generation error: expected 63 ",
+    "uncorrelated Affective Provo structures but generated ",
+    EXPECTED_UNCORRELATED_CANDIDATES,
+    "."
+  )
+}
+
+
+if (EXPECTED_CANDIDATES_PER_DV != 127) {
+  
+  stop(
+    "Internal candidate-generation error: expected 127 ",
+    "unique combined structures per DV but generated ",
+    EXPECTED_CANDIDATES_PER_DV,
+    "."
+  )
+}
+
+
+# ------------------------------------------------------------
+# 6.3B Verify Expected Candidate Counts
+# ------------------------------------------------------------
+
+candidate_count_check <- final_df %>%
+  count(
+    `Dependent Variable Name`,
+    `Random-Slope Structure`,
+    name = "N_Candidates"
+  )
+
+
+bad_correlated_counts <- candidate_count_check %>%
+  filter(
+    `Random-Slope Structure` == "Correlated",
+    N_Candidates !=
+      EXPECTED_CORRELATED_CANDIDATES
+  )
+
+
+bad_uncorrelated_counts <- candidate_count_check %>%
+  filter(
+    `Random-Slope Structure` == "Uncorrelated",
+    N_Candidates !=
+      EXPECTED_UNCORRELATED_CANDIDATES
+  )
+
+
+if (
+  nrow(bad_correlated_counts) > 0 ||
+  nrow(bad_uncorrelated_counts) > 0
+) {
+  
+  print(
+    candidate_count_check
+  )
+  
+  stop(
+    "Unexpected Step 2 / Step 3 candidate count detected. ",
+    "Each Affective Provo DV should contain exactly ",
+    EXPECTED_CORRELATED_CANDIDATES,
+    " correlated-family candidates and ",
+    EXPECTED_UNCORRELATED_CANDIDATES,
+    " uncorrelated-family candidates."
+  )
+}
+
+
+dv_candidate_count_check <- final_df %>%
+  count(
+    `Dependent Variable Name`,
+    name = "N_Combined_Candidates"
+  )
+
+
+if (
+  any(
+    dv_candidate_count_check$N_Combined_Candidates !=
+    EXPECTED_CANDIDATES_PER_DV
+  )
+) {
+  
+  print(
+    dv_candidate_count_check
+  )
+  
+  stop(
+    "Unexpected combined candidate count detected. ",
+    "Each Affective Provo DV should contain exactly ",
+    EXPECTED_CANDIDATES_PER_DV,
+    " unique correlated + uncorrelated candidate models."
+  )
+}
+
+
+if (nrow(final_df) != EXPECTED_TOTAL_CANDIDATES) {
+  
+  stop(
+    "Unexpected total number of Step 4 candidate rows. ",
+    "Expected ",
+    EXPECTED_TOTAL_CANDIDATES,
+    " rows across all DVs but found ",
+    nrow(final_df),
+    "."
+  )
+}
+
+
+message(
+  "Candidate-count validation passed: ",
+  EXPECTED_CORRELATED_CANDIDATES,
+  " correlated candidates + ",
+  EXPECTED_UNCORRELATED_CANDIDATES,
+  " uncorrelated candidates = ",
+  EXPECTED_CANDIDATES_PER_DV,
+  " unique candidates per DV."
+)
+
+
+# ------------------------------------------------------------
+# 6.3C Verify Exact Candidate Structures Within Each Family
+# ------------------------------------------------------------
+# Count validation alone cannot establish that the correct
+# candidate structures are present.
+#
+# Correlated family:
+#   Random-intercept-only structure plus all 63 structures
+#   containing at least one random slope.
+#
+# Uncorrelated family:
+#   The same 63 slope-containing structures, without a second
+#   copy of the random-intercept-only structure.
+# ------------------------------------------------------------
+
+candidate_structure_errors <- character(0)
+
+
+for (dv_name in names(DV_INFO)) {
+  
+  
+  # ----------------------------------------------------------
+  # Correlated Family
+  # ----------------------------------------------------------
+  
+  observed_correlated <- final_df %>%
+    filter(
+      `Dependent Variable Name` == dv_name,
+      `Random-Slope Structure` == "Correlated"
+    ) %>%
+    pull(candidate)
+  
+  
+  duplicate_correlated <- unique(
+    observed_correlated[
+      duplicated(
+        observed_correlated
+      )
+    ]
+  )
+  
+  
+  missing_correlated <- setdiff(
+    EXPECTED_CORRELATED_STRUCTURES,
+    observed_correlated
+  )
+  
+  
+  unexpected_correlated <- setdiff(
+    observed_correlated,
+    EXPECTED_CORRELATED_STRUCTURES
+  )
+  
+  
+  if (
+    length(duplicate_correlated) > 0 ||
+    length(missing_correlated) > 0 ||
+    length(unexpected_correlated) > 0
+  ) {
+    
+    candidate_structure_errors <- c(
+      candidate_structure_errors,
+      paste0(
+        dv_name,
+        " / Correlated: ",
+        "duplicates=[",
+        paste(
+          duplicate_correlated,
+          collapse = ", "
+        ),
+        "]; missing=[",
+        paste(
+          missing_correlated,
+          collapse = ", "
+        ),
+        "]; unexpected=[",
+        paste(
+          unexpected_correlated,
+          collapse = ", "
+        ),
+        "]"
+      )
+    )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # Uncorrelated Family
+  # ----------------------------------------------------------
+  
+  observed_uncorrelated <- final_df %>%
+    filter(
+      `Dependent Variable Name` == dv_name,
+      `Random-Slope Structure` == "Uncorrelated"
+    ) %>%
+    pull(candidate)
+  
+  
+  duplicate_uncorrelated <- unique(
+    observed_uncorrelated[
+      duplicated(
+        observed_uncorrelated
+      )
+    ]
+  )
+  
+  
+  missing_uncorrelated <- setdiff(
+    EXPECTED_UNCORRELATED_STRUCTURES,
+    observed_uncorrelated
+  )
+  
+  
+  unexpected_uncorrelated <- setdiff(
+    observed_uncorrelated,
+    EXPECTED_UNCORRELATED_STRUCTURES
+  )
+  
+  
+  if (
+    length(duplicate_uncorrelated) > 0 ||
+    length(missing_uncorrelated) > 0 ||
+    length(unexpected_uncorrelated) > 0
+  ) {
+    
+    candidate_structure_errors <- c(
+      candidate_structure_errors,
+      paste0(
+        dv_name,
+        " / Uncorrelated: ",
+        "duplicates=[",
+        paste(
+          duplicate_uncorrelated,
+          collapse = ", "
+        ),
+        "]; missing=[",
+        paste(
+          missing_uncorrelated,
+          collapse = ", "
+        ),
+        "]; unexpected=[",
+        paste(
+          unexpected_uncorrelated,
+          collapse = ", "
+        ),
+        "]"
+      )
+    )
+  }
+}
+
+
+if (length(candidate_structure_errors) > 0) {
+  
+  stop(
+    "Candidate-structure validation failed:\n",
+    paste(
+      candidate_structure_errors,
+      collapse = "\n"
+    )
+  )
+}
+
+
+message(
+  "Candidate-structure validation passed: each DV contains ",
+  "the expected 64 correlated-family structures and 63 ",
+  "uncorrelated-family structures."
+)
+
+
+# ------------------------------------------------------------
+# 6.3D Verify Relationship Between Structure Families
+# ------------------------------------------------------------
+# Every slope-containing correlated candidate must have a
+# corresponding uncorrelated candidate.
+#
+# The only candidate permitted to occur exclusively in the
+# correlated family is:
+#
+#       1
+#
+# because the random-intercept-only model has no random-effect
+# correlation parameters to remove.
+# ------------------------------------------------------------
+
+for (dv_name in names(DV_INFO)) {
+  
+  corr_candidates <- final_df %>%
+    filter(
+      `Dependent Variable Name` == dv_name,
+      `Random-Slope Structure` == "Correlated"
+    ) %>%
+    pull(candidate)
+  
+  
+  uncorr_candidates <- final_df %>%
+    filter(
+      `Dependent Variable Name` == dv_name,
+      `Random-Slope Structure` == "Uncorrelated"
+    ) %>%
+    pull(candidate)
+  
+  
+  correlated_slope_candidates <- setdiff(
+    corr_candidates,
+    "1"
+  )
+  
+  
+  if (
+    !setequal(
+      correlated_slope_candidates,
+      uncorr_candidates
+    )
+  ) {
+    
+    missing_from_uncorrelated <- setdiff(
+      correlated_slope_candidates,
+      uncorr_candidates
+    )
+    
+    unexpected_in_uncorrelated <- setdiff(
+      uncorr_candidates,
+      correlated_slope_candidates
+    )
+    
+    stop(
+      "Correlated/uncorrelated candidate-family mismatch for ",
+      dv_name,
+      ".\n",
+      "Missing from uncorrelated: ",
+      paste(
+        missing_from_uncorrelated,
+        collapse = " | "
+      ),
+      "\n",
+      "Unexpected in uncorrelated: ",
+      paste(
+        unexpected_in_uncorrelated,
+        collapse = " | "
+      )
+    )
+  }
+  
+  
+  if (!"1" %in% corr_candidates) {
+    
+    stop(
+      "The correlated family is missing the shared ",
+      "random-intercept-only candidate for ",
+      dv_name,
+      "."
+    )
+  }
+  
+  
+  if ("1" %in% uncorr_candidates) {
+    
+    stop(
+      "The uncorrelated family unexpectedly contains a ",
+      "duplicate random-intercept-only candidate for ",
+      dv_name,
+      "."
+    )
+  }
+}
+
+
+message(
+  "Cross-family candidate validation passed: all 63 ",
+  "slope-containing structures occur under both ",
+  "parameterizations, while the random-intercept-only ",
+  "candidate is represented once."
+)
+
+
+# ------------------------------------------------------------
+# 6.4 Verify Observation Counts Across Combined Candidates
+# ------------------------------------------------------------
+# Step 2 and Step 3 must use exactly the same DV-specific
+# analysis sample for direct information-criterion comparison.
+# ------------------------------------------------------------
+
+final_df <- final_df %>%
+  mutate(
+    nobs = suppressWarnings(
+      as.numeric(nobs)
+    )
+  )
+
+
+if (any(!is.finite(final_df$nobs))) {
+  
+  stop(
+    "Missing, invalid, or non-finite nobs values detected in ",
+    "the combined Step 2 / Step 3 results."
+  )
+}
+
+
+nobs_check <- final_df %>%
+  group_by(
+    `Dependent Variable Name`
+  ) %>%
+  summarise(
+    N_Distinct_Nobs =
+      n_distinct(nobs),
+    
+    Min_Nobs =
+      min(nobs),
+    
+    Max_Nobs =
+      max(nobs),
+    
+    .groups = "drop"
+  )
+
+
+if (
+  any(
+    nobs_check$N_Distinct_Nobs != 1
+  )
+) {
+  
+  print(
+    nobs_check
+  )
+  
+  stop(
+    "Step 2 and Step 3 candidates do not use identical ",
+    "observation counts for at least one DV. Combined ",
+    "AIC/BIC comparison should not proceed."
+  )
+}
+
+
+message(
+  "Observation-count validation passed: all Step 2 / Step 3 ",
+  "candidates use identical nobs within each DV."
