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I am looking at the sample kurtosis of a fairly skewed random variable, and the results seem inconsistent. To simply illustrate the problem, I looked at the sample kurtosis of a log-normal RV. In R (which I am slowly learning): library(moments); samp_size = 2048; n_trial = 4096; kvals <- rep(NA,1,n_trial); #preallo...
Say I have a database of around a million words, and I want to get an intuitive idea about exactly how a particular, quite infrequent, word is distributed throughout this data. My goal is to be able to see clearly whether this word tends to cluster together, or whether it is relatively evenly spaced. What would be some...
In multiple linear regression, I can understand the correlations between residual and predictors are zero, but what is the expected correlation between residual and the criterion variable? Should it expected to be zero or highly correlated? What's the meaning of that?
When I work on data analysis projects I often store data in comma or tab-delimited (CSV, TSV) data files. While data often belongs in a dedicated database management system. For many of my applications, this would be overdoing things. I can edit CSV and TSV files in Excel (or presumably another Spreadsheet program). T...
I am going to host a training session to teach healthcare staff how to use control chart (c-chart to be specific), and I need to tell that why these rules (Western Electric Rules) are so called rules that when pattern is matched, outbreak can be considered as a probability. I have read the article "Control Charts 101: ...
In a previous question I asked about tools for editing CSV files. Gavin linked to a comment on R Help by Duncan Murdoch suggesting that Data Interchange Format is a more reliable way to store data than CSV. For some applications a dedicated database management system is what is needed. However, for small scale data ana...
I am trying to analyse some data using a mixed effect model. The data I collected represent the weight of some young animals of different genotype over time. I am using the approach proposed here: https://gribblelab.wordpress.com/2009/03/09/repeated-measures-anova-using-r/ In particular I'm using solution #2 So I have ...
After reading a dataset: dataset <- read.csv("forR.csv") How can I get R to give me the number of cases it contains? Also, will the returned value include of exclude cases omitted with na.omit(dataset)?
Suppose $\hat{m} = \frac{1}{N}\sum_{i=1}^{N}(X_i)$ where $X_i \sim N(m,\sigma)$. Are the following steps correct? \begin{align}\operatorname{Var}\left\{(\hat{m}-m)^2\right\} &= \mathrm E\left\{(\hat{m}-m)^4\right\} - \mathrm E^2\left\{(\hat{m}-m)^2\right\}\\&= 3\mathrm E^2\left\{(\hat{m}-m)^2\right\} - \mathrm E^2\left...
I have a need to analyze an experiment that had a binomial outcome and categorical predictors. For context we sent out an email to our customers and encouraged them to register their account online (did register or did not register online). There are different nine groups that received the email. The groups are segment...
I wish to cluster users together in a database, with each user represented by a number of features that are both discrete and continuous in nature. The aim is to define a small number of archetypal "users" with specific set of features. All other users are then categorized as being similar to one or other of these ar...
I have some data which, after lots of searching, I concluded would probably benefit from using a linear mixed effects model. I think I have an interesting result here, but I am having a little trouble figuring out how to interpret all of the results. This is what I get from the summary() function in R: > summary(nonzer...
I have fit a linear model and I now doing a lack-of-fit test. If the model has a good fit, the residual deviance should follow a $\chi^2$ distribution. The model I just ran has a very poor fit, and now I want to show this visually. I have used the following R code to plot the value of the residual deviance and the $\ch...
Let $\{x_i\}_{i=1}^n$ be a sample from a multivariate Gaussian distribution ${\cal N}(0, \Sigma_X)$ and $\{y_i\}_{i=1}^m$ be a sample from ${\cal N}(0, \Sigma_Y)$. Are there hypothesis tests for $\Sigma_X = \Sigma_Y$? Pointers to relevant literature would be very appreciated.
What way (ways?) is there to visually explain what is ANOVA? Any references, link(s) (R packages?) will be welcomed.
Suppose we are to estimate a expectation problem $E(f(X))$, where $X$ is a random variable with known distribution, by simulation and Large Law of numbers estimator. Antithetic method is a way to reduce variance of estimator in such cases. If $X$ is a 1D random variable with cdf $F$, antithetic method is applied as fol...
I'm working in a piece of software designed for satellite image classification based on various features of objects in the image. The software provides various built-in features like the mean of the values in the object, the maximum and minimum of the values etc. However, I want to use the median of the values. I don't...
