mixed multinomial models

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).

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.

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