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I have two measures from each of 20 studies. Random-effects meta analysis has been performed for each of the two measures, and for each measure I have two values to indicate data variability, cross-study (random effect) variance $\tau^2$ and its chi-square test statistic $Q$. Now I'd like to compare the cross-study var...
An L1 estimator minimizes the absolute difference between $Y$ and $x\beta$, whereas an M-estimator minimizes some function of the residuals. But the objective function needs to be differentiable right? Then why is an L1-estimator a special case of M-estimator?
I have four different time series of hourly measurements: The heat consumption inside a house The temperature outside the house The solar radiation The wind speed I want to be able to predict the heat consumption inside the house. There is a clear seasonal trend, both on a yearly basis, and on a daily basis. Since th...
I'm analyzing the residuals from a regression model fit to a dataset that covers several years worth of data. I want to report the sum of the residuals from that model, by year, as a measure of how the overall error for each year changes over time. Is this an acceptable way to report residuals? Here is an example of m...
If r between X and Y is 0.74, then r-squared is 55%. According to many 'rules of thumb' and others, the effect size (in this case r) is considered 'moderate' or 'medium'. As such, only 55% of the variance in Y can be explained by X. The remaining 45% remain unexplained. Question 1: Given the above, how good is r when ...
Let $X_1,X_2,X_3,\cdots,X_9$ be a random sample of size $9$ from a normal distribution, $\mathcal{N}(\mu,\sigma^2)$. If $\sigma$ is unknown, find the expected value of the length of a $95\%$ confidence interval for $\mu$ provided the interval is based on the random variable $3(\overline{X}-\mu)/S$. Can you please hel...
I have a trial where the measurement is the deviation about a target value. There are 8 subjects - 4 treatment, 4 control. Each subject has undertaken the trial 4 times. Thus, I have 32 values, nested within groups. Obviously this is a rather small number Essentially, my treatment is effective if it minimises the abso...
I would like to fit a model of the form weight ~ bs(height) + id, where id is a factor (so I have several observations per every id). There are perhaps 100k values of id. Does anyone know the best way to go about fitting this? I have tried the mgcv package, but I do not think it was designed for problems this large ...
Self organizing maps are claimed to be able to visualize/cluster high-dimensional data in a smaller dimensional space. I have some difficulties in understanding this statement. Consider a six-dimensional data set; the codebook vector/reference vector is also six-dimensional. According to the SOM algorithm, updating t...
So I am using the R code behind Fig. 3.14 in Dynamic Linear Models With R (p. 124-5) to make a dynamic version of a simple pair trading model: $$ Y = \alpha + \beta X. $$ If I use log returns (diff(log(P)) in R, P being a timeseries of equity prices) I get results that makes sense, they are pretty similar to the sta...
Could someone please explain what the difference is between the two, and perhaps avoid the worst statistical jargon? I am currently using the dlm package to model dynamic regressions as can be seen on p.122-5 in Dynamic Linear Models with R, and I don't really grasp the theoretical difference between using dlmFilter an...
I have nested structure design with the following model: Yijklt = m + ai + bij + rijk + sikl + (bs)ijkl + eijkl where i = 1, 2, ..................., s; number of sets j = 1, 2, ........................, r; number of replications k = 1, 2, ........................., m; males l = 1,2,............................, f;...
Is there a method to understand if two lines are (more or less) parallel? I have two lines generated from linear regressions and I would like to understand if they are parallel. In other words, I would like to get the different of the slopes of those two lines. Is there an R function to calculate this? EDIT: ... and ho...
I have a set of data I ran on a simulation using R with a population size (N) of 1000, sample mean of 64.93, and a standard deviation of 27.61. The distribution is positively skewed and a Wilks-Shapiro test done in JMP shows that the data is not normally distributed. I need the confidence intervals of this data to be...
In our experimental design, we are assessing the effect of TMS on decision making. Our data is not normally distributed because our assesment test results in mean count data (ultimatum game). Besides, even randomized the previous test decisions are different across subjects as it is not possible to equalize in our case...
I have tested gender difference on the relationship between Variable A and B using linear model (GLM command in SPSS). I have found that the interaction of A (covariate/independent variable) with gender (factor) on B (dependent variable) is statistically significant. This means that the relationship between A and B di...