I have a time series with an exponential moving average and I want to calculate a moving return of the EMA over the last m periods (something like a smoothed moving return). Let's say: Y(t) is the value of the time series at time period t S(t) is the value of an EMA of Y at time period t Now R(t) is the return of the E...
Is there any GUI for R that makes it easier for a beginner to start learning and programming in that language?
My name is Tuhin. I came up with a couple of questions when I was doing an analysis in R. I did a logistic regression analysis in R and tried to check how good the model fits the data. But, I got stuck as I could not get the pseudo R square value for the model which could give me some idea about the variation explained...
I am looking for applied references to data augmentation (preferably with some written code). Either online references are books would be great. I found this book online: http://www.amazon.com/Bayesian-Missing-Data-Problems-Biostatistics/dp/142007749X/ref=sr_1_1?ie=UTF8&s=books&qid=1291905761&sr=1-1 But with no review...
I have a set of data with 4 input variables and 1 result field (they're all numerical values). I want to determine the influence of variable #4 on the outcomes, so it makes sense to try to fix the other 3 inputs and the compare the results versus the value of var #4. I realize I'm probably using horrendous statistics t...
Dear everyone - I've noticed something strange that I can't explain, can you? In summary: the manual approach to calculating a confidence interval in a logistic regression model, and the R function confint() give different results. I've been going through Hosmer & Lemeshow's Applied logistic regression (2nd edition). ...
I have an irregularly spaced XTS time series (with POSIXct values as index type). How can I build a new time series sampled at a let's say 10 minute interval, but with each sample moment aligned to a round time (13:00:00, 13:10:00, 13:20:00, ...). If a resampling moment doesn't fall exactly on a original series value, ...
I'm trying to transition to R from using SPSS. In the past, I've setup my data in the wide format for my repeated measures ANOVAs in SPSS. How do I need to setup my data to run nlme()? The data is balanced. It has within-subjects variables of trial type(3 levels) each measured on 8 times, and a between-subjects factor ...
For this dataset: data my; input x y; datalines; -122.413582861209 37.7828877716232 -122.417876547159 37.7848288325307 ; proc print; run; The output and related tables are: How can I import, save and use these values to their maximum precision?
I am relating age to a binary outcome in a logistic model (or, more to the point I would like to). However, the distribution of the ages looks like this: nn <- 1000 age <- c(rpois(nn / 3, lambda = 0.5), rnorm(nn / 3, mean = 10, sd = 2), runif(nn / 3, min = 0, max = 15)) age <- age[which(age > 0)] How ...
I'm implementing PCA using eigenvalue decomposition in Matlab. I know Matlab has PCA implemented, but it helps me understand all the technicalities when I write code. I've been following the guidance from here, but I'm getting different results in comparison to built-in function princomp. Could anybody look at it and ...
My (very basic) knowledge of the Tobit regression model isn't from a class, like I would prefer. Instead, I have picked up pieces of information here and there through several Internet searches. My best guess at the assumptions for truncated regression are that they are very similar to the ordinary least squares (OLS) ...
I want to cluster a graph using the FCM algorithm, I used the adjacency matrix of the graph as the data, and the "Euclidean" distance as metric. The problem is that the adjacency matrix is full of zero's (depends actually on the degree of the node) and my network is a kinda huge more than 2000 node. For the results I ...
Hi my apologies first, I'm a biologist and not so good in statistics. In my study I'm studying the effect of concentration of feed on growth of a certain specimen. I have with me the different concentrations and the growth data for each concentration. What do you suggest is the best statistical test to find out the bes...
I have a linear mixed-effect model which I hope will answer the question of whether an increase in the frequency of use of one word leads to an increase of the frequency of use of that word by another person in a conversation, factoring out random effects of subject and topic of conversation. The basic model I've come ...
In Excel or Google Docs you can readily construct a Cumulative Distribution Function for the Normal distribution using the NORMDIST function (X, Mean, Standard Deviation). I am trying to do the same for a Lognormal distribution using the LOGNORMALDIST function that has the same parameters (X, Mean, Standard Deviation)...
I am trying to predict the outcome of a random variable x, which is a real-valued number. In some cases I can observe another variable y1, which should approximate x. I model y1 as a Gaussian distribution with mean of 0 and an empirically estimated standard deviation, and use the probability density function of that Ga...