+)
+
+
+# ------------------------------------------------------------
+# 6.5 Calculate Combined AIC/BIC Differences
+# ------------------------------------------------------------
+
+final_df <- final_df %>%
+  group_by(
+    `Dependent Variable Name`
+  ) %>%
+  mutate(
+    
+    combined_min_aic =
+      min(
+        aic,
+        na.rm = TRUE
+      ),
+    
+    combined_min_bic =
+      min(
+        bic,
+        na.rm = TRUE
+      ),
+    
+    combined_delta_aic =
+      aic -
+      combined_min_aic,
+    
+    combined_delta_bic =
+      bic -
+      combined_min_bic,
+    
+    eligible_min_aic =
+      if (
+        any(
+          selection_eligible %in% TRUE
+        )
+      ) {
+        
+        min(
+          aic[
+            selection_eligible %in% TRUE
+          ],
+          na.rm = TRUE
+        )
+        
+      } else {
+        
+        NA_real_
+      },
+    
+    eligible_min_bic =
+      if (
+        any(
+          selection_eligible %in% TRUE
+        )
+      ) {
+        
+        min(
+          bic[
+            selection_eligible %in% TRUE
+          ],
+          na.rm = TRUE
+        )
+        
+      } else {
+        
+        NA_real_
+      },
+    
+    eligible_delta_aic =
+      ifelse(
+        selection_eligible %in% TRUE,
+        aic - eligible_min_aic,
+        NA_real_
+      ),
+    
+    eligible_delta_bic =
+      ifelse(
+        selection_eligible %in% TRUE,
+        bic - eligible_min_bic,
+        NA_real_
+      )
+    
+  ) %>%
+  ungroup() %>%
+  select(
+    -combined_min_aic,
+    -combined_min_bic,
+    -eligible_min_aic,
+    -eligible_min_bic
+  )
+
+
+
+
+# ============================================================
+# CELL 7 — ORDER, RANK, AND REORGANIZE MERGED RESULTS
+# ============================================================
+# Purpose:
+#   Order the combined candidate set according to the Step 4
+#   model-selection rule, assign within-DV ordering variables,
+#   and place the primary comparison metadata and diagnostics
+#   at the front of the merged table.
+#
+# Ordering:
+#   1. Stage of Reading
+#   2. selection_eligible = TRUE before FALSE
+#   3. BIC ascending
+#
+# Ranking:
+#
+#   Step 4 Overall Order
+#       → position of every candidate within its DV after
+#         applying the Step 4 ordering rule
+#
+#   Step 4 Eligible Rank
+#       → BIC rank among selection-eligible candidates only;
+#         ineligible candidates receive NA
+#
+# The complete original Step 2 / Step 3 ranking information is
+# retained after the primary Step 4 comparison columns.
+# ============================================================
+
+
+# ------------------------------------------------------------
+# 7.1 Sort Final Candidate Table
+# ------------------------------------------------------------
+
+final_df <- final_df %>%
+  arrange(
+    `Stage of Reading`,
+    desc(
+      selection_eligible
+    ),
+    bic
+  )
+
+
+# ------------------------------------------------------------
+# 7.2 Add Within-DV Step 4 Ordering and Eligible Rank
+# ------------------------------------------------------------
+# Because candidates have already been ordered by:
+#
+#   1. selection eligibility
+#   2. BIC
+#
+# row_number() gives the overall Step 4 position within each
+# DV, while cumsum(selection_eligible) gives the BIC ordering
+# among eligible candidates.
+# ------------------------------------------------------------
+
+final_df <- final_df %>%
+  group_by(
+    `Dependent Variable Name`
+  ) %>%
+  mutate(
+    
+    `Step 4 Overall Order` =
+      row_number(),
+    
+    `Step 4 Eligible Rank` =
+      ifelse(
+        selection_eligible %in% TRUE,
+        cumsum(
+          selection_eligible %in% TRUE
+        ),
+        NA_integer_
+      )
+    
+  ) %>%
+  ungroup()
+
+
+# ------------------------------------------------------------
+# 7.3 Reorder Columns
+# ------------------------------------------------------------
+
+priority_cols <- c(
+  "Stage of Reading",
+  "Reading Measure",
+  "Measure Abbreviation",
+  "Dependent Variable Name",
+  "Random-Slope Structure",
+  "Source Step",
+  "selection_eligible",
+  "Step 4 Overall Order",
+  "Step 4 Eligible Rank",
+  "eligible_delta_bic",
+  "bic",
+  "eligible_delta_aic",
+  "aic",
+  "combined_delta_bic",
+  "combined_delta_aic",
+  "candidate",
+  "re_formula",
+  "converged",
+  "singular",
+  "optimizer",
+  "selected_via",
+  "nobs",
+  "llf",
+  "status",
+  "warnings",
+  "Source Workbook"
+)
+
+
+priority_cols <- priority_cols[
+  priority_cols %in% names(final_df)
+]
+
+
+final_df <- final_df %>%
+  select(
+    all_of(priority_cols),
+    everything()
+  )
+
+
+
+
+
+# ============================================================
+# CELL 8 — STEP 4 BEST-MODEL SUMMARY
+# ============================================================
+# Purpose:
+#   Create a compact summary containing the preferred
+#   selection-eligible candidate for each duration DV after
+#   correlated and uncorrelated random-slope structures have
+#   been combined.
+#
+# Selection rule:
+#
+#   1. Candidate must be selection eligible:
+#
+#          converged = TRUE
+#          singular  = FALSE
+#
+#   2. Among eligible candidates, select minimum BIC.
+#
+# Because Step 4 Eligible Rank was calculated after applying
+# this same ordering rule, the selected candidate should have:
+#
+#       Step 4 Eligible Rank = 1
+#
+# for each DV having at least one eligible candidate.
+#
+# This summary does not replace the complete candidate table.
+# It provides the final preferred random-slope structure for
+# each reading measure under the prespecified Step 4 rule.
+# ============================================================
+
+best_model_summary <- final_df %>%
+  filter(
+    selection_eligible %in% TRUE,
+    `Step 4 Eligible Rank` == 1
+  ) %>%
+  arrange(
+    `Stage of Reading`
+  )
+
+
+# ------------------------------------------------------------
+# Verify One Preferred Model per DV
+# ------------------------------------------------------------
+
+summary_dv_check <- best_model_summary %>%
+  count(
+    `Dependent Variable Name`,
+    name = "N_Selected"
+  )
+
+
+# ------------------------------------------------------------
+# Detect Multiple Preferred Models Within a DV
+# ------------------------------------------------------------
+
+if (
+  nrow(summary_dv_check) > 0 &&
+  any(
+    summary_dv_check$N_Selected != 1
+  )
+) {
+  
+  print(
+    summary_dv_check
+  )
+  
+  stop(
+    "The Step 4 best-model summary contains multiple selected ",
+    "models for at least one DV."
+  )
+}
+
+
+# ------------------------------------------------------------
+# Detect DVs Without an Eligible Preferred Model
+# ------------------------------------------------------------
+
+selected_dvs <- unique(
+  best_model_summary$`Dependent Variable Name`
+)
+
+missing_selected_dvs <- setdiff(
+  names(DV_INFO),
+  selected_dvs
+)
+
+
+if (length(missing_selected_dvs) > 0) {
+  
+  warning(
+    "No selection-eligible Step 4 candidate was identified for: ",
+    paste(
+      missing_selected_dvs,
+      collapse = ", "
+    )
+  )
+}
+
+
+# ------------------------------------------------------------
+# Confirm Complete Best-Model Summary When Available
+# ------------------------------------------------------------
+
+if (length(missing_selected_dvs) == 0) {
+  
+  message(
+    "Best-model validation passed: exactly one preferred ",
+    "selection-eligible candidate was identified for every DV."
+  )
+}
+
+
+
+
+
+# ============================================================
+# CELL 9 — FORMAT AND SAVE STEP 4 WORKBOOK
+# ============================================================
+# Purpose:
+#   Export:
+#
+#       Merged_Results
+#           → complete combined candidate table
+#
+#       Best_Model_Summary
+#           → best selection-eligible BIC candidate per DV
+#
+#       Structure_Check
+#           → confirms presence of both correlated and
+#             uncorrelated model families for every DV
+#
+# Formatting:
+#   - Header styling
+#   - Stage-specific row shading
+#   - Borders
+#   - Automatic column widths
+#   - Frozen header rows
+#   - Excel filters
+# ============================================================
+
+wb <- createWorkbook()
+
+
+# ------------------------------------------------------------
+# 9.1 Add Worksheets
+# ------------------------------------------------------------
+
+addWorksheet(
+  wb,
+  "Merged_Results"
+)
+
+addWorksheet(
+  wb,
+  "Best_Model_Summary"
+)
+
+addWorksheet(
+  wb,
+  "Structure_Check"
+)
+
+
+# ------------------------------------------------------------
+# 9.2 Write Data
+# ------------------------------------------------------------
+
+writeData(
+  wb,
+  "Merged_Results",
+  final_df,
+  withFilter = TRUE
+)
+
+writeData(
+  wb,
+  "Best_Model_Summary",
+  best_model_summary,
+  withFilter = TRUE
+)
+
+writeData(
+  wb,
+  "Structure_Check",
+  structure_check,
+  withFilter = TRUE
+)
+
+
+
+
+
+# ============================================================
+# CELL 10 — EXCEL STYLING
+# ============================================================
+
+
+# ------------------------------------------------------------
+# 10.1 Define Styles
+# ------------------------------------------------------------
+
+style_header <- createStyle(
+  textDecoration = "bold",
+  halign = "center",
+  valign = "center",
+  border = "TopBottomLeftRight",
+  borderStyle = "thin"
+)
+
+
+style_border <- createStyle(
+  border = "TopBottomLeftRight",
+  borderStyle = "thin"
+)
+
+
+style_stage1 <- createStyle(
+  fgFill = "#E0F7FA"
+)
+
+style_stage2 <- createStyle(
+  fgFill = "#E8F5E9"
+)
+
+style_stage3 <- createStyle(
+  fgFill = "#FFF3E0"
+)
+
+style_stage4 <- createStyle(
+  fgFill = "#F3E5F5"
+)
+
+
+# ------------------------------------------------------------
+# 10.2 Apply Header Style
+# ------------------------------------------------------------
+
+addStyle(
+  wb,
+  "Merged_Results",
+  style_header,
+  rows = 1,
+  cols = seq_len(
+    ncol(final_df)
+  ),
+  gridExpand = TRUE,
+  stack = TRUE
+)
+
+
+if (ncol(best_model_summary) > 0) {
+
+  addStyle(
+    wb,
+    "Best_Model_Summary",
+    style_header,
+    rows = 1,
+    cols = seq_len(
+      ncol(best_model_summary)
+    ),
+    gridExpand = TRUE,
+    stack = TRUE
+  )
+}
+
+
+addStyle(
+  wb,
+  "Structure_Check",
+  style_header,
+  rows = 1,
+  cols = seq_len(
+    ncol(structure_check)
+  ),
+  gridExpand = TRUE,
+  stack = TRUE
+)
+
+
+
+
+
+# ============================================================
+# CELL 11 — STAGE-SPECIFIC ROW FORMATTING
+# ============================================================
+
+message(
+  "Applying stage-specific formatting..."