I want to regress two series (one big series divided in half) with the mean of the big series. I do that because I would like to "investigate" the relationship between those two subseries and the mean. Does this make any sense for you? When running the code below, I don't understand why I don't get p-value: > x = rno...
What is the difference between spatial dependence and spatial heterogeneity? My question is motivated by readings in model specification problems in spatial econometrics, in particular Anselin (2010).
Gelman & Hill 2007 mention several times throughout their book that: "Roughly speaking, if a coefficient estimate is more than 2 standard errors away from zero, then it is called statistically significant. " However, when they use this rule throughout this book I find the conclusions inconsistent. For example from the ...
What non-parametric methods exist to assess whether two random samples belong to the same distribution?
I have a sample taken from a population that I know to have a highly positive skew, although I know nothing else about the population. My sample displays a similar skew. Sample size is 120. Is it incorrect to transform (Box-Cox) my sample to normality to perform simple parametric tests like a mean with a confidence ...
I want to find some particular individuals in a population, ones with a special genetic makeup for instance. I estimate the population to be 10000 and I'm hoping to find one of 45 individuals. I sample 2000 but still haven't found any. Assuming my sampling is random, how do I put a figure on the likelihood of that happ...
I need to study in depth the on/off problem with different approaches: frequentist, bayesian - frequentist hybrid, profile likelihood. The on/off problem is a counting experiment where you observe $n_{on}$ events when the source is "on" in the time $T_{on}$ and $n_{off}$ events when the source is "off" in time $T_{off}...
My job is to develop a classification that groups together diagnoses of similar cost and procedures of similar cost, by similar anatomy. For instance a hip replacement would not be in the same group as a heart transplant as they cost different amounts and are not clinically similar. We revise this huge classification y...
I am not sure how I would analyse this data: The experiment is looking at the accuracy of emotion recognition in children with ADHD. The children will be asked to identify what emotion a face is portraying (out of 6 expressions; happiness, sadness, fear, anger, disgust and neutral). They will firstly be shown the pho...
Is ANOVA valid for binomial data? I have 7 binomial groups and I want to test whether the distributions of all of the groups are equal or whether the distribution of the first group is significantly different than the distribution of groups 2-7. What tests would accomplish this? I was thinking of just combining groups ...
I am trying to fit informed prior distributions to data using MLE, and F occasionally provides a best fit (lowest AIC value). I am starting with only very basic knowledge of probability theory, so I am not even confident that it is appropriate to fit an F in these cases. One of the interesting aspects of probability t...
I often confuse symbols :, \|, / and * in the R formulas, particularly when fitting mixed models with lme4. Can somebody explain clearly the differences between them? Later edit by @amoeba (Jan 2018): this question had a long and extremely confusing R code. I cut it all out for the benefit of future readers. Please see...
I was just wondering if it is possible to pool the data into groups before doing prcomp() in R? I have i.e. 100 individuals (rows) and 50 measurements(cols) with individuals being grouped in separate populations (20 in the first, 30 in the second, 15 in the third...etc). Now PCA can give scores of individuals or measur...
Q: Does there exist experimental evidence supporting Tufte-style, minimalist, data-speak visualizations over the chart-junked visualizations of, say, Nigel Holmes? I asked how to add chart-junk to R plots here and responders threw a hefty amount of snark back at me. So, surely, there must be some experimental evidence...
I don't have much experience with statistics (my education included 8 credits of pure statistics, another 8 of related subjects). I mostly learned about distributions and significance tests for distribution parameters, and a bit about linear regression. I also had some factor and component analysis, but have completely...
Given the random variable $$Y = \max(X_1, X_2, \ldots, X_n)$$ where $X_i$ are IID uniform variables, how do I calculate the PDF of $Y$?
Summary: Am I correlating two independent variables? Is that the problem? Let's say I have data point for square footage of a house and the asking price. Now, I can ask "Does square footage (x) determine price (y)?" This is intuituve, and makes sense. R-squared would end up saying "Square footage explains X% of ...
I would be very grateful if someone could explain to me how hidden markov models are used to generate a sequence alignment. I was trying to read on it, however ended up in attaining basic concepts and I'm interested in the mechanism that takes place in between the two points: I input 2 or more sequences (first) and get...