I have fit a few mixed effects models (particularly longitudinal models) using lme4 in R but would like to really master the models and the code that goes with them. However, before diving in with both feet (and buying some books) I want to be sure that I am learning the right library. I have used lme4 up to now becaus...
I understand that in One-Way ANOVA two alternative F-Ratios have been derived to be robust when homogeneity of variance has been violated. Tomarkin and Serlin (1986) review amongst other techniques the Brown-Forsythe and Welch F-Ratios and conclude that both control the type I error rate well. So far I have only come a...
I am modeling a random variable ($Y$) which is the sum of some ~15-40k independent Bernoulli random variables ($X_i$), each with a different success probability ($p_i$). Formally, $Y=\sum X_i$ where $\Pr(X_i=1)=p_i$ and $\Pr(X_i=0)=1-p_i$. I am interested in quickly answering queries such as $\Pr(Y\leq k)$ (where $k$ i...
I asked this question yesterday on StackOverflow, and got an answer, but we agreed that it seems a bit hackish and there may be a better way to look at it. The question: I would like calculate the Newey-West (HAC) standard errors for a vector (in this case a vector of stock returns). The function NeweyWest() in the san...
I have a dataset where the difficulty level of my items and skill of my participants is unknown, but I would like to be able to extract some metric of how individual participants do on the test. What comes to mind initially is to use an item response theory model. However, I have two a priori constraints that makes me...
I've got some data about airline flights (in a data frame called flights) and I would like to see if the flight time has any effect on the probability of a significantly delayed arrival (meaning 10 or more minutes). I figured I'd use logistic regression, with the flight time as the predictor and whether or not each fli...
Diagonal elements of Psi (...) represent independent noise variances for each of the variables C.M. Bishop, Pattern Recognition and Machine Learning ...but I'm not clear on what does the Psi signify. I've applied FA to a series of images, received Psi matrix and now struggling with interpreting the results.
I am fitting a stepwise logistic regression on a set of data in SPSS. In the procedure, I am fitting my model to a random subset that is approx. 60% of the total sample, which is about 330 cases. What I find interesting is that every time I re-sample my data, I am getting different variables popping in and out in the ...
I got a slight confusion on the backpropagation algorithm used in multilayer perceptron (MLP). The error is adjusted by the cost function. In backpropagation, we are trying to adjust the weight of the hidden layers. The output error I can understand, that is, e = d - y [Without the subscripts]. The questions are: How ...
The underlying model of PLS is that a given $n \times m$ matrix $X$ and $n$ vector $y$ are related by $$X = T P' + E,$$ $$y = T q' + f,$$ where $T$ is a latent $n \times k$ matrix, and $E, f$ are noise terms (sssuming $X, y$ are centered). PLS produces estimates of $T, P, q$, and a 'shortcut' vector of regression c...
I need to cluster units into $k$ clusters to minimize within-group sum of squares (WSS), but I need to ensure that the clusters each contain at least $m$ units. Any idea if any of R's clustering functions allow for clustering into $k$ clusters subject to a minimum cluster size constraint? kmeans() does not seem to of...
I think that after apply PCA the covariance between components is reduced since the aim of PCA is to maximize variance. Covariance is needed by Factor analysis and thus it does not make sense to operate on the data in PCA space. Does this make any sense? Does someone have any other explanation?
I need to detect Out Of Shelf situations in reatil stores. What I had in mind is to assume that purchase frequency of some article (SKU) has certain ditribution (I tried with Poisson) and then calculate probability (according to that distribution) of that specific article was not bought since last purchase, and if that...
I'm a new guy here. Hopefully, I'm asking this question to right forum. Problem: We have data of a group of people (P1, P2, P3). They rank their expertise (1-10, where higher number is better) in a list of components (G1, G2, G3). P1 P2 P3 -------------- G1 | 8 4 7 G2 | 7 3 7 G3 | 9 6 5 Also, we have...
In a logit model, is there a smarter way to determine the effect of an independent ordinal variable than to use dummy variables for each level?