+)
+
+
+rows_s1 <- which(
+  final_df$`Stage of Reading` == 1
+) + 1
+
+rows_s2 <- which(
+  final_df$`Stage of Reading` == 2
+) + 1
+
+rows_s3 <- which(
+  final_df$`Stage of Reading` == 3
+) + 1
+
+rows_s4 <- which(
+  final_df$`Stage of Reading` == 4
+) + 1
+
+
+if (length(rows_s1) > 0) {
+
+  addStyle(
+    wb,
+    "Merged_Results",
+    style_stage1,
+    rows = rows_s1,
+    cols = seq_len(
+      ncol(final_df)
+    ),
+    gridExpand = TRUE,
+    stack = TRUE
+  )
+}
+
+
+if (length(rows_s2) > 0) {
+
+  addStyle(
+    wb,
+    "Merged_Results",
+    style_stage2,
+    rows = rows_s2,
+    cols = seq_len(
+      ncol(final_df)
+    ),
+    gridExpand = TRUE,
+    stack = TRUE
+  )
+}
+
+
+if (length(rows_s3) > 0) {
+
+  addStyle(
+    wb,
+    "Merged_Results",
+    style_stage3,
+    rows = rows_s3,
+    cols = seq_len(
+      ncol(final_df)
+    ),
+    gridExpand = TRUE,
+    stack = TRUE
+  )
+}
+
+
+if (length(rows_s4) > 0) {
+
+  addStyle(
+    wb,
+    "Merged_Results",
+    style_stage4,
+    rows = rows_s4,
+    cols = seq_len(
+      ncol(final_df)
+    ),
+    gridExpand = TRUE,
+    stack = TRUE
+  )
+}
+
+
+
+
+
+# ============================================================
+# CELL 12 — BORDERS, WIDTHS, AND FREEZE PANES
+# ============================================================
+
+
+# ------------------------------------------------------------
+# 12.1 Borders — Merged Results
+# ------------------------------------------------------------
+
+addStyle(
+  wb,
+  "Merged_Results",
+  style_border,
+  rows = seq_len(
+    nrow(final_df) + 1
+  ),
+  cols = seq_len(
+    ncol(final_df)
+  ),
+  gridExpand = TRUE,
+  stack = TRUE
+)
+
+
+# ------------------------------------------------------------
+# 12.2 Borders — Best Model Summary
+# ------------------------------------------------------------
+
+if (
+  nrow(best_model_summary) > 0 &&
+  ncol(best_model_summary) > 0
+) {
+
+  addStyle(
+    wb,
+    "Best_Model_Summary",
+    style_border,
+    rows = seq_len(
+      nrow(best_model_summary) + 1
+    ),
+    cols = seq_len(
+      ncol(best_model_summary)
+    ),
+    gridExpand = TRUE,
+    stack = TRUE
+  )
+}
+
+
+# ------------------------------------------------------------
+# 12.3 Borders — Structure Check
+# ------------------------------------------------------------
+
+addStyle(
+  wb,
+  "Structure_Check",
+  style_border,
+  rows = seq_len(
+    nrow(structure_check) + 1
+  ),
+  cols = seq_len(
+    ncol(structure_check)
+  ),
+  gridExpand = TRUE,
+  stack = TRUE
+)
+
+
+# ------------------------------------------------------------
+# 12.4 Automatic Column Widths
+# ------------------------------------------------------------
+
+setColWidths(
+  wb,
+  "Merged_Results",
+  cols = seq_len(
+    ncol(final_df)
+  ),
+  widths = "auto"
+)
+
+
+if (ncol(best_model_summary) > 0) {
+
+  setColWidths(
+    wb,
+    "Best_Model_Summary",
+    cols = seq_len(
+      ncol(best_model_summary)
+    ),
+    widths = "auto"
+  )
+}
+
+
+setColWidths(
+  wb,
+  "Structure_Check",
+  cols = seq_len(
+    ncol(structure_check)
+  ),
+  widths = "auto"
+)
+
+
+# ------------------------------------------------------------
+# 12.5 Freeze Header Rows
+# ------------------------------------------------------------
+
+freezePane(
+  wb,
+  "Merged_Results",
+  firstRow = TRUE
+)
+
+freezePane(
+  wb,
+  "Best_Model_Summary",
+  firstRow = TRUE
+)
+
+freezePane(
+  wb,
+  "Structure_Check",
+  firstRow = TRUE
+)
+
+
+
+
+
+# ============================================================
+# CELL 13 — SAVE STEP 4 WORKBOOK
+# ============================================================
+
+saveWorkbook(
+  wb,
+  MERGED_OUTPUT_PATH,
+  overwrite = TRUE
+)
+
+
+message(
+  "\n",
+  strrep("=", 80)
+)
+
+message(
+  "STEP 4 COMPLETED SUCCESSFULLY"
+)
+
+message(
+  "Dataset: Affective Provo"
+)
+
+message(
+  "Merged candidate models: ",
+  format(
+    nrow(final_df),
+    big.mark = ","
+  )
+)
+
+message(
+  "Duration DVs: ",
+  length(DV_INFO)
+)
+
+message(
+  "Output: ",
+  MERGED_OUTPUT_PATH
+)
+
+message(
+  strrep("=", 80)
+)

05-Research_Program-Affective_Provo/01-Fixation_Duration_Research/01-LME_Model_Structure/01-Scripts/Step-5-Filtering_the_Best_Random_Slope.R

@@ -0,0 +1,2981 @@
+# ============================================================
+# COPYRIGHT, LICENSING, AND SCHOLARLY CITATION
+# ============================================================
+# Copyright (c) 2026 Mohit Gupta
+# License: MIT
+# SPDX-License-Identifier: MIT
+#
+# This script contains original computational software
+# developed by Mohit Gupta for the AffLex-Provo
+# Research Program.
+#
+# Citation:
+# Researchers using this software in published research
+# are strongly requested to cite the AffLex-Provo repository:
+# https://huggingface.co/datasets/mohitg2/AffLex-Provo
+#
+# Third-party datasets and externally sourced materials
+# remain subject to their respective original licenses.
+#
+# See the applicable repository LICENSE file for the
+# complete MIT License terms.
+# ============================================================
+
+# ============================================================
+# STEP 5 — FINAL RANDOM-SLOPE STRUCTURE DECISION (Affective Provo)
+# ============================================================
+#
+#
+# REQUIRED R VERSION: R version 4.5.2 (2025-10-31)
+#
+#
+# Purpose:
+#   Determine the final participant-level random-slope
+#   structure for each duration-based dependent variable after
+#   combining the Step 2 correlated and Step 3 uncorrelated
+#   candidate searches in Step 4.
+#
+# Dataset:
+#   Affective Provo
+#
+# Input:
+#   Step-4_Merged_Correlated-Uncorrelated_Slopes_Affective_Provo.xlsx
+#
+# Decision framework:
+#
+#   1. Retain only selection-eligible models:
+#
+#          converged = TRUE
+#          singular  = FALSE
+#
+#   2. Across the complete eligible Step 4 candidate set for
+#      each DV, identify the random-slope composition associated
+#      with the minimum BIC.
+#
+#   3. Once that slope composition has been selected, compare
+#      the correlated and uncorrelated parameterizations of
+#      that SAME random-slope composition.
+#
+#   4. If both parameterizations are available and the selected
+#      structure contains at least one random slope, calculate
+#      a likelihood-ratio statistic:
+#
+#          LR = 2 × (logLik_correlated - logLik_uncorrelated)
+#
+#      The degrees-of-freedom difference equals the number of
+#      covariance parameters present in the correlated model
+#      but absent from the uncorrelated model:
+#
+#          q(q - 1) / 2
+#
+#      where:
+#
+#          q = 1 + number of participant-level random slopes
+#
+#      The correlated parameterization is retained when:
+#
+#          p < .05
+#
+#      Otherwise, the uncorrelated parameterization is retained
+#      on grounds of parsimony.
+#
+#   5. If only one parameterization of the selected slope
+#      composition is selection eligible, retain the available
+#      eligible parameterization.
+#
+#   6. The random-intercept-only candidate:
+#
+#          1
+#
+#      is represented only once in Step 4 because correlated
+#      versus uncorrelated parameterization is not defined when
+#      there are no participant-level random slopes and hence
+#      no covariance parameters to estimate.
+#
+# Relationship to the original analysis:
+#
+#   This reproduces the decision hierarchy used in the original
+#   analysis:
+#
+#       minimum-BIC slope composition
+#           ↓
+#       matched correlated / uncorrelated comparison
+#           ↓
+#       LRT for covariance parameters
+#           ↓
+#       correlated if significant,
+#       uncorrelated if nonsignificant
+#
+#   The present implementation retains additional safeguards
+#   introduced in the revised pipeline, including explicit
+#   convergence, singularity, finite-statistic, and observation-
+#   count validation.
+#
+# Important:
+#   Step 5 does NOT refit models.
+#
+#   It operates on model statistics already generated in
+#   Steps 2 and 3 and consolidated in Step 4.
+#
+# Paper 1 candidate random slopes:
+#
+#       - Length
+#       - Predictability
+#       - Frequency
+#       - Valence
+#       - Arousal
+#       - Dominance
+#
+# Output:
+#   Step-5_Final_Random-Slope_Decisions_Affective_Provo.xlsx
+#
+# Sheets:
+#
+#   Final_Decisions
+#       → final selected structure for each DV
+#
+#   Selected_Structure_Comparison
+#       → correlated and uncorrelated parameterizations of the
+#         minimum-BIC selected slope composition
+#
+# Design principles:
+#   - convergence-aware
+#   - singularity-aware
+#   - minimum-BIC slope-composition selection
+#   - matched parameterization comparison
+#   - LRT-based covariance decision
+#   - identical decision principle across duration DVs
+#   - fully reproducible
+# ============================================================
+
+
+
+# ============================================================
+# CELL 1 — PACKAGE INSTALLATION AND INITIALIZATION
+# ============================================================
+
+REQUIRED_PACKAGES <- c(
+  "readxl",
+  "openxlsx",
+  "dplyr",
+  "stringr",
+  "here"
+)
+
+
+# ------------------------------------------------------------
+# 1.1 Identify Missing Packages
+# ------------------------------------------------------------
+
+MISSING_PACKAGES <- REQUIRED_PACKAGES[
+  !vapply(
+    REQUIRED_PACKAGES,
+    requireNamespace,
+    quietly = TRUE,
+    FUN.VALUE = logical(1)
+  )
+]
+
+
+# ------------------------------------------------------------
+# 1.2 Install Missing Packages
+# ------------------------------------------------------------
+
+if (length(MISSING_PACKAGES) > 0) {
+
+  message(
+    "Installing missing package(s): ",
+    paste(MISSING_PACKAGES, collapse = ", ")
+  )
+
+  install.packages(
+    MISSING_PACKAGES,
+    repos = "https://cloud.r-project.org",
+    dependencies = TRUE
+  )
+
+} else {
+
+  message(
+    "All required packages are already installed."
+  )
+}
+
+
+# ------------------------------------------------------------
+# 1.3 Load Required Packages
+# ------------------------------------------------------------
+
+suppressPackageStartupMessages({
+
+  library(readxl)
+  library(openxlsx)
+
+  library(dplyr)
+  library(stringr)
+
+  library(here)
+})
+
+
+message(
+  "Package initialization complete: ",
+  length(REQUIRED_PACKAGES),
+  " required packages available."
+)
+
+
+
+
+
+# ============================================================
+# CELL 2 — PROJECT PATHS
+# ============================================================
+# Purpose:
+#   Define the Step 4 input workbook and Step 5 output workbook.