I just noticed that integrating a univariate random variable's quantile function (inverse cdf) from p=0 to p=1 produces the variable's mean. I haven't heard of this relationship before now, so I'm wondering: Is this always the case? If so, is this relationship widely known? Here is an example in python: from math impor...
I need to vary the window width (span) of a LOESS smoothing filter to select a given effective lowpass filter frequency. When I was using Savitzky-Golay for smoothing I found this technical report which related the window size to frequency, but have not found anything similar online for LOESS. The LOESS values will be ...
Following my question here, when is it appropriate (or inappropriate) to report r squared for a bivariate linear correlation. As explained in the earlier question, r = 0.74 which results in r squared of 55%. The size of r is an excellent outcome but when r squared is taken into account (especially when 45% of the varia...
Is there any statistical test that is parametric and non-parametric? This question was asked by an interview panel. Is it valid question?
I'm curious how an online dating systems might use survey data to determine matches. Suppose they have outcome data from past matches (e.g., 1 = happily married, 0 = no 2nd date). Next, let's suppose they had 2 preference questions, "How much do you enjoy outdoor activities? (1=strongly dislike, 5 = strongly like)" ...
I have a sequence of observations and I would like to determine if the observations in the sequence are mutually independent. Wald-Wolfowitz is a non-parametric test that can be used to check for randomness in the sequence. I think I have a general idea of how to formulate the problem, but don't want to sprain my brain...
I have data from a market research survey which covers behaviour of different customer groups. To be specific, I am looking at the number of channels that a customer will visit before they buy a product. I would like to know whether the value of the customer (as measured by the value of the product they buy) is a mean...
I want to compare model $A$ with 5 variables and model $B$ with 3 variables. I want to use the likelihood ratio test to do this. Note that this is logistic regression. How do I do this in SAS?
Thinking about a supposedly simple but interesting problem, I'd like to write some code to forecast consumable I'll need in the near future given the full history of my previous purchases. I'm sure this kind of problem has some more generic and well studied definition (someone suggested this is related to some concepts...
Are there any packages to do piecewise linear regression, which can detect the multiple knots automatically? Thanks. When I use the strucchange package. I could not detect the change points. I have no idea how it detects the change points. From the plots, I could see there are several points I want it could help me to ...
Can anyone show me what the connection between bootstrap methods and maximum likelihood is? I was told that as the number of bootstraps goes to infinity, the statistics like confidence intervals, mean, variance and stability are same values that maximum likelihood would estimate.
Basically all I want to do is predict a scalar response using some curves. I've got as far as doing a regression (using fRegress from the fda package) but have no idea how to apply the results to a NEW set of curves (for prediction). I have N=536 curves, and 536 scalar responses. Here's what I've done so far: I've cre...
Suppose you have a population and some measurement which you could do on each member of the population (e.g. the population could be all the people in the world, and the measurement could be height). So one can regard this measurement as a random variable $X$ on the population, with some mean $\mu$ and variance $\sigm...
I want to perform a test of independence for a contingency table where the Y characteristic codes for whether an individual go to school or not, and X stands for its gender (MA, male; FE, female). A typical contingency table would be: +-----+-----------+-----------------+ \| X/Y \| Go School \| No Go to school \| +-----+-...
I'm trying to solve a couple of exercises in Gelman and Hill 2007. The datasets they use are all on a website, however, every time I try to import the files I get an error: pollution=read.table("pollution.dta") Error in scan(file, what, nmax, sep, dec, quote, skip, nlines, na.strings, : line 1 did not have 2 e...
I'm wondering if it makes a difference in interpretation whether only the dependent, both the dependent and independent, or only the independent variables are log transformed. Consider the case of log(DV) = Intercept + B1*IV + Error I can interpret the IV as the percent increase but how does this change when I have ...
For learning GHSOM I figured out I should study SOM as a first step. Now, I know the basics of SOM, about weighted vectors and euclidean distances: when the human brain cannot easily process more than two dimensions of data, SOM will cluster, or in other words, map the data from high dimensions into lower ones (from th...
