multinomial mixed logit model mlogit r-package

Question

I discovered the mlogit-package for multinomial logit models in search of estimating a multinomial mixed logit model. After reading the excellent vignette I discovered that I could not apply my data on any of the described examples.

I now write in hope of help with my problem and created a minimal example to illustrate my situation.

The Problem is as follows: There are words with the consonant 'Q' somewhere. Now an experiment was conducted with people who were tasked to listen to these words and say if they heard a Q, an U or some OTHER consonant. This has to modeled in dependence of some factors like syllable position or real/non-real-word.

In the minimal example I created 4 people and their answers with the syllable position.

library(mlogit)
library(nnet)
set.seed(1234)
data <- data.frame(personID = as.factor(sample(1:4, 40, replace=TRUE)),
               decision = as.factor(sample(c("Q","U", "other"), 40, replace=TRUE)),
               syllable = as.factor(sample(1:4, 40, replace=TRUE)))
summary(data)
 personID  decision  syllable
 1:11     other:10   1:18    
 2:10     Q    :18   2: 9    
 3:10     U    :12   3: 5    
 4: 9                4: 8 

As far as I know nnet's multinomfunction does not cover mixed models.

modNnet1 <- multinom(decision ~ syllable, data=data)

First I used the mlogit.data-function to reshape the file. After discussion with a colleague we came to the conclusion that there is no alternative.specific.variable.

 dataMod <- mlogit.data(data, shape="wide", choice="decision", id.var="personID")

 mod1 <- mlogit(formula = decision ~ 0|syllable,
           data = dataMod,
           reflevel="Q", rpar=c(personID="n"), panel=TRUE)
  Error in names(sup.coef) <- names.sup.coef : 
    'names' attribute [1] must be the same length as the vector [0]

 mod2 <- mlogit(formula = decision ~ personID|syllable,
           data = dataMod,
           reflevel="Q", rpar=c(personID="n"), panel=TRUE)
  Error in solve.default(H, g[!fixed]) : 
     Lapack routine dgesv: system is exactly singular: U[3,3] = 0

No I do not know what to do, so I ask for help in here. But I believe this kind of problem can be solved with mlogit and I just don't see it yet ;)

Answer 1

The rpar argument accepts only alternative-specific variables. There is no need to specify the person-specific id in the model formula -- this is handled by including id.var = something in the mlogit.data command. For example, if you had an alternative specific covariate acov, you could allow random slopes for acov across a panel:

N = 200
dat <- data.frame(personID = as.factor(sample(1:4, N, replace=TRUE)),
               decision = as.factor(sample(c("Q","U", "other"), N, replace=TRUE)),
               syllable = as.factor(sample(1:4, N, replace=TRUE)),
               acov.Q = rnorm(N), acov.U = rnorm(N), acov.other = rnorm(N))
dataMod <- mlogit.data(dat, shape="wide", choice="decision", id.var="personID", varying = 4:6)
mlogit(formula = decision ~ acov|syllable, rpar = c(acov = "n"), panel = T, data = dataMod)

It seems you are trying to fit a model with a random, person-specific intercept for each alternative (not random slopes). Unfortunately, I don't think you can do so in mlogit (but see this post).

One option that would work to fit random intercepts in the absence of alternative-specific covariates is MCMCglmm.

library(MCMCglmm)
priors = list(R = list(fix = 1, V = 0.5 * diag(2), n = 2),
              G = list(G1 = list(V = diag(2), n = 2)))
m <- MCMCglmm(decision ~ -1 + trait + syllable,
              random = ~ idh(trait):personID,
              rcov = ~ us(trait):units,
              prior = priors,
              nitt = 30000, thin = 20, burnin = 10000,
              family = "categorical",
              data = dat)

Relevant issues are prior selection, convergence of Markov chains, etc. Florian Jaeger's lab's blog has a short tutorial on multinomial models via MCMCglmm that you might find helpful, in addition to the MCMCglmm documentation.