+#
+# Directory:
+#
+#   05-Research_Program-Affective_Provo/
+#     01-Fixation_Duration_Research/
+#       01-LME_Model_Structure/
+#         02-Results/
+# ============================================================
+
+PROJECT_ROOT <- here()
+
+
+RESULTS_DIR <- here(
+  "05-Research_Program-Affective_Provo",
+  "01-Fixation_Duration_Research",
+  "01-LME_Model_Structure",
+  "02-Results"
+)
+
+
+INPUT_FILE <- file.path(
+  RESULTS_DIR,
+  "Step-4_Merged_Correlated-Uncorrelated_Slopes_Affective_Provo.xlsx"
+)
+
+
+OUTPUT_FILE <- file.path(
+  RESULTS_DIR,
+  "Step-5_Final_Random-Slope_Decisions_Affective_Provo.xlsx"
+)
+
+
+# ------------------------------------------------------------
+# 2.1 Validate Input
+# ------------------------------------------------------------
+
+if (!dir.exists(RESULTS_DIR)) {
+
+  stop(
+    "Results directory not found: ",
+    RESULTS_DIR
+  )
+}
+
+
+if (!file.exists(INPUT_FILE)) {
+
+  stop(
+    "Step 4 merged workbook not found: ",
+    INPUT_FILE
+  )
+}
+
+
+# ------------------------------------------------------------
+# 2.2 Report Resolved Paths
+# ------------------------------------------------------------
+
+message(
+  "PROJECT_ROOT: ",
+  PROJECT_ROOT
+)
+
+message(
+  "RESULTS_DIR: ",
+  RESULTS_DIR
+)
+
+message(
+  "INPUT_FILE: ",
+  INPUT_FILE
+)
+
+message(
+  "OUTPUT_FILE: ",
+  OUTPUT_FILE
+)
+
+
+
+
+
+# ============================================================
+# CELL 3 — LOAD AND VALIDATE STEP 4 RESULTS
+# ============================================================
+# Purpose:
+#   Load the complete merged candidate table produced by
+#   Step 4 and validate the columns required for the final
+#   model-selection procedure.
+#
+# Validation includes:
+#   - required columns
+#   - finite AIC/BIC/log-likelihood values
+#   - positive integer observation counts
+#   - valid logical diagnostic values
+#   - consistency of selection_eligible with convergence and
+#     singularity
+#   - valid random-slope structure labels
+#   - presence of both parameterizations for every DV
+# ============================================================
+
+
+# ------------------------------------------------------------
+# 3.1 Load Merged Candidate Table
+# ------------------------------------------------------------
+
+df_all <- read_excel(
+  INPUT_FILE,
+  sheet = "Merged_Results"
+)
+
+
+if (nrow(df_all) == 0) {
+  
+  stop(
+    "Step 4 Merged_Results sheet contains no candidate models."
+  )
+}
+
+
+message(
+  "Merged Step 4 candidate rows loaded: ",
+  format(
+    nrow(df_all),
+    big.mark = ","
+  )
+)
+
+
+# ------------------------------------------------------------
+# 3.2 Validate Required Columns
+# ------------------------------------------------------------
+
+REQUIRED_COLUMNS <- c(
+  "Stage of Reading",
+  "Reading Measure",
+  "Dependent Variable Name",
+  "Random-Slope Structure",
+  "selection_eligible",
+  "re_formula",
+  "aic",
+  "bic",
+  "llf",
+  "nobs",
+  "converged",
+  "singular"
+)
+
+
+missing_columns <- setdiff(
+  REQUIRED_COLUMNS,
+  names(df_all)
+)
+
+
+if (length(missing_columns) > 0) {
+  
+  stop(
+    "Step 4 workbook is missing required column(s): ",
+    paste(
+      missing_columns,
+      collapse = ", "
+    )
+  )
+}
+
+
+# ------------------------------------------------------------
+# 3.3 Normalize and Validate Required Numeric Columns
+# ------------------------------------------------------------
+
+df_all <- df_all %>%
+  mutate(
+    aic = suppressWarnings(
+      as.numeric(aic)
+    ),
+    bic = suppressWarnings(
+      as.numeric(bic)
+    ),
+    llf = suppressWarnings(
+      as.numeric(llf)
+    ),
+    nobs = suppressWarnings(
+      as.numeric(nobs)
+    )
+  )
+
+
+if (
+  any(!is.finite(df_all$aic)) ||
+  any(!is.finite(df_all$bic)) ||
+  any(!is.finite(df_all$llf))
+) {
+  
+  stop(
+    "Missing, invalid, or non-finite AIC/BIC/log-likelihood ",
+    "values detected in the Step 4 merged results."
+  )
+}
+
+
+if (
+  any(!is.finite(df_all$nobs)) ||
+  any(df_all$nobs <= 0) ||
+  any(df_all$nobs != floor(df_all$nobs))
+) {
+  
+  stop(
+    "Missing, invalid, non-positive, or non-integer nobs ",
+    "values detected in the Step 4 merged results."
+  )
+}
+
+
+df_all <- df_all %>%
+  mutate(
+    nobs = as.integer(nobs)
+  )
+
+
+# ------------------------------------------------------------
+# 3.4 Normalize Logical Columns
+# ------------------------------------------------------------
+
+to_logical_safe <- function(x) {
+  
+  if (is.logical(x)) {
+    return(x)
+  }
+  
+  x_chr <- toupper(
+    trimws(
+      as.character(x)
+    )
+  )
+  
+  case_when(
+    x_chr %in% c(
+      "TRUE",
+      "T",
+      "1"
+    ) ~ TRUE,
+    
+    x_chr %in% c(
+      "FALSE",
+      "F",
+      "0"
+    ) ~ FALSE,
+    
+    TRUE ~ NA
+  )
+}
+
+
+df_all <- df_all %>%
+  mutate(
+    selection_eligible =
+      to_logical_safe(
+        selection_eligible
+      ),
+    
+    converged =
+      to_logical_safe(
+        converged
+      ),
+    
+    singular =
+      to_logical_safe(
+        singular
+      )
+  )
+
+
+# ------------------------------------------------------------
+# 3.4A Validate Normalized Logical Columns
+# ------------------------------------------------------------
+
+if (anyNA(df_all$converged)) {
+  
+  stop(
+    "Missing or invalid logical value(s) detected in ",
+    "'converged' in the Step 4 merged results."
+  )
+}
+
+
+if (anyNA(df_all$singular)) {
+  
+  stop(
+    "Missing or invalid logical value(s) detected in ",
+    "'singular' in the Step 4 merged results."
+  )
+}
+
+
+if (anyNA(df_all$selection_eligible)) {
+  
+  stop(
+    "Missing or invalid logical value(s) detected in ",
+    "'selection_eligible' in the Step 4 merged results."
+  )
+}
+
+
+# ------------------------------------------------------------
+# 3.5 Verify Selection Eligibility
+# ------------------------------------------------------------
+
+expected_eligibility <- (
+  df_all$converged %in% TRUE &
+    df_all$singular %in% FALSE
+)
+
+
+eligibility_mismatch <- which(
+  df_all$selection_eligible !=
+    expected_eligibility
+)
+
+
+if (length(eligibility_mismatch) > 0) {
+  
+  stop(
+    "selection_eligible is inconsistent with converged / ",
+    "singular for ",
+    length(eligibility_mismatch),
+    " candidate(s) in the Step 4 merged results."
+  )
+}
+
+
+# ------------------------------------------------------------
+# 3.6 Validate Random-Slope Structure Labels
+# ------------------------------------------------------------
+
+valid_structure_labels <- c(
+  "Correlated",
+  "Uncorrelated"
+)
+
+
+unexpected_structure_labels <- setdiff(
+  unique(
+    df_all$`Random-Slope Structure`
+  ),
+  valid_structure_labels
+)
+
+
+if (length(unexpected_structure_labels) > 0) {
+  
+  stop(
+    "Unexpected Random-Slope Structure label(s): ",
+    paste(
+      unexpected_structure_labels,
+      collapse = ", "
+    )
+  )
+}
+
+
+# ------------------------------------------------------------
+# 3.7 Validate Random-Slope Formula Values
+# ------------------------------------------------------------
+
+if (
+  any(
+    is.na(
+      df_all$re_formula
+    )
+  ) ||
+  any(
+    !nzchar(
+      trimws(
+        as.character(
+          df_all$re_formula
+        )
+      )
+    )
+  )
+) {
+  
+  stop(
+    "Missing or empty re_formula value(s) detected in the ",
+    "Step 4 merged results."
+  )
+}
+
+
+# ------------------------------------------------------------
+# 3.8 Verify Parameterization Coverage Within Each DV
+# ------------------------------------------------------------
+
+parameterization_check <- df_all %>%
+  distinct(
+    `Dependent Variable Name`,
+    `Random-Slope Structure`
+  ) %>%
+  count(
+    `Dependent Variable Name`,
+    name = "N_Parameterizations"
+  )
+
+
+if (
+  any(
+    parameterization_check$N_Parameterizations != 2
+  )
+) {
+  
+  print(
+    parameterization_check
+  )
+  
+  stop(
+    "At least one DV does not contain both correlated and ",
+    "uncorrelated candidate models in the Step 4 results."
+  )
+}
+
+
+message(
+  "Parameterization validation passed: correlated and ",
+  "uncorrelated candidate families are present for every DV."
+)
+
+
+
+# ============================================================
+# CELL 4 — DEFINE ELIGIBLE FINAL-SELECTION CANDIDATES
+# ============================================================
+# Purpose:
+#   Restrict final model selection to numerically acceptable
+#   candidate models.
+#
+# Eligibility rule inherited from Steps 2–4:
+#
+#       converged = TRUE
+#       singular  = FALSE
+#
+# Step 4 already stores this rule in selection_eligible.
+#
+# The conditions are checked again here so Step 5 does not
+# depend blindly on a single imported flag.
+# ============================================================
+
+df_eligible <- df_all %>%
+  filter(
+    selection_eligible %in% TRUE,
+    converged %in% TRUE,
+    singular %in% FALSE,
+    is.finite(bic),
+    is.finite(aic),
+    is.finite(llf)
+  )
+
+
+message(
+  "Total merged candidates      : ",
+  format(
+    nrow(df_all),
+    big.mark = ","
+  )
+)
+
+
+message(
+  "Selection-eligible candidates: ",
+  format(
+    nrow(df_eligible),
+    big.mark = ","
+  )
+)
+
+
+if (nrow(df_eligible) == 0) {
+  
+  stop(
+    "No selection-eligible candidate models remain."
+  )
+}
+
+
+# ------------------------------------------------------------
+# Verify Every DV Has at Least One Eligible Candidate
+# ------------------------------------------------------------
+
+eligible_dv_check <- df_eligible %>%
+  distinct(
+    `Dependent Variable Name`
+  )
+
+
+missing_eligible_dvs <- setdiff(
+  unique(
+    df_all$`Dependent Variable Name`
+  ),
+  eligible_dv_check$`Dependent Variable Name`
+)
+
+
+if (length(missing_eligible_dvs) > 0) {
+  
+  stop(
+    "No selection-eligible candidate remains for: ",
+    paste(
+      missing_eligible_dvs,
+      collapse = ", "
+    )
+  )
+}
+
+
+message(
+  "Eligibility validation passed: every DV contains at least ",
+  "one converged, nonsingular candidate."
+)
+
+
+
+# ============================================================
+# CELL 5 — HELPER FUNCTIONS FOR FINAL DECISION
+# ============================================================
+# Purpose:
+#   Define helper functions required to reproduce the original
+#   Step 5 decision framework.
+#
+# The decision occurs in two stages:
+#
+#   Stage 1:
+#       Identify the random-slope composition associated with
+#       the minimum BIC among all eligible candidates.
+#
+#   Stage 2:
+#       Compare correlated and uncorrelated parameterizations
+#       of that SAME random-slope composition.
+#
+# Formula comparison ignores whitespace and ordering of slope
+# terms so logically equivalent candidate structures can be
+# matched safely.