This R code simulates Gaussian mixed effects data with one random effect and one fixed effect. How would I modify that code to simulate Binomial mixed effects data with one random effect and one fixed effect?
If I am looking at an ivreg2 equation where: ivreg2 y1 x2 x3 x4 (x1 = x5 x6) and I know that x5 and x6 are endogenous variables (i.e. they are motivated by latent, unmeasurable characteristics) and there are no other viable alternatives, does IV 2sls work? Is it biased? Inconsistent?
Can anybody point me out a good reference for the Tukey-Kramer test? Secondly, suppose that we want to compare the mean of the group called "male" and the group called "female" (each group is composed of 10 sample). I executed this test with JMP and it gives to me a comparison table like the following: female ...
I asked this question on Stackoverflow: https://stackoverflow.com/questions/8142118/incidence-rate-ratios-in-r-poisson-regression and was advised to post here instead. I have data that looks like this sex agecat cases population 1 male 0-4 12 126526 2 male 5-9 12 128375 3 female 0-4 11 12928...
Perhaps my question is very simple, however I could not get a reliable solution for my problem. Here is my problem: Consider something as 'event' if this causes me a monetary loss equal to or above $x$ amount (say in USD). The number of such events (in a particular time interval, like say 10 years) follows a Poisson d...
I'm working on improving a random forest model. I've done some clustering of the data using the pvclust package in R. I use ward and euclidean distances. My question is how do I go from the results of the clustering analysis to a better random forest. Do I need to run multiple rf objects with data split along the e...
I have run a survey with many respondents. There was a pool of questions, and each respondent was asked 3 of the questions (chosen uniformly at random and independently for each respondent). Now I'm interested in comparing the fraction of respondents who answered question $i$ correctly to the fraction who answered que...
Wikipedia suggests that one way to look at inter-rater reliability is to use a random effects model to compute intraclass correlation. The example of intraclass correlation talks about looking at $$\frac{\sigma_\alpha^2}{\sigma_\alpha^2+\sigma_\epsilon^2}$$ from a model $$Y_{ij} = \mu + \alpha_i + \epsilon_{ij}$$ "whe...
What methods exist to test for the existence of any sort of dependence in a time series? This is in contrast to something like auto-correlation, which tests for a particular type of dependency. Is there something that can say if dependencies exist, in general, without necessarily determining what kind? I have heard o...
I have built a Kalman Filter model for flu forecasting as shown below. Y - Target Variable X1 - Predictor1 X2 - Predictor2 While forecasting into the future, I will NOT have data for all three variables. So, I am predicting X1 and X2 using two Kalman filters. The code is below x1.model <- dlmModSeas(52) + dlmModPoly(...
Following the question here, someone suggested that I could just look at the B column in SPSS "Parameter Estimates" table to interpret the interaction. For instance, the B column for one of my tests is as following: Intercept: .724 [Gender = 1.00]: .140 [Gender = 2.00]: 0 [Gender = 1.00] * Income: .620 [Gender = 2.00...
I am comparing three relatively simple GLMs having a Gamma distribution with AIC and BIC. The aim is to identify the effects of fertilizers (fdung), year and site on biomass of a specific grass species. Hence, the aim is not to predict new values but merely to identify the effects of the three factors. Here are the mod...
Suppose we have $N_A$ and $N_B$ samples from population A and B respectively. For each sample, we have his/her weight and height. What interests us is whether there are a significant difference in weight between A and B. A t-test can do this easily. But we also know there is strong correlation between height and weight...
I have some species $\times$ year matrices and analyse the temporal dynamics by regressing distance between years on $\sqrt{ {\rm time \ lag} }$. Since the data points are not independent and since I get $(n^2-n)/2$ distances for a time series of length $n$, it's problematic to use the standard way of determining the s...
First of all, I am very new to this subject. I have been using weka some days to familiarize myself and reading about data mining to understand it. I have a dataset (from UCI, german credit data) and I need to classify it. I have been trying different tree algorithms using different attributes instead of all and I wish...
Kenward and Roger (1997) proposed an approximation for an $F$-test of fixed effects in a linear mixed-effects model through (1) inflating the estimated variance-covariance matrix of the fixed and random effects and (2) adjusting the degrees of freedom (DF). In their paper they state that, when the approximation is appl...
