[R-sig-ME] MCMCglmm zero inflated poisson model issue

[Rebecca Hooper]

Dear List,

I am building a zero inflated poisson model in MCMCglmm, and am
experiencing some issues with my model, specifically with prior
specification.

My response variable is number of offspring per year, and is 85% zeros. My
predictor variables are categorical: one has four levels (social style) and
one has three levels (time period). The random effect is individual
identity. My code is as follows:

#### main effects model ####

m1 <- MCMCglmm(N.OFFSPR.YR ~ trait-1 +
at.level(trait,1):tp +
at.level(trait,1):social.style,
random=~us(trait):ANIMAL_ID,
rcov=~us(trait):units,
prior=prior_overdisp,
data=rm,
family="zipoisson",
verbose=FALSE,
burnin = 15000,
pl = TRUE,
singular.ok=TRUE,
nitt=40000,
thin = 20)

#### interaction model ####

m2 <- MCMCglmm(N.OFFSPR.