+# ============================================================
+
+
+# ------------------------------------------------------------
+# 5.1 Normalize Random-Slope Formula
+# ------------------------------------------------------------
+
+normalize_re_formula <- function(x) {
+  
+  str_replace_all(
+    x,
+    "\\s+",
+    ""
+  )
+}
+
+
+# ------------------------------------------------------------
+# 5.2 Extract Random-Slope Terms
+# ------------------------------------------------------------
+
+extract_random_slopes <- function(
+    re_formula
+) {
+  
+  if (
+    length(re_formula) != 1 ||
+    is.na(re_formula)
+  ) {
+    
+    return(
+      character(0)
+    )
+  }
+  
+  
+  normalized <- normalize_re_formula(
+    re_formula
+  )
+  
+  
+  if (normalized == "1") {
+    
+    return(
+      character(0)
+    )
+  }
+  
+  
+  terms <- str_split(
+    normalized,
+    fixed("+"),
+    simplify = FALSE
+  )[[1]]
+  
+  
+  slopes <- terms[
+    terms != "1" &
+      nzchar(terms)
+  ]
+  
+  
+  sort(
+    unique(
+      slopes
+    )
+  )
+}
+
+
+# ------------------------------------------------------------
+# 5.3 Count Candidate Random Slopes
+# ------------------------------------------------------------
+
+count_random_slopes <- function(
+    re_formula
+) {
+  
+  as.integer(
+    length(
+      extract_random_slopes(
+        re_formula
+      )
+    )
+  )
+}
+
+
+# ------------------------------------------------------------
+# 5.4 Create Canonical Slope-Set Key
+# ------------------------------------------------------------
+# Purpose:
+#   Produce an ordering-independent identifier for each random-
+#   slope composition.
+#
+# Examples:
+#
+#       1
+#           → "1"
+#
+#       1 + Length + Valence + Arousal
+#       1 + Arousal + Length + Valence
+#
+#           → "Arousal|Length|Valence"
+# ------------------------------------------------------------
+
+canonical_slope_key <- function(
+    re_formula
+) {
+  
+  slopes <- extract_random_slopes(
+    re_formula
+  )
+  
+  
+  if (length(slopes) == 0) {
+    
+    return(
+      "1"
+    )
+  }
+  
+  
+  paste(
+    slopes,
+    collapse = "|"
+  )
+}
+
+
+# ------------------------------------------------------------
+# 5.5 Calculate Covariance-Parameter Difference
+# ------------------------------------------------------------
+# For a participant-level random-effects structure containing:
+#
+#       q = intercept + random slopes
+#
+# the correlated covariance matrix contains:
+#
+#       q(q + 1) / 2
+#
+# variance/covariance parameters.
+#
+# The corresponding uncorrelated model contains:
+#
+#       q
+#
+# variance parameters.
+#
+# Therefore the number of covariance parameters removed by the
+# uncorrelated parameterization is:
+#
+#       q(q - 1) / 2
+#
+# Examples:
+#
+#   1 slope:
+#       q = 2
+#       df = 1
+#
+#   2 slopes:
+#       q = 3
+#       df = 3
+#
+#   3 slopes:
+#       q = 4
+#       df = 6
+#
+#   6 slopes:
+#       q = 7
+#       df = 21
+# ------------------------------------------------------------
+
+covariance_df_difference <- function(
+    re_formula
+) {
+  
+  n_slopes <- count_random_slopes(
+    re_formula
+  )
+  
+  
+  q <- 1L + n_slopes
+  
+  
+  as.integer(
+    q * (q - 1L) / 2L
+  )
+}
+
+
+
+
+
+# ============================================================
+# CELL 6 — SELECT MINIMUM-BIC RANDOM-SLOPE COMPOSITION
+# ============================================================
+# Purpose:
+#   Reproduce the first stage of the original Step 5 decision
+#   procedure.
+#
+# For each DV:
+#
+#   1. Consider all selection-eligible Step 4 candidates across
+#      both correlated and uncorrelated parameterizations.
+#
+#   2. Identify the candidate having the minimum BIC.
+#
+#   3. Use the random-slope composition of that candidate as
+#      the selected slope structure.
+#
+#   4. Retrieve every eligible parameterization of that SAME
+#      slope composition.
+#
+# Thus BIC selects the slope composition before the covariance
+# parameterization is decided.
+#
+# This deliberately differs from selecting the best correlated
+# and best uncorrelated structures independently.
+# ============================================================
+
+
+# ------------------------------------------------------------
+# 6.1 Add Canonical Slope-Composition Keys
+# ------------------------------------------------------------
+
+df_eligible <- df_eligible %>%
+  mutate(
+    Slope_Set_Key = vapply(
+      re_formula,
+      canonical_slope_key,
+      character(1)
+    )
+  )
+
+
+# ------------------------------------------------------------
+# 6.2 Identify Global Minimum-BIC Candidate Within Each DV
+# ------------------------------------------------------------
+
+minimum_bic_candidates <- df_eligible %>%
+  group_by(
+    `Stage of Reading`,
+    `Reading Measure`,
+    `Dependent Variable Name`
+  ) %>%
+  filter(
+    bic == min(
+      bic,
+      na.rm = TRUE
+    )
+  ) %>%
+  ungroup()
+
+
+# ------------------------------------------------------------
+# 6.3 Detect Exact Global Minimum-BIC Ties
+# ------------------------------------------------------------
+# An exact tie between DIFFERENT slope compositions cannot be
+# resolved by the prespecified minimum-BIC rule and therefore
+# causes an explicit stop.
+#
+# Multiple minimum-BIC rows representing the SAME slope
+# composition under different parameterizations do not create
+# a slope-selection ambiguity.
+# ------------------------------------------------------------
+
+global_bic_tie_check <- minimum_bic_candidates %>%
+  group_by(
+    `Dependent Variable Name`
+  ) %>%
+  summarise(
+    N_Min_BIC_Rows = n(),
+    N_Min_BIC_Slope_Sets =
+      n_distinct(
+        Slope_Set_Key
+      ),
+    .groups = "drop"
+  )
+
+
+ambiguous_global_ties <- global_bic_tie_check %>%
+  filter(
+    N_Min_BIC_Slope_Sets > 1
+  )
+
+
+if (nrow(ambiguous_global_ties) > 0) {
+  
+  print(
+    ambiguous_global_ties
+  )
+  
+  
+  tied_models <- minimum_bic_candidates %>%
+    semi_join(
+      ambiguous_global_ties,
+      by = "Dependent Variable Name"
+    ) %>%
+    select(
+      `Stage of Reading`,
+      `Reading Measure`,
+      `Dependent Variable Name`,
+      `Random-Slope Structure`,
+      re_formula,
+      Slope_Set_Key,
+      aic,
+      bic,
+      llf,
+      nobs
+    )
+  
+  
+  print(
+    tied_models
+  )
+  
+  
+  stop(
+    "Exact minimum-BIC tie detected between different ",
+    "random-slope compositions for at least one DV. ",
+    "Step 5 stopped rather than resolving the slope-selection ",
+    "ambiguity by row order."
+  )
+}
+
+
+# ------------------------------------------------------------
+# 6.4 Define One Selected Slope Composition per DV
+# ------------------------------------------------------------
+
+selected_slope_structures <- minimum_bic_candidates %>%
+  group_by(
+    `Stage of Reading`,
+    `Reading Measure`,
+    `Dependent Variable Name`
+  ) %>%
+  slice(
+    1
+  ) %>%
+  ungroup() %>%
+  transmute(
+    `Stage of Reading`,
+    `Reading Measure`,
+    `Dependent Variable Name`,
+    
+    Selected_Random_Slope_Structure =
+      re_formula,
+    
+    Selected_Slope_Set_Key =
+      Slope_Set_Key,
+    
+    Selected_Structure_Minimum_BIC =
+      bic
+  )
+
+
+# ------------------------------------------------------------
+# 6.5 Verify One Selected Slope Composition per DV
+# ------------------------------------------------------------
+
+if (
+  nrow(selected_slope_structures) !=
+  n_distinct(
+    df_all$`Dependent Variable Name`
+  )
+) {
+  
+  stop(
+    "Step 5 did not identify exactly one minimum-BIC slope ",
+    "composition for every DV."
+  )
+}
+
+
+# ------------------------------------------------------------
+# 6.6 Retrieve Matched Parameterizations
+# ------------------------------------------------------------
+# Retrieve only models having the SAME slope composition as the
+# globally selected minimum-BIC structure.
+#
+# For slope-containing structures this can yield:
+#
+#       one correlated model
+#       one uncorrelated model
+#
+# provided both are selection eligible.
+#
+# For the intercept-only structure:
+#
+#       1
+#
+# only one row exists because Step 4 intentionally represents
+# that shared model once.
+# ------------------------------------------------------------
+
+selected_structure_comparison <- df_eligible %>%
+  inner_join(
+    selected_slope_structures %>%
+      select(
+        `Dependent Variable Name`,
+        Selected_Slope_Set_Key
+      ),
+    by = "Dependent Variable Name"
+  ) %>%
+  filter(
+    Slope_Set_Key ==
+      Selected_Slope_Set_Key
+  ) %>%
+  arrange(
+    `Stage of Reading`,
+    `Random-Slope Structure`
+  )
+
+
+# ------------------------------------------------------------
+# 6.7 Validate Matched Comparison Sets
+# ------------------------------------------------------------
+
+comparison_count_check <- selected_structure_comparison %>%
+  count(
+    `Dependent Variable Name`,
+    `Random-Slope Structure`,
+    name = "N_Models"
+  )
+
+
+if (
+  any(
+    comparison_count_check$N_Models > 1
+  )
+) {
+  
+  print(
+    comparison_count_check
+  )
+  
+  stop(
+    "Duplicate eligible models detected for the same DV, ",
+    "slope composition, and covariance parameterization."
+  )
+}
+
+
+# ------------------------------------------------------------
+# 6.8 Report Selected Slope Structures
+# ------------------------------------------------------------
+
+message(
+  "\nMinimum-BIC random-slope compositions:"
+)
+
+
+for (
+  i in seq_len(
+    nrow(
+      selected_slope_structures
+    )
+  )
+) {
+  
+  message(
+    "Stage ",
+    selected_slope_structures$
+      `Stage of Reading`[i],
+    " — ",
+    selected_slope_structures$
+      `Dependent Variable Name`[i],
+    " — ",
+    selected_slope_structures$
+      Selected_Random_Slope_Structure[i],
+    " | minimum BIC=",
+    round(
+      selected_slope_structures$
+        Selected_Structure_Minimum_BIC[i],
+      3
+    )
+  )
+}
+
+
+message(
+  "Minimum-BIC slope-composition selection completed."
+)
+
+
+
+
+
+# ============================================================
+# CELL 7 — MATCHED CORRELATED/UNCORRELATED DECISION ENGINE
+# ============================================================
+# Purpose:
+#   Determine the final participant-level random-effects
+#   parameterization after the minimum-BIC slope composition
+#   has been selected.
+#
+# Decision hierarchy:
+#
+#   CASE A — selected structure is random-intercept only
+#
+#       The structure:
+#
+#           1
+#
+#       contains no participant-level random slopes and hence
+#       no covariance parameters.
+#
+#       Correlated versus uncorrelated parameterization is
+#       therefore not applicable. Retain the shared
+#       random-intercept-only structure.
+#
+#   CASE B — both matched parameterizations are eligible
+#
+#       Compare correlated and uncorrelated versions of the
+#       SAME selected slope composition using:
+#
+#           LR = 2 × (logLik_corr - logLik_uncorr)
+#
+#       with:
+#
+#           df = q(q - 1) / 2
+#
+#       where q equals the participant intercept plus the
+#       selected random slopes.