I have the vector x <- c(1, 2, 3, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10) (my actual vector has a length of >10,000) and I would like to find the intervals where the 90% of the density lies. Is quantile(x, probs=c(...
I have two data series that plot median age at death over time. Both series demonstrate an increased age at death over time, but one much lower than another. I want to determine if the increase in the age at death of the lower sample is significantly different than that of the upper sample. Here are the data, ordered...
In MATLAB, I've written two snippets of code that compute the PDF of a multivariate normal distribution. However there's a difference in the values these two methods produce and I can't figure out why. I've narrowed the problem down to something having to do with computing the inverse of the covariance matrix. Inaccura...
I am working on a web based project that will track a person's symptoms and drugs and nutrients they intake. For example thyroid patients symptoms of fatigue vs the dose of thyroid and also how much selenium, iodine, vitamin A, protein, etc they get from food or supplements. I've added a basic set of descriptive sta...
I have noisy time series which I need to segment into those portions with a zero mean and those portions without a zero mean. Finding the boundaries as accurately as possible is important (clearly where the boundary precisely lies is a bit subjective). I think a cusum variant could be adapted to do this but as cusum is...
Based on the answer to a previous question, For which distributions are the parameterizations in BUGS and R different? I have been transforming R parameterizations to JAGS parameterizations, but I have been getting errors so I am asking a separate question to clarify that the transformation is correct. R's ?dweibull st...
First, I am no expert but I am analyzing some marketing data. I have information on two versions of the same site, and I have data on the number of times people filled out a form on each version of the site. I want to know if one of the site variation performs better at generating more filled out forms. Sample data: da...
I have following type of data. I have evaluated 10 individuals each repeated 10 times. I have 10x10 relation matrix (relationship between all combination of the individuals). set.seed(1234) mydata <- data.frame (gen = factor(rep(1:10, each = 10)), repl = factor(rep(1:10, 10)), ...
There is one medical data set which contains 3 treatments: A, B, and C. The response variable is Yes/No. However, due to a specific medical reason, the dataset needs to be split into several sub-datasets. The major research question is to compare the difference of proportions between $P_A$, $P_B$ and $P_C$. If I did n...
There are m disjoint sets Xi and a function f : [1..n] → [1..m] such that Yj = Xf(j). I am given oracles / samples from random variables xi and yj which uniformly select elements from Xi and Yj respectively, but each sample from xi and yj has a cost (independent of i or j). I would like to compute f by sampling from ...
I'm building a Getting Things Done app. My principle complaint with most GTD / TODO apps is they show me too much. When I'm at work, I don't want to see tasks I'm planning to do on the weekend. When I'm at home, I don't want to see work tasks. When out running errands, I just want to see my errands tasks, etc. I've bee...
Update: Sorry for another update but I've found some possible solutions with fractional polynomials and the competing risk-package that I need some help with. The problem I can't find an easy way to do a time dependent coefficient analysis is in R. I want to be able to take my variables coefficient and do it into a ti...
I know that ARIMA is one approach widely used in forecasting of univariate time series. What are some computational intelligence based methods that are reported to be successfully used in the same area? If possible, please recommend some articles/reports presenting such approaches. Thanks in advance.
We analyze blood vessel samples of patients in an organ bath which gives us force values. Each subject (patient) donates two types of blood vessels (pulmonary vein and pulmonary artery). The organ bath measurements include dose-response curves with a pharmaceutical, i.e. different concentrations are applied. From what ...
I'm new to data analysis. I was wondering how I could recognize hyped (fake) growth and word of mouth (true) growth in Google Trends specifically (but I guess it applies even to stock markets and the rest). For example, the image below is based on the Google Trends plot when you search for 'iPhone': (Orange, magenta, ...
I am currently trying to verify and evaluate a personalized recommender system I am working on, which seems like a huge task. Evaluating a static recommender system is rather easy and can be done with a simple bayesian framework the fast way. But my problem lies in how to find a good way to measure the degree and quali...
I would like to measure the impact of an intervention using a form of time series or some related technique (like segmented regression). I would like to use the Schools and Staffing Survey, which assesses my variable of interest over time, however, the respondents are different at each time point. I assume different r...
