[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


	[[alternative HTML version deleted]]