+#
+#       Decision:
+#
+#           p < .05  → Correlated
+#           p >= .05 → Uncorrelated
+#
+#   CASE C — only one matched parameterization is eligible
+#
+#       Retain the available eligible parameterization.
+#
+# Important:
+#   The LRT is performed only after slope composition has been
+#   fixed. Thus the two compared models contain exactly the same
+#   random-effects variables and differ only in whether their
+#   participant-level covariance parameters are estimated.
+# ============================================================
+
+
+results_summary <- list()
+
+
+dv_registry <- df_all %>%
+  distinct(
+    `Stage of Reading`,
+    `Reading Measure`,
+    `Dependent Variable Name`
+  ) %>%
+  arrange(
+    `Stage of Reading`
+  )
+
+
+message(
+  "\n",
+  strrep("=", 80)
+)
+
+
+message(
+  "STARTING STEP 5 — FINAL RANDOM-SLOPE DECISIONS"
+)
+
+
+message(
+  "Dataset: Affective Provo"
+)
+
+
+message(
+  "Stage 1: minimum-BIC eligible slope composition"
+)
+
+
+message(
+  "Stage 2: matched correlated/uncorrelated LRT"
+)
+
+
+message(
+  strrep("=", 80)
+)
+
+
+for (i in seq_len(nrow(dv_registry))) {
+  
+  
+  # ----------------------------------------------------------
+  # 7.1 Current DV Metadata
+  # ----------------------------------------------------------
+  
+  stage <- dv_registry$
+    `Stage of Reading`[i]
+  
+  measure <- dv_registry$
+    `Reading Measure`[i]
+  
+  dv <- dv_registry$
+    `Dependent Variable Name`[i]
+  
+  
+  message(
+    "\n",
+    strrep("-", 72)
+  )
+  
+  
+  message(
+    "Stage ",
+    stage,
+    " — ",
+    measure,
+    " — ",
+    dv
+  )
+  
+  
+  # ----------------------------------------------------------
+  # 7.2 Retrieve Selected Slope Composition
+  # ----------------------------------------------------------
+  
+  selected_row <- selected_slope_structures %>%
+    filter(
+      `Dependent Variable Name` == dv
+    )
+  
+  
+  if (nrow(selected_row) != 1) {
+    
+    stop(
+      "Expected exactly one selected minimum-BIC slope ",
+      "composition for ",
+      dv,
+      ", but found ",
+      nrow(selected_row),
+      "."
+    )
+  }
+  
+  
+  selected_formula <-
+    selected_row$
+    Selected_Random_Slope_Structure[1]
+  
+  
+  selected_key <-
+    selected_row$
+    Selected_Slope_Set_Key[1]
+  
+  
+  selected_min_bic <-
+    selected_row$
+    Selected_Structure_Minimum_BIC[1]
+  
+  
+  n_random_slopes <-
+    count_random_slopes(
+      selected_formula
+    )
+  
+  
+  # ----------------------------------------------------------
+  # 7.3 Retrieve Matched Parameterizations
+  # ----------------------------------------------------------
+  
+  comparison_set <- selected_structure_comparison %>%
+    filter(
+      `Dependent Variable Name` == dv,
+      Slope_Set_Key == selected_key
+    )
+  
+  
+  row_corr <- comparison_set %>%
+    filter(
+      `Random-Slope Structure` ==
+        "Correlated"
+    )
+  
+  
+  row_uncorr <- comparison_set %>%
+    filter(
+      `Random-Slope Structure` ==
+        "Uncorrelated"
+    )
+  
+  
+  corr_ok <- (
+    nrow(row_corr) == 1
+  )
+  
+  
+  uncorr_ok <- (
+    nrow(row_uncorr) == 1
+  )
+  
+  
+  # ----------------------------------------------------------
+  # 7.4 Initialize Decision Variables
+  # ----------------------------------------------------------
+  
+  winner_type <- "None"
+  
+  winner_formula <- selected_formula
+  
+  winner_bic <- NA_real_
+  
+  winner_aic <- NA_real_
+  
+  winner_llf <- NA_real_
+  
+  winner_nobs <- NA_integer_
+  
+  decision_method <- NA_character_
+  
+  decision_reason <- NA_character_
+  
+  lrt_statistic <- NA_real_
+  
+  lrt_df <- NA_integer_
+  
+  lrt_p_value <- NA_real_
+  
+  
+  # ----------------------------------------------------------
+  # 7.5 CASE A — Random-Intercept-Only Structure
+  # ----------------------------------------------------------
+  
+  if (n_random_slopes == 0L) {
+    
+    
+    if (!corr_ok) {
+      
+      stop(
+        "The selected random-intercept-only candidate is ",
+        "missing from the correlated/shared Step 4 family for ",
+        dv,
+        "."
+      )
+    }
+    
+    
+    if (uncorr_ok) {
+      
+      stop(
+        "The random-intercept-only candidate unexpectedly ",
+        "appears in the uncorrelated family for ",
+        dv,
+        ". Step 4 should represent this shared structure once."
+      )
+    }
+    
+    
+    winner_type <-
+      "Random Intercept Only"
+    
+    
+    winner_formula <-
+      row_corr$re_formula[1]
+    
+    
+    winner_bic <-
+      row_corr$bic[1]
+    
+    
+    winner_aic <-
+      row_corr$aic[1]
+    
+    
+    winner_llf <-
+      row_corr$llf[1]
+    
+    
+    winner_nobs <-
+      row_corr$nobs[1]
+    
+    
+    lrt_df <- 0L
+    
+    
+    decision_method <-
+      "Minimum BIC; covariance comparison not applicable"
+    
+    
+    decision_reason <- paste(
+      "The minimum-BIC eligible candidate was the",
+      "random-intercept-only structure. Because it contains",
+      "no participant-level random slopes, there are no",
+      "random-effect covariance parameters to test and",
+      "correlated versus uncorrelated parameterization is",
+      "not applicable."
+    )
+    
+    
+    # ----------------------------------------------------------
+    # 7.6 CASE B — Both Matched Parameterizations Available
+    # ----------------------------------------------------------
+    
+  } else if (
+    corr_ok &&
+    uncorr_ok
+  ) {
+    
+    
+    # --------------------------------------------------------
+    # Verify Equal Observation Counts
+    # --------------------------------------------------------
+    
+    if (
+      row_corr$nobs[1] !=
+      row_uncorr$nobs[1]
+    ) {
+      
+      stop(
+        "Cannot perform matched correlated/uncorrelated ",
+        "comparison for ",
+        dv,
+        ": observation counts differ."
+      )
+    }
+    
+    
+    # --------------------------------------------------------
+    # Verify Same Selected Slope Composition
+    # --------------------------------------------------------
+    
+    corr_key <- canonical_slope_key(
+      row_corr$re_formula[1]
+    )
+    
+    
+    uncorr_key <- canonical_slope_key(
+      row_uncorr$re_formula[1]
+    )
+    
+    
+    if (
+      corr_key != selected_key ||
+      uncorr_key != selected_key
+    ) {
+      
+      stop(
+        "Matched parameterization comparison failed for ",
+        dv,
+        ": correlated and uncorrelated models do not contain ",
+        "the selected random-slope composition."
+      )
+    }
+    
+    
+    # --------------------------------------------------------
+    # Calculate LRT Degrees of Freedom
+    # --------------------------------------------------------
+    
+    lrt_df <- covariance_df_difference(
+      selected_formula
+    )
+    
+    
+    if (lrt_df <= 0L) {
+      
+      stop(
+        "Internal LRT error for ",
+        dv,
+        ": a slope-containing structure produced a ",
+        "non-positive covariance-parameter df difference."
+      )
+    }
+    
+    
+    # --------------------------------------------------------
+    # Calculate Likelihood-Ratio Statistic
+    # --------------------------------------------------------
+    
+    raw_lrt_statistic <- (
+      2 *
+        (
+          row_corr$llf[1] -
+            row_uncorr$llf[1]
+        )
+    )
+    
+    
+    # Small negative values can arise from numerical optimizer
+    # differences even though the correlated model is the less
+    # constrained parameterization.
+    
+    lrt_statistic <- max(
+      0,
+      raw_lrt_statistic
+    )
+    
+    
+    lrt_p_value <- pchisq(
+      lrt_statistic,
+      df = lrt_df,
+      lower.tail = FALSE
+    )
+    
+    
+    # --------------------------------------------------------
+    # Apply Original Decision Rule
+    # --------------------------------------------------------
+    
+    if (lrt_p_value < 0.05) {
+      
+      winner_type <-
+        "Correlated"
+      
+      winner_formula <-
+        row_corr$re_formula[1]
+      
+      winner_bic <-
+        row_corr$bic[1]
+      
+      winner_aic <-
+        row_corr$aic[1]
+      
+      winner_llf <-
+        row_corr$llf[1]
+      
+      winner_nobs <-
+        row_corr$nobs[1]
+      
+      
+      decision_reason <- paste0(
+        "The selected minimum-BIC slope composition was ",
+        "available under both parameterizations. The matched ",
+        "correlated-versus-uncorrelated likelihood-ratio test ",
+        "was significant (p=",
+        sprintf(
+          "%.4f",
+          lrt_p_value
+        ),
+        "), so the correlated parameterization was retained."
+      )
+      
+      
+    } else {
+      
+      winner_type <-
+        "Uncorrelated"
+      
+      winner_formula <-
+        row_uncorr$re_formula[1]
+      
+      winner_bic <-
+        row_uncorr$bic[1]
+      
+      winner_aic <-
+        row_uncorr$aic[1]
+      
+      winner_llf <-
+        row_uncorr$llf[1]
+      
+      winner_nobs <-
+        row_uncorr$nobs[1]
+      
+      
+      decision_reason <- paste0(
+        "The selected minimum-BIC slope composition was ",
+        "available under both parameterizations. The matched ",
+        "correlated-versus-uncorrelated likelihood-ratio test ",
+        "was not significant (p=",
+        sprintf(
+          "%.4f",
+          lrt_p_value
+        ),
+        "), so the uncorrelated parameterization was retained ",
+        "on grounds of parsimony."
+      )
+    }
+    
+    
+    decision_method <-
+      "Minimum-BIC slope composition + matched LRT"
+    
+    
+    # ----------------------------------------------------------
+    # 7.7 CASE C — Only Correlated Parameterization Available
+    # ----------------------------------------------------------
+    
+  } else if (
+    corr_ok &&
+    !uncorr_ok
+  ) {
+    
+    
+    winner_type <-
+      "Correlated"
+    
+    
+    winner_formula <-
+      row_corr$re_formula[1]
+    
+    
+    winner_bic <-
+      row_corr$bic[1]
+    
+    
+    winner_aic <-
+      row_corr$aic[1]
+    
+    
+    winner_llf <-
+      row_corr$llf[1]
+    
+    
+    winner_nobs <-
+      row_corr$nobs[1]
+    
+    
+    decision_method <-
+      "Minimum-BIC slope composition; only correlated eligible"
+    
+    
+    decision_reason <- paste(
+      "The selected minimum-BIC slope composition had no",
+      "selection-eligible uncorrelated counterpart; the",
+      "eligible correlated parameterization was retained."
+    )
+    
+    
+    # ----------------------------------------------------------
+    # 7.8 CASE C — Only Uncorrelated Parameterization Available
+    # ----------------------------------------------------------
+    
+  } else if (
+    !corr_ok &&
+    uncorr_ok
+  ) {
+    
+    
+    winner_type <-
+      "Uncorrelated"
+    
+    
+    winner_formula <-
+      row_uncorr$re_formula[1]
+    
+    
+    winner_bic <-
+      row_uncorr$bic[1]
+    
+    
+    winner_aic <-
+      row_uncorr$aic[1]
+    
+    
+    winner_llf <-
+      row_uncorr$llf[1]
+    
+    
+    winner_nobs <-
+      row_uncorr$nobs[1]
+    
+    
+    decision_method <-
+      "Minimum-BIC slope composition; only uncorrelated eligible"
+    
+    
+    decision_reason <- paste(
+      "The selected minimum-BIC slope composition had no",
+      "selection-eligible correlated counterpart; the",
+      "eligible uncorrelated parameterization was retained."