I have a set of game characters of a single shape (A) but a different size (small (1) to big (5)) and so the set of characters is (A1,A2,A3,A4,A5). They interact with eachother in a game grid in a pair-wise fashion, an interaction during which one will win and one will lose a battle. This goes on for a finite amount of...
I am doing a salary comparison depending on 2 cities. Very similar to this website So you select a source city, then a destination city, your current salary in the source city and it will output the "comparable" salary in the destination city. I want to confirm that what I am doing is correct, just bare with me for a m...
I have some triangulated 3D meshes. The statistics for the triangle areas are: Min 0.000 Max 2341.141 Mean 56.317 Std dev 98.720 So, does it mean anything particularly useful about the standard deviation or suggest there are bugs in calculating it, when the figures work out like the above? The areas are certainly ...
Brief Summary Why is it more common for logistic regression (with odds ratios) to be used in cohort studies with binary outcomes, as opposed to Poisson regression (with relative risks)? Background Undergraduate and graduate statistics and epidemiology courses, in my experience, generally teach that logistic regression...
This question is similar to another question I had recently posted but I have a follow on. In classical linear regression, we have $$\hat{\beta } \sim N(\beta,(X^{T}X)^{-1}\sigma^2).$$ Using this, one builds individual hypotheses of the significance of the coefficients, as done in the book by Tibshirani et al. My que...
I am trying to replicate the calculation that SAS and SPSS do for the partial autocorrelation function (PACF). In SAS it is produced through Proc Arima. The PACF values are the coefficients of an autoregression of the series of interest on lagged values of the series. My variable of interest is sales so I calculate lag...
I'll let Wikipedia explain how NPS is calculated: The Net Promoter Score is obtained by asking customers a single question on a 0 to 10 rating scale, where 10 is "extremely likely" and 0 is "not at all likely": "How likely is it that you would recommend our company to a friend or colleague?" Based on their respo...
I have a training data set that I've done some cluster analysis on using R's pvclust package. I have a dendrogram of the results and am currently looking for the best way to use the information to create a model(s) of the data. Can anyone recommend a resource to walk me thru the process of going from clustering to pr...
In Which Economic Indicators Best Predict Presidential Elections?, Nate Silver references a variable called "Incumbent Party Margin of Victory" for US presidential elections. I was wondering, is there a free source for this data?
I would like to know whether it makes sense to study the plots of residuals with respect to the dependent variable when I've got a univariate regression. If it makes sense, what does a strong, linear, growing correlation between residuals (on the y-axis) and the estimated values of the dependent variable (on the x-axis...
Is there a function in R that will take the mu and Sigma of an arithmetic-covariance matrix and return the mu and Sigma of a log-based covariance matrix? I have the code for a function implementing the reverse -- from log-covariance to linear covariance -- in R (pasted below in case this is helpful). Note that this cod...
I have a large data table (~500,000 rows) of normalized metrics (by Z-score) that looks like this: +------+---------------+---------------+---------------+---------------+ \| ID \| M1 \| M2 \| M3 \| M4 \| +------+---------------+---------------+---------------+---------------+ \| ...
I'm doing some spatial pattern analysis. After looking over some work on Markov Point Processes, I'm finding that all of the pairwise interaction processes are 'repulsive'. In "Statistical Inference and Simulation for Spatial Point Processes" by Moller, he states simply that 'the attractive case is not well defined'. ...
I am completing a project for a client using general linear model (GLM command) in SPSS/PASW (Ver. 17) Basically, the project is designed to find out if factors such as gender and age affect the relationship between Variables A and B. In this case, Variable A is the independent variable (IV) Variable B is the depe...
I am going to be using R for text analysis (mostly clustering, classification and some visualization) and was wondering what mechanisms R provides for handling high dimensional, sparse data sets. If I understand correctly, R does provide some packages (e.g., matrix library) for handling large and sparse matrices - whic...
I have 3 trials each on 87 animals in each of 2 contexts (some missing data; no missing data = 64 animals). Within a context, I have many specific measures (time to enter, number of times returning to shelter, etc), so I want to develop 2 to 3 composite behavior scores that describe the behavior in that context (call ...

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