Let: Standard deviation of random variable $A =\sigma_{1}=5$ Standard deviation of random variable $B=\sigma_{2}=4$ Then the variance of A+B is: $Var(w_{1}A+w_{2}B)= w_{1}^{2}\sigma_{1}^{2}+w_{2}^{2}\sigma_{2}^{2} +2w_{1}w_{2}p_{1,2}\sigma_{1}\sigma_{2}$ Where: $p_{1,2}$ is the correlation between the two random variab...
Does anyone know how to create a nice looking summary table in JMP for several variables? I use Tables>Summary and the table I get has one row that includes for example mean(var1) mean(var2) mean(var3) median(var1) median(var2) median(var3) and so on. I would like each variable to have row of its own, with columns rep...
Say we have two Gaussian random vectors $p(x_1) = N(0,\Sigma_1), p(x_2) = N(0,\Sigma_2)$, is there a well known result for the expectation of their product $E[x_1x_2^T]$ without assuming independence?
I have heard that many problems in Mathematical Statistics can be stated and solved in terms of Symplectic Geometry. Unfortunately this was a pretty vague statement and I am interested in something more concrete. Also there seem to be some books written form this perspective, but I couldn't find any.
What are some of the main pitfalls of using linear mixed-effects models? What are the most important things to test/watch out for in assessing the appropriateness of your model? When comparing models of the same dataset, what are the most important things to look for?
I'm planning to start writing R packages. I thought it would be good to study the source code of existing packages in order to learn the conventions of package construction. My criteria for good packages to study: Simple statistical/technical ideas: The point is to learn about the mechanics of package construction. Un...
This image show a histogram (200 bins) of accumulated distances from a radar distance meter (very noisy). The peak around 7 meters is an object. At thought this looked kind of like a normal distribution, at least if you ignore values <4m (which for this application is reasonable). I have also achieved a reasonable fit ...
Should small sample sizes of 5 and less be included in reports? This is an area of medical training that is currently being reported only to the course level trainers and statistically not included in reports to upper management. All of the data is mined from course-level surveys.
I am doing multiple regression with some data (5 predictors, 1 response). Since the response is discrete and non-negative, I thought I would try Poisson regression. However, the data are significantly overdispersed (variance > mean), so I am now trying negative binomial regression. I was able to fit the model with this...
When building a CART model (specifically classification tree) using rpart (in R), it is sometimes obvious that there are variables (X's) that are meaningful for predicting some of the outcome (y) variables - while other predictors are relevant for other y's only. How can it be estimated, which explanatory variable is "...
Motivation I have a prior on a random variable $X\sim \beta^\prime(\alpha,\beta)$ that I would like to use in JAGS. JAGS does not support the $\beta^\prime$ distribution, but it does support the $F$ distributions, and the F distribution is related to the $\beta^\prime(\alpha,\beta)$ like this: $$\text{if } X\sim \beta^...
I have conducted a confirmatory factor analysis (CFA) to test the fit of a model with 5 factors and 5 items per factor. I used the modification indices to alter the model until I obtained statistics indicating an acceptable fit of the model to my data. As others have done in my area I then conducted a principal compon...
In a regression, the interaction term wipes out both related direct effects. Do I drop the interaction or report the outcome? The interaction was not part of the original hypothesis.
All, I am trying to study the GBM package in R. I. I wanted to try and figure out where the deviance, initial value, gradient and terminal node estimates came from. Please see this snippet: To start out, I was not sure where the Bernoulli deviance came from. I expected that the deviance, would be -2 multiplied by th...
Let's say you have a process that generates data according to r = sin(t) + epsilon, where epsilon ~ N(0,V) is Gaussian noise. The unconditional variance of r is 0.5 + V. Let's say we're forecasting r with a model m, and that our forecast is "perfect" in that m = sin(t). Construct v = r - m, which is the forecast error...
When I tell my non-statistical friends I am a grad student pursuing a PhD in statistics they naturally say "oh so you want to be a professor?". I tell them no I actually plan to work in industry. Then they respond with, "and do what?". I have not found a good response to this question. I want to give them a range o...
The title might be a bit misleading. Unfortunately statistics is not my area of forte, so gentle guidance along the right path is much appreciated. That said, here's my problem: I'm working on analyzing precise time measurements from an experimental process. I have 16 measurement groups. Of these, one should (on averag...
This is only for my high school senior project, so it doesn't have to be perfect. I'm doing a project on global warming, and I want to survey people for their opinions. I know that if I use a convenience sample of my classmates, I'll have a lot of bias. I was wondering if there was a site on the Internet where I could ...