+    )
+    
+    
+    # ----------------------------------------------------------
+    # 7.9 No Matched Eligible Parameterization
+    # ----------------------------------------------------------
+    
+  } else {
+    
+    
+    winner_type <-
+      "None"
+    
+    
+    winner_formula <-
+      NA_character_
+    
+    
+    decision_method <-
+      "No eligible matched parameterization"
+    
+    
+    decision_reason <- paste(
+      "No selection-eligible parameterization was available",
+      "for the selected minimum-BIC slope composition."
+    )
+  }
+  
+  
+  # ----------------------------------------------------------
+  # 7.10 Store Final Decision
+  # ----------------------------------------------------------
+  
+  results_summary[[dv]] <- tibble(
+    
+    Stage =
+      stage,
+    
+    Reading_Measure =
+      measure,
+    
+    DV =
+      dv,
+    
+    
+    Selected_Slope_Structure =
+      selected_formula,
+    
+    
+    Selected_N_Random_Slopes =
+      n_random_slopes,
+    
+    
+    Minimum_BIC_For_Slope_Selection =
+      selected_min_bic,
+    
+    
+    Correlated_Available =
+      corr_ok,
+    
+    
+    BIC_Correlated =
+      if (corr_ok) {
+        row_corr$bic[1]
+      } else {
+        NA_real_
+      },
+    
+    
+    AIC_Correlated =
+      if (corr_ok) {
+        row_corr$aic[1]
+      } else {
+        NA_real_
+      },
+    
+    
+    LogLik_Correlated =
+      if (corr_ok) {
+        row_corr$llf[1]
+      } else {
+        NA_real_
+      },
+    
+    
+    Uncorrelated_Available =
+      uncorr_ok,
+    
+    
+    BIC_Uncorrelated =
+      if (uncorr_ok) {
+        row_uncorr$bic[1]
+      } else {
+        NA_real_
+      },
+    
+    
+    AIC_Uncorrelated =
+      if (uncorr_ok) {
+        row_uncorr$aic[1]
+      } else {
+        NA_real_
+      },
+    
+    
+    LogLik_Uncorrelated =
+      if (uncorr_ok) {
+        row_uncorr$llf[1]
+      } else {
+        NA_real_
+      },
+    
+    
+    LRT_Statistic =
+      lrt_statistic,
+    
+    
+    LRT_df =
+      lrt_df,
+    
+    
+    LRT_p_value =
+      lrt_p_value,
+    
+    
+    Final_Structure_Type =
+      winner_type,
+    
+    
+    Final_Random_Slope_Structure =
+      winner_formula,
+    
+    
+    Final_N_Random_Slopes =
+      if (!is.na(winner_formula)) {
+        count_random_slopes(
+          winner_formula
+        )
+      } else {
+        NA_integer_
+      },
+    
+    
+    Final_BIC =
+      winner_bic,
+    
+    
+    Final_AIC =
+      winner_aic,
+    
+    
+    Final_LogLik =
+      winner_llf,
+    
+    
+    Final_N =
+      winner_nobs,
+    
+    
+    Decision_Method =
+      decision_method,
+    
+    
+    Decision_Reason =
+      decision_reason
+  )
+  
+  
+  # ----------------------------------------------------------
+  # 7.11 Report Final Decision
+  # ----------------------------------------------------------
+  
+  message(
+    "Selected slopes    : ",
+    selected_formula
+  )
+  
+  
+  message(
+    "Number of slopes   : ",
+    n_random_slopes
+  )
+  
+  
+  message(
+    "Minimum BIC        : ",
+    round(
+      selected_min_bic,
+      3
+    )
+  )
+  
+  
+  message(
+    "Correlated match   : ",
+    if (corr_ok) {
+      paste0(
+        "BIC=",
+        round(
+          row_corr$bic[1],
+          3
+        )
+      )
+    } else {
+      "Not eligible / unavailable"
+    }
+  )
+  
+  
+  message(
+    "Uncorrelated match : ",
+    if (uncorr_ok) {
+      paste0(
+        "BIC=",
+        round(
+          row_uncorr$bic[1],
+          3
+        )
+      )
+    } else {
+      "Not eligible / unavailable"
+    }
+  )
+  
+  
+  message(
+    "LRT                : ",
+    if (is.na(lrt_p_value)) {
+      "Not applicable"
+    } else {
+      paste0(
+        "Chi-square=",
+        round(
+          lrt_statistic,
+          3
+        ),
+        ", df=",
+        lrt_df,
+        ", p=",
+        sprintf(
+          "%.4f",
+          lrt_p_value
+        )
+      )
+    }
+  )
+  
+  
+  message(
+    "Final structure    : ",
+    winner_type
+  )
+  
+  
+  message(
+    "Decision method    : ",
+    decision_method
+  )
+}
+
+
+
+
+
+# ============================================================
+# CELL 8 — ASSEMBLE FINAL DECISION TABLE
+# ============================================================
+# Purpose:
+#   Combine the DV-specific decisions generated in Cell 7 into
+#   one ordered final decision table.
+#
+# The resulting table records:
+#
+#   - minimum-BIC selected random-slope composition
+#   - number of selected random slopes
+#   - matched correlated model statistics
+#   - matched uncorrelated model statistics
+#   - LRT statistic
+#   - LRT degrees of freedom
+#   - LRT p-value
+#   - final covariance parameterization
+#   - final random-slope structure
+#   - final fit statistics
+#   - decision method and interpretation
+# ============================================================
+
+
+final_decisions <- bind_rows(
+  results_summary
+) %>%
+  arrange(
+    Stage
+  )
+
+
+print(
+  final_decisions
+)
+
+
+
+
+
+# ============================================================
+# CELL 9 — FINAL CONSISTENCY CHECKS
+# ============================================================
+# Purpose:
+#   Perform defensive validation of the completed Step 5
+#   decision table before results are exported.
+#
+# Checks:
+#   1. Exactly one decision row exists for every duration DV.
+#   2. Dependent-variable identifiers are unique.
+#   3. Reading-stage identifiers are unique.
+#   4. Final structure labels are valid.
+#   5. Selected models contain finite BIC/AIC/log-likelihood.
+#   6. Selected models contain valid positive observation
+#      counts.
+#   7. Final random-slope counts agree with the selected
+#      random-slope formula.
+#   8. Every LRT has valid statistic, df, and p-value.
+#   9. LRTs occur only for slope-containing structures having
+#      both matched parameterizations available.
+#  10. Random-intercept-only selections do not receive an LRT.
+# ============================================================
+
+
+# ------------------------------------------------------------
+# 9.1 One Final Decision Per DV
+# ------------------------------------------------------------
+
+if (
+  nrow(final_decisions) !=
+  nrow(dv_registry)
+) {
+  
+  stop(
+    "Final decision table does not contain exactly one row ",
+    "for every duration DV."
+  )
+}
+
+
+# ------------------------------------------------------------
+# 9.2 Confirm DV Uniqueness
+# ------------------------------------------------------------
+
+if (
+  anyDuplicated(
+    final_decisions$DV
+  ) > 0
+) {
+  
+  stop(
+    "Duplicate dependent-variable decisions detected in the ",
+    "final Step 5 decision table."
+  )
+}
+
+
+# ------------------------------------------------------------
+# 9.3 Confirm Stage Uniqueness
+# ------------------------------------------------------------
+
+if (
+  anyDuplicated(
+    final_decisions$Stage
+  ) > 0
+) {
+  
+  stop(
+    "Duplicate reading-stage decisions detected."
+  )
+}
+
+
+# ------------------------------------------------------------
+# 9.4 Validate Final Structure Labels
+# ------------------------------------------------------------
+
+valid_final_structure_types <- c(
+  "Correlated",
+  "Uncorrelated",
+  "Random Intercept Only",
+  "None"
+)
+
+
+unexpected_final_structure_types <- setdiff(
+  unique(
+    final_decisions$Final_Structure_Type
+  ),
+  valid_final_structure_types
+)
+
+
+if (
+  length(
+    unexpected_final_structure_types
+  ) > 0
+) {
+  
+  stop(
+    "Unexpected final random-effects structure type(s): ",
+    paste(
+      unexpected_final_structure_types,
+      collapse = ", "
+    )
+  )
+}
+
+
+# ------------------------------------------------------------
+# 9.5 Identify DVs With a Selected Final Model
+# ------------------------------------------------------------
+
+has_final_model <- (
+  final_decisions$Final_Structure_Type !=
+    "None"
+)
+
+
+# ------------------------------------------------------------
+# 9.6 Validate Final Fit Statistics
+# ------------------------------------------------------------
+
+if (
+  any(
+    has_final_model &
+    (
+      !is.finite(
+        final_decisions$Final_BIC
+      ) |
+      !is.finite(
+        final_decisions$Final_AIC
+      ) |
+      !is.finite(
+        final_decisions$Final_LogLik
+      )
+    )
+  )
+) {
+  
+  stop(
+    "At least one selected final model has a missing, invalid, ",
+    "or non-finite BIC/AIC/log-likelihood value."
+  )
+}
+
+
+# ------------------------------------------------------------
+# 9.7 Validate Final Observation Counts
+# ------------------------------------------------------------
+
+if (
+  any(
+    has_final_model &
+    (
+      is.na(
+        final_decisions$Final_N
+      ) |
+      final_decisions$Final_N <= 0
+    )
+  )
+) {
+  
+  stop(
+    "At least one selected final model has a missing or ",
+    "non-positive observation count."
+  )
+}
+
+
+# ------------------------------------------------------------
+# 9.8 Validate Final Random-Slope Structures
+# ------------------------------------------------------------
+
+if (
+  any(
+    has_final_model &
+    is.na(
+      final_decisions$
+      Final_Random_Slope_Structure
+    )
+  )
+) {
+  
+  stop(
+    "At least one selected final model is missing its random-",
+    "slope structure specification."
+  )
+}
+
+
+# ------------------------------------------------------------
+# 9.9 Verify Final Random-Slope Counts
+# ------------------------------------------------------------
+
+expected_final_slope_counts <- vapply(
+  final_decisions$
+    Final_Random_Slope_Structure,
+  function(x) {
+    
+    if (is.na(x)) {
+      
+      return(
+        NA_integer_
+      )
+    }
+    
+    
+    count_random_slopes(
+      x
+    )
+  },
+  integer(1)
+)
+
+
+slope_count_mismatch <- which(
+  has_final_model &
+    (
+      is.na(
+        final_decisions$
+          Final_N_Random_Slopes
+      ) |
+        final_decisions$
+        Final_N_Random_Slopes !=
+        expected_final_slope_counts
+    )
+)
+
+
+if (
+  length(
+    slope_count_mismatch
+  ) > 0
+) {
+  
+  stop(
+    "Final random-slope count is inconsistent with the ",
+    "selected random-slope formula for ",
+    length(
+      slope_count_mismatch
+    ),
+    " DV(s)."
