# mixed logit model

### Updated slides on GLM, GLMM, plyr, etc. available

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Some of you asked for the slides to the Mixed effect regression class I taught at the 2013 LSA Summer Institute in Ann Arbor, MI. The class covered some Generalized Linear Model, Generalized Linear Mixed Models, extensions beyond the linear model, simulation-based approaches to assessing the validity (or power) of your analysis, data summarization and visualization, and reporting of results. The class included slides from Maureen Gillespie, Dave Kleinschmidt, and Judith Degen (see above link). Dave even came by to Ann Arbor and gave his lecture on the awesome power of plyr (and reshape etc.), which I recommend. You might also just browse through them to get an idea of some new libraries (such as Stargazer for quick and nice looking latex tables). There’s also a small example to work through for time series analysis (for beginners).

Almost all slides were created in knitr and latex (very conveniently integrated into RStudio — I know some purists hate it, but comm’on), so that the code on the slides is the code that generated the output on the slides. Feedback welcome.

### Is my analysis problematic? A simulation-based example

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This post is in reply to a recent question on in ling-R-lang by Meredith Tamminga. Meredith was wondering whether an analysis she had in mind for her project was circular, causing the pattern of results predicted by the hypothesis that she was interested in testing. I felt her question (described below in more detail) was an interesting example that might best be answered with some simulations. Reasoning through an analysis can, of course, help a lot in understanding (or better, as in Meredith’s case, anticipating) problems with the interpretation of the results. Not all too infrequently, however, I find that intuition fails or isn’t sufficiently conclusive. In those cases, simulations can be a powerful tool in understanding your analysis. So, I decided to give it a go and use this as an example of how one might approach this type of question.

### Tutorial on Regression and Mixed Models at Penn State

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Last week (02/3-5/10), I had the pleasure to give the inaugural CLS Graduate Student Young Scientist Colloquium (“An information theoretic perspective on language production”) at the Center for Language Science at Penn State (State College).

I also gave two 3h-lectures on regression and mixed models. The slides for Day 1 introduce linear regression, generalized linear models, and generalized linear mixed models.  I am using example analyses of real psycholinguistic data sets from Harald Baayen’s languageR library (freely available through the free stats package R). The slides for Day 2 go through problems and solutions for regression models. For more information have a look at the online lectures available via the HLP lab wiki. I’ve uploaded the pdf slides and an R script. There also might be a pod cast available at some point. Feedback welcome. I’ll be giving a similar workshop at McGill in May, so watch for more materials.

I had an intensive and fun visit, meeting with researchers from Psychology, Communication and Disorders, Linguistics, Spanish, German, etc.  I learned a lot about bilingualism (not only though)  and a bit about anticipatory motor planning. So thanks to everyone there who helped to organize the visit, especially Jorge Valdes and Jee Sook Park. And thanks to Judith Kroll for the awesome cake (see below). Goes without saying that it was a pleasure meeting the unofficial mayor of State College, too ;). See you all at CUNY! Read the rest of this entry »

### Some thoughts on the sensitivity of mixed models to (two types of) outliers

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Outliers are a nasty problem for both ANOVA or regression analyses, though at least some folks  consider them more of a problem for the latter type of analysis. So, I thought I post some of my thoughts on a recent discussion about outliers that took place at CUNY 2009. Hopefully, some of you will react and enlighten me/us (maybe there are some data, some simulations out there that may speak to the issues I mention below?). I first summarize a case where one outlier out of 400 apparently drove the result of a regression analysis, but wouldn’t have done so if the researchers had used ANO(C)OVA. After that I’ll have some simulation data for you on  another type of “outlier” (I am not even sure whether outlier is the right word): the case where a few levels of a group-level predictor may be driving the result. That is, how do we make sure that our results aren’t just due to item-specific or subject-specific properties. Read the rest of this entry »

