[R-sig-ME] Multinomial mixed model in MCMCglmm, correcting for genealogy with random effects?

[Annemarie Verkerk]

Dear all,

I have a three-way response variable and a mixture of continuous &
categorical explanatory variables that I model in MCMCglmm. These are
linguistic data from related languages and I want to correct for
genealogy. I have given up on the idea of doing this with a full
phylogeny, which is possible in MCMCglmm but I cannot reach convergence.

So I have decided to use different grouping variables (representing
different hypotheses on how the languages are related). If I had a
continuous response variable, I would use random effects, both
intercepts & slopes if the model would converge, for the different
explanatory variables. If the slopes all point in the same direction for
the different groupings, I would feel confident that the effect of that
variable is relevant.

But with a categorical response variable, random effects seem to work
differently. I have read about them on prof. Bolker's github
(https://bbolker.github.io/mixedmodels-misc/ecostats_chap.html) where
they are also called "conditional modes", but he does not verbally
interpret the findings. Hence I have three questions:

1. Can I correct for genealogy using random effects?

2. How to interpret output like on Ben Bolker's page above? For
instance, if the CI of a grouping/family does not overlap with 0, does
that mean that grouping/family is divergent? If so, in what way is it
divergent? (To me, it seems like random effects for multinomial models
do not relate to the explanatory variables, which confuses me.)

3. Is my MCMCglmm code below correct for what I need to do (i.e. correct
for shared descent of the individual datapoints)?:

IJ <- (1/3) * (diag(2) + matrix(1, 2, 2))

prior = list(R = list(V = IJ, fix = 1),
             G=list(G1 = list(V = diag(2), n = 2)))

m_full <- MCMCglmm(factor(3way_response) ~ trait:(latitude + longitude +
cont1 + cont2 + cat1),
                   random = ~us(trait):grouping1,
                   rcov = ~us(trait):units,
                   prior = prior,
                   data = x,
                   family = "categorical",
                   verbose = FALSE,
                   nitt=550000000,
                   thin=1000000,
                   burnin=50000000,
                   pl=FALSE,
                   pr=TRUE,
                   slice=TRUE)

(I add "pr=TRUE" in the MCMCglmm call to get output on random effects in
m_full$Sol.)

Apologies for the long message, but I would be very, very thankful for
any help you can offer. Also pointers to good sources on how to
understand this aspect of multinomial regression are very welcome.

With best wishes,
Annemarie


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