+  )
+}
+
+
+# ------------------------------------------------------------
+# 9.10 Validate LRT Results
+# ------------------------------------------------------------
+
+lrt_performed <- (
+  !is.na(
+    final_decisions$LRT_p_value
+  )
+)
+
+
+if (
+  any(
+    lrt_performed &
+    (
+      !is.finite(
+        final_decisions$LRT_Statistic
+      ) |
+      final_decisions$LRT_Statistic < 0 |
+      is.na(
+        final_decisions$LRT_df
+      ) |
+      final_decisions$LRT_df <= 0 |
+      !is.finite(
+        final_decisions$LRT_p_value
+      ) |
+      final_decisions$LRT_p_value < 0 |
+      final_decisions$LRT_p_value > 1
+    )
+  )
+) {
+  
+  stop(
+    "Invalid likelihood-ratio test result detected."
+  )
+}
+
+
+# ------------------------------------------------------------
+# 9.11 Verify LRT Is Restricted to Matched Slope Models
+# ------------------------------------------------------------
+
+if (
+  any(
+    lrt_performed &
+    (
+      !final_decisions$
+      Correlated_Available |
+      !final_decisions$
+      Uncorrelated_Available |
+      final_decisions$
+      Selected_N_Random_Slopes <= 0
+    )
+  )
+) {
+  
+  stop(
+    "An LRT was recorded without two matched eligible ",
+    "slope-containing parameterizations."
+  )
+}
+
+
+# ------------------------------------------------------------
+# 9.12 Verify LRT Degrees of Freedom
+# ------------------------------------------------------------
+
+expected_lrt_df <- vapply(
+  final_decisions$
+    Selected_Slope_Structure,
+  covariance_df_difference,
+  integer(1)
+)
+
+
+lrt_df_mismatch <- which(
+  lrt_performed &
+    (
+      final_decisions$LRT_df !=
+        expected_lrt_df
+    )
+)
+
+
+if (
+  length(
+    lrt_df_mismatch
+  ) > 0
+) {
+  
+  stop(
+    "LRT degrees of freedom are inconsistent with the ",
+    "selected random-slope composition for ",
+    length(
+      lrt_df_mismatch
+    ),
+    " DV(s)."
+  )
+}
+
+
+# ------------------------------------------------------------
+# 9.13 Verify Random-Intercept-Only Handling
+# ------------------------------------------------------------
+
+intercept_only <- (
+  final_decisions$
+    Selected_N_Random_Slopes == 0
+)
+
+
+if (
+  any(
+    intercept_only &
+    !is.na(
+      final_decisions$LRT_p_value
+    )
+  )
+) {
+  
+  stop(
+    "Random-intercept-only structures must not receive a ",
+    "correlated-versus-uncorrelated LRT."
+  )
+}
+
+
+if (
+  any(
+    intercept_only &
+    final_decisions$
+    Final_Structure_Type !=
+    "Random Intercept Only"
+  )
+) {
+  
+  stop(
+    "A selected random-intercept-only structure received an ",
+    "unexpected final parameterization label."
+  )
+}
+
+
+# ------------------------------------------------------------
+# 9.14 Validate LRT-Based Final Decisions
+# ------------------------------------------------------------
+
+if (
+  any(
+    lrt_performed &
+    final_decisions$LRT_p_value < 0.05 &
+    final_decisions$Final_Structure_Type !=
+    "Correlated"
+  )
+) {
+  
+  stop(
+    "At least one significant matched LRT did not produce a ",
+    "correlated final structure."
+  )
+}
+
+
+if (
+  any(
+    lrt_performed &
+    final_decisions$LRT_p_value >= 0.05 &
+    final_decisions$Final_Structure_Type !=
+    "Uncorrelated"
+  )
+) {
+  
+  stop(
+    "At least one nonsignificant matched LRT did not produce ",
+    "an uncorrelated final structure."
+  )
+}
+
+
+# ------------------------------------------------------------
+# 9.15 Warn if Any DV Has No Final Eligible Model
+# ------------------------------------------------------------
+
+if (
+  any(
+    final_decisions$
+    Final_Structure_Type ==
+    "None"
+  )
+) {
+  
+  no_model_dvs <- final_decisions$DV[
+    final_decisions$
+      Final_Structure_Type ==
+      "None"
+  ]
+  
+  
+  warning(
+    "No final selection-eligible random-effects model was ",
+    "identified for: ",
+    paste(
+      no_model_dvs,
+      collapse = ", "
+    )
+  )
+}
+
+
+# ------------------------------------------------------------
+# 9.16 Confirm Successful Final Validation
+# ------------------------------------------------------------
+
+if (
+  all(
+    final_decisions$
+    Final_Structure_Type !=
+    "None"
+  )
+) {
+  
+  message(
+    "Final consistency checks passed: exactly one valid final ",
+    "random-effects decision was identified for every DV."
+  )
+}
+
+
+
+
+
+# ============================================================
+# CELL 10 — CREATE FINAL STEP 5 WORKBOOK
+# ============================================================
+# Purpose:
+#   Export:
+#
+#       Final_Decisions
+#           → final random-slope and covariance decision for
+#             each duration DV
+#
+#       Selected_Structure_Comparison
+#           → eligible correlated and uncorrelated versions of
+#             the minimum-BIC selected slope composition
+#
+# This output mirrors the two-stage decision framework:
+#
+#       BIC selects slope composition
+#           ↓
+#       matched LRT selects covariance parameterization
+# ============================================================
+
+
+wb <- createWorkbook()
+
+
+# ------------------------------------------------------------
+# 10.1 Final Decisions
+# ------------------------------------------------------------
+
+addWorksheet(
+  wb,
+  "Final_Decisions"
+)
+
+
+writeData(
+  wb,
+  "Final_Decisions",
+  final_decisions,
+  withFilter = TRUE
+)
+
+
+# ------------------------------------------------------------
+# 10.2 Selected Structure Comparison
+# ------------------------------------------------------------
+
+addWorksheet(
+  wb,
+  "Selected_Structure_Comparison"
+)
+
+
+writeData(
+  wb,
+  "Selected_Structure_Comparison",
+  selected_structure_comparison,
+  withFilter = TRUE
+)
+
+
+
+
+
+# ============================================================
+# CELL 11 — EXCEL STYLING
+# ============================================================
+
+
+# ------------------------------------------------------------
+# 11.1 Define Styles
+# ------------------------------------------------------------
+
+style_header <- createStyle(
+  textDecoration = "bold",
+  halign = "center",
+  valign = "center",
+  border = "TopBottomLeftRight",
+  borderStyle = "thin"
+)
+
+
+style_border <- createStyle(
+  border = "TopBottomLeftRight",
+  borderStyle = "thin"
+)
+
+
+style_stage1 <- createStyle(
+  fgFill = "#E0F7FA"
+)
+
+
+style_stage2 <- createStyle(
+  fgFill = "#E8F5E9"
+)
+
+
+style_stage3 <- createStyle(
+  fgFill = "#FFF3E0"
+)
+
+
+style_stage4 <- createStyle(
+  fgFill = "#F3E5F5"
+)
+
+
+# ------------------------------------------------------------
+# 11.2 Apply Header Styles
+# ------------------------------------------------------------
+
+addStyle(
+  wb,
+  "Final_Decisions",
+  style_header,
+  rows = 1,
+  cols = seq_len(
+    ncol(final_decisions)
+  ),
+  gridExpand = TRUE,
+  stack = TRUE
+)
+
+
+addStyle(
+  wb,
+  "Selected_Structure_Comparison",
+  style_header,
+  rows = 1,
+  cols = seq_len(
+    ncol(
+      selected_structure_comparison
+    )
+  ),
+  gridExpand = TRUE,
+  stack = TRUE
+)
+
+
+
+
+
+# ============================================================
+# CELL 12 — STAGE-SPECIFIC FINAL-DECISION FORMATTING
+# ============================================================
+
+
+rows_s1 <- which(
+  final_decisions$Stage == 1
+) + 1
+
+rows_s2 <- which(
+  final_decisions$Stage == 2
+) + 1
+
+rows_s3 <- which(
+  final_decisions$Stage == 3
+) + 1
+
+rows_s4 <- which(
+  final_decisions$Stage == 4
+) + 1
+
+
+if (length(rows_s1) > 0) {
+
+  addStyle(
+    wb,
+    "Final_Decisions",
+    style_stage1,
+    rows = rows_s1,
+    cols = seq_len(
+      ncol(final_decisions)
+    ),
+    gridExpand = TRUE,
+    stack = TRUE
+  )
+}
+
+
+if (length(rows_s2) > 0) {
+
+  addStyle(
+    wb,
+    "Final_Decisions",
+    style_stage2,
+    rows = rows_s2,
+    cols = seq_len(
+      ncol(final_decisions)
+    ),
+    gridExpand = TRUE,
+    stack = TRUE
+  )
+}
+
+
+if (length(rows_s3) > 0) {
+
+  addStyle(
+    wb,
+    "Final_Decisions",
+    style_stage3,
+    rows = rows_s3,
+    cols = seq_len(
+      ncol(final_decisions)
+    ),
+    gridExpand = TRUE,
+    stack = TRUE
+  )
+}
+
+
+if (length(rows_s4) > 0) {
+
+  addStyle(
+    wb,
+    "Final_Decisions",
+    style_stage4,
+    rows = rows_s4,
+    cols = seq_len(
+      ncol(final_decisions)
+    ),
+    gridExpand = TRUE,
+    stack = TRUE
+  )
+}
+
+
+
+
+
+# ============================================================
+# CELL 13 — BORDERS, WIDTHS, AND FREEZE PANES
+# ============================================================
+
+
+# ------------------------------------------------------------
+# 13.1 Final Decisions
+# ------------------------------------------------------------
+
+addStyle(
+  wb,
+  "Final_Decisions",
+  style_border,
+  rows = seq_len(
+    nrow(final_decisions) + 1
+  ),
+  cols = seq_len(
+    ncol(final_decisions)
+  ),
+  gridExpand = TRUE,
+  stack = TRUE
+)
+
+
+setColWidths(
+  wb,
+  "Final_Decisions",
+  cols = seq_len(
+    ncol(final_decisions)
+  ),
+  widths = "auto"
+)
+
+
+freezePane(
+  wb,
+  "Final_Decisions",
+  firstRow = TRUE
+)
+
+
+# ------------------------------------------------------------
+# 13.2 Selected Structure Comparison
+# ------------------------------------------------------------
+
+addStyle(
+  wb,
+  "Selected_Structure_Comparison",
+  style_border,
+  rows = seq_len(
+    nrow(
+      selected_structure_comparison
+    ) + 1
+  ),
+  cols = seq_len(
+    ncol(
+      selected_structure_comparison
+    )
+  ),
+  gridExpand = TRUE,
+  stack = TRUE
+)
+
+
+setColWidths(
+  wb,
+  "Selected_Structure_Comparison",
+  cols = seq_len(
+    ncol(
+      selected_structure_comparison
+    )
+  ),
+  widths = "auto"
+)
+
+
+freezePane(
+  wb,
+  "Selected_Structure_Comparison",
+  firstRow = TRUE
+)
+
+
+
+
+
+# ============================================================
+# CELL 14 — SAVE FINAL STEP 5 WORKBOOK
+# ============================================================
+
+saveWorkbook(
+  wb,
+  OUTPUT_FILE,
+  overwrite = TRUE
+)
+
+
+message(
+  "\n",
+  strrep("=", 80)
+)
+
+message(
+  "STEP 5 COMPLETED SUCCESSFULLY"
+)
+
+message(
+  "Dataset: Affective Provo"
+)
+
+message(
+  "Final DV decisions: ",
+  nrow(
+    final_decisions
+  )
+)
+
+message(
+  "Output: ",
+  OUTPUT_FILE
+)
+
+message(
+  strrep("=", 80)
+)