I am looking for some statistics (and probability, I guess) interview questions, from the most basic through the more advanced. Answers are not necessary (although links to specific questions on this site would do well).
I am teaching myself DLM's using R's dlm package and have two strange results. I am modeling a time series using three combined elements: a trend (dlmModPoly), seasonality (dlmModTrig), and moving seasonality (dlmModReg). The first strange result is with the $f (one-step-ahead foreacast) result. Most of this forecast a...
Lets say for example a class of students and their grades are the data set. Lets say there are around 35 students. Here is what you know: Your mark The class average The median mark The standard deviation Are there any other conclusions about this data that can be made given this information? Thanks
I need to calculate the sample size required for an observational study in which incidence of disease is 19-29%. Population affected is 600,000 people. The study has two samples similar on baseline characteristics treated with two different drugs. Statistical analysis will be chi-square and Fisher's test. I have to d...
Assume we have a sensor field with dimension M*M. In order to apply any data compression technique, first I want to know what is the compression limit or minimum entropy of the entire sensor field. How could I compute the minimum entropy or compression limit for the sensor field? or Actually I want to have the theore...
Is there a principled way to estimate factor scores when you have ordinal, discrete variables. I have $n$ ordinal, discrete, variables. If I make the assumption that underlying each response is a continuous, normally distributed variable, then I can calculate an $n\times n$ polychoric correlation matrix. I can then run...
I think, I read this quote some where: For every field "x" there exists a field "computational x" Has anyone else read this or remembers reading anything close to this? If I remember correctly, it was by Dr. Jan de Leeuw. Can anyone please tell if my memory fails me here? (I could not find any link after a lot of goo...
The annual returns on stocks and treasury bonds over the next 12 months are uncertain. Suppose that these returns can be described by normal distributions with stocks having a mean of 15% and a standard deviation of 20%, and bonds having a mean of 6% and a standard deviation of 9%. Which asset is more likely to have ...
I'm using multinomial probit to estimate some parameters, and I keep seeing references to the fact that MNP was considered computationally "intractible" relative to binomial probit up until the early 21st century. The question is: why? I get that adding variables makes things take longer (I've got a background in CS), ...
Could anyone kindly provide an explanation (mathematically or non-mathematically) about the non-existence of the intercept term in conditional logistic regression? Is the interpretation of the coefficients similar to that of (unconditional) logistic regression?
The library languageR provides a method (pvals.fnc) to do MCMC significance testing of the fixed effects in a mixed effect regression model fit using lmer. However, pvals.fnc gives an error when the lmer model includes random slopes. Is there a way to do an MCMC hypothesis test of such models? If so, how? (To be ac...
I am wondering if there is any reasonably simple way of calculating the following problem: Drawing, with replacement, $n$ balls from a bin of $N$ different colored balls, with a known probability of drawing each color of ball, what is the expected number of "unique" balls, i.e., balls with no other ball of the same col...
Is there a way to get the number of parameters of a linear model like that? model <- lm(Y~X1+X2) I would like to get the number 3 somehow (intercept + X1 + X2). I looked for something like this in the structures that lm, summary(model) and anova(model) return, but I didn't figure it out. In case I don't get an answer,...
Working off a fairly limited statistical understanding, so apologies in advance if this question is ludicrously basic. This has to have happened to other people who have successfully solved this issue, but searching for what I think are relevant terms is getting me things like "Karlin's Conjecture for Random Replaceme...
I was reading Robert Serfling's 1980 book "Approximation Theorems of Mathematical Statistics" and came across the following construction of the Dvoretzky–Kiefer–Wolfowitz inequality for arbitrary distributions $F$, which DKW prove for distributions on $[0,1]$. Given independent $X_i$ with d.f. F and defined on a comm...
Background I am generally interested in learning appropriate methods of using data to specify priors. A previous question asks how to elicit priors from experts and received some good recommendations. Here, I am interested in learning how to specify a prior using data. I plan to use these priors in a meta-analysis to s...
I have found some distributions for which BUGS and R have different parameterizations: Normal, log-Normal, and Weibull. For each of these, I gather that the second parameter used by R needs to be inverse transformed (1/parameter) before being used in BUGS (or JAGS in my case). Does anyone know of a comprehensive list ...
