transform glmer model into MCMCglmm: how to define the priors?

Hi,

You will need priors for this model: the
observation-level (units) effects are not identifiable.
The random effect covariance structures are 2x2 matrices.
For these models I fix the residual covariance matrix at

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

where k is the number of categories in the response:


A starting prior might look something like:

prior=list(R=list(V=IJ, fix=1), G=list(G1=list(V=diag(2),
nu=2, alpha.mu=c(0,0), alpha.V=diag(2)*1000)))


Although I haven't seen it done (although I don't know
the literature on multinomial models) it might make sense
to have the random effect covarinace matrix proportional
to IJ and estimate a single variance component (rather
than a 2x2 covariance matrix). The rational behind the IJ
matrix is that the propensity to belong to a category
varies over random effects, but variation in the
propensity is equal for all categories, and the
propensity for two categories are uncorrelated. In
non-multinomial models such an assumption would be
represented by an identity matrix (i.e. trait:author) but
for multinomial models this is a bit trickier because
things are parameterised in terms of differences from a
base-line category.

The error you are getting does not look like it is a
MCMCglmm issue. Could you post the data (or a
reproducible example) so I can check?


Cheers,

Jarrod




Quoting Anne Krause
<anne.krause at frequenz.uni-freiburg.de> on Tue, 17 Mar
2015 18:06:48 +0100:

Dear list members,
I am a linguist who would like to use MCMCglmm in order

to

model change in language morphology. I have a 3-level
dependent variable (unordered) which are 3 realisations

of

a morphological form in German. Say, I call them A, B,

and

C - A and B share the same vowel, B and C share the
suffixation.
I did not know about MCMCglmm until recently; therefore

I

worked with two glmer models, looking at vowel and
suffixation separately. However, I have been criticised

for

the clumsy model interpretation, and I am sure that the
output of a MCMCglmm would be more straightforward and
convincing.

My glmer looks like this:
model <- glmer(vowel~frequency+year+recency+
                  frequency*recency+
                  (1|verb)+(1|author), data=imp,
                  family=binomial)
- where ?vowel? differentiates between AB on the one

hand

and C on the other hand,
- ?frequency? and ?year? are numeric fixed variables

and

?recency? a categorical fixed variable (7 levels),
- ?verb? and ?author? are categorical random variables

The model for the dependent variable ?suffix? is
practically the same (part of the criticism), ?suffix?
distinguishing between A on the one hand and BC on the
other hand.

Trying to transform this into an MCMCglmm, I managed to

get

as far as this:
model2 <- MCMCglmm(form~trait:frequency+trait:recency+
                  trait:year-1,
                  random=~us(trait):author,
                  rcov=~us(trait):units,
                  data=imp, family="categorical",)
(?form? now distinguishing between all 3 three levels

of

the dependent variable A, B, and C)

I am well aware that this model is running without

priors.

Whichever prior I tried gave me the error ?V is the

wrong

dimension for some prior$G/prior$R elements? and I have

no

idea (after reading through the general description,

the

tutorial, the course notes and entries in this mailing
list) how these priors are defined. I guess there is no
rule of thumb, but I hope this short explanation of my
variables is enough for someone of you to point out a
solution (or a starting point for me). I also need to
include the second random from above (?verb?) and the
interaction between ?frequency? and ?recency?.

Even though model2 is running, I cannot call the

summary

for it (error: ?Error in get(as.character(FUN), mode =
"function", envir = envir) :   object 'C:\Users\Anne
Krause\some_directory.Rdata' of mode 'function' was not
found?), which probably has to do with the fact that I

did

not include priors (?!).

Thank you so much in advance for help and/ or comments,
pointers or the like!

Best, Anne