### Nagelkerke and CoxSnell Pseudo R2 for Mixed Logit Models

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What to do when you need an intuitive measure of model quality for your logit (logistic) model? The problem is that logit models don’t have a nice measure such as R-square for linear models, which has a super intuitive interpretation. However, several pseudo R-square measures have been suggested are some are more commonly used (e.g. Nagelkerke R2). In R, some model-fitting procedures for ordinary logistic regression provide the Nagelkerke R-square as part of the standard output (e.g. lrm in Harrell’s Design package). However, no such measure is provided for the most widely used mixed logit model-fitting procedure (lmer in Bates’ lme4 library). Below I provide some code that provides Nagelkerke and CoxSnell pseudo R-squares for mixed logit models. Read the rest of this entry »

### Multinomial random effects models in R

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This post is partly a response to this message. The author of that question is working on ordered categorical data. For that specific case, there are several packages in R that might work, none of which I’ve tried. The most promising is the function `DPolmm()` from DPpackage. It’s worth noting, though, that in that package you are committed to a Dirichlet Process prior for the random effects (instead of the more standard Gaussian). A different package, mprobit allows one clustering factor. This could be suitable, depending on the data set. MNP, mlogit, multinomRob, vbmp, `nnet`, and msm all offer some capability of modeling ordered categorical data, and it’s possible that one of them allows for random effects (though I haven’t discovered any yet). MCMCpack may also be useful, as it provides MCMC implementations for a large class of regression models. `lrm()` from the `Design` package handles ordered categorical data, and clustered bootstrap sampling can be used for a single cluster effect.

I’ve recently had some success using MCMCglmm for the analysis of unordered multinomial data, and want to post a quick annotated example here. It should be noted that the tutorial on the CRAN page is extremely useful, and I encourage anyone using the package to work through it.

I’m going to cheat a bit in my choice of data sets, in that I won’t be using data from a real experiment with a multinomial (or polychotomous) outcome. Instead, I want to use a publicly available data set with some relevance to language research. I also need a categorical dependent variable with more than two levels for this demo to be interesting. Looking through the data sets provided in the `languageR` package, I noticed that the `dative` data set has a column `SemanticClass` which has five levels. We’ll use this as our dependent variable for this example. We’ll investigate whether the semantic class of a ditransitive event is influenced by the modality in which it is produced (spoken or written).

```library(MCMCglmm)
data("dative", package = "languageR")

k <- length(levels(dative\$SemanticClass))
I <- diag(k-1)
J <- matrix(rep(1, (k-1)^2), c(k-1, k-1))

m <- MCMCglmm(SemanticClass ~ -1 + trait + Modality,
random = ~ us(trait):Verb + us(Modality):Verb,
rcov = ~ us(trait):units,
prior = list(
R = list(fix=1, V=0.5 * (I + J), n = 4),
G = list(
G1 = list(V = diag(4), n = 4),
G2 = list(V = diag(2), n = 2))),
burnin = 15000,
nitt = 40000,
family = "categorical",
data = dative)```

Read on for an explanation of this model specification, along with some functions for evaluating the model fit.

### Jaeger (2008), J Memory Language, 59, 434-446 (ANOVA)

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Since I get asked for the R code I promised in my 2008 JML paper on mixed logit models every now and then, I have posted it here. If you find this code useful, please consider citing the Jaeger (2008) paper:

Please note, however, that the data analyzed in that paper is not mine and you need to acquire it from the Inbal Arnon, who conducted the study. With Inbal’s permission, here’s the data file I used:

• Data from the comprehension component of Study 2 from Arnon, Inbal. “Rethinking child difficulty: The effect of NP type on children’s processing of relative clauses in Hebrew.” Journal of Child Language 37.01 (2010): 27-57.

If you try to work your way through my paper, you may also find the following wiki pages from our lab with readings and more code helpful:

http://wiki.bcs.rochester.edu/HlpLab/StatsCourses/

As a quick intro you may find the talks from a recent workshop on the conceptual background, common issues and solutions for ordinary and multilevel regression models that some colleagues (Dale Barr, Roger Levy, Harald Baayen, Victor Kuperman, Austin Frank) and I gave at the CUNY sentence processing conference 2009 useful. The talk slides are all linked to the schedule on that page. You’ll find detailed walk-throughs, R code, and a conceptual overviews.

I appreciate if you leave a comment here in case this was useful. It helps to see what we should be posting. cheers.