I have to run repeated correlations. If one of them reach the significant value (as given in the Pearson table), how can I be sure that it isn't actually a false positive? I'm pretty new in the statistical analysis, so I apologize if my question seems naive. Thanks for any answers.
I want to perform model comparison according to several criteria using R. My dataframe's name is df head(df) Y X1 X2 X3 X4 1 18 307 130 3504 12.0 2 15 350 165 3693 11.5 3 18 318 150 3436 11.0 4 16 304 150 3433 12.0 5 17 302 140 3449 10.5 6 15 429 198 4341 10.0 I want to compare all possible combinations wit...
I've been having some trouble with this story problem. Any help you could give me would be really appreciated. A store manager monitors the store's temperature by taking 4 independent temperature readings at 4 locations where, if the system is working correctly, the temp. is normally distributed with a mean of 68 de...
What is the best way to divide Cross Validated/Stack Overflow/Server fault reputations into separate bins, considering reputation systems tend to be highly skewed? For example: Suppose I want a set of 64 bins - 0-250,250-500,500-100...10,000-11,000. Is there a method that takes into account the number of users that ha...
I have a random events generator. I know in advance the set of event that can be generated (in my case I have only three possible events). The probabilities of the events are not known. I need to estimate these probabilities. For that I run an experiment. For example I generate 20 events. So, I have a sequence of event...
Is there a 'limit' function in R? help(lim) or help(limit) weren't useful. And in general, is R suitable for mathematical computations?
I flip a coin 20 times and get 14 heads. I want to calculate the p-value of the hypothesis that my coin is fair. What probability should I calculate? Wikipedia says that I need to calculate the probability to get 14 or more heads in 20 flips. Why is it 14 "or more"? Why not 14 or less?
I recently fit 4 multiple regression models for the same predictor/response data. Two of the models I fit with Poisson regression. model.pois <- glm(Response ~ P1 + P2 +...+ P5, family=poisson(), ...) model.pois.inter <- glm(Response ~ (P1 + P2 +...+ P5)^2, family=poisson(), ...) Two of the models I fit with negative ...
I am planing a pre-post treatment-control design study with a large number of pre-treatment measurements. I have subjects divided into a control group and a treatment group. For both groups, I will collect hourly data for one year prior to the start of the treatment and then continue collecting data for another year. T...
I would like to create an "equilibrated histogram" with roughly the same number of data points in each bin. The second restriction I have is that I should have only 4 bins. Given the following list of numbers below, how can I achieve that? -2.153, -1.732, -1.699, -1.559, -1.355, -1.306, -1.151, -1.129, -0.636, 0.4085, ...
I have several OLS models with robust s.e.'s that predict an outcome variable Y. For instance: Model 1: $Y=B_0 +B_1X_1$ Model 2: $Y=B_0 + B_1X_1 + B_2X_2$ Model 3: $Y=B_0 +B_1X_1 + B_2X_2 +B_3X_3$ I am interested in giving an average effect for $B_1$ across Models 1-3 with an accompanied 95% CI. Can I just take the a...
Roughly speaking a p-value gives a probability of the observed outcome of an experiment given the hypothesis (model). Having this probability (p-value) we want to judge our hypothesis (how likely it is). But wouldn't it be more natural to calculate the probability of the hypothesis given the observed outcome? In more d...
As a biologist, many of the research projects I work on at some point involve collaboration with a statistician, whether it be for simple advice or for implementing and testing a model for my data. My statistics colleagues admit that they do a significant amount of collaboration, insomuch that the tenure review process...
I am trying to view the output from the GBM package for boosted trees in R. Below I am fitting a single tree without any sampling in order to compare the tree to the complete dataset. First, create the data set: set.seed(1973) ############## CREATE DATA############################################# N <- 1000 X1 <- ru...
I have data which has several properties (metadata, as key value pairs, where the keyspace is shared over the whole dataset) per object. I took a sample of objects and divided them in n groups according to an unknown algorithm. What statistical methods or algorithm exists to find the relevant properties and their weig...
How does one approach the problem of modeling a "birth-death process" where the arrivals are dependent on the current state in the following way: if the population is above a certain point, the probability of an arrival decreases. Basically, I'm interested in complicating (slightly) an existing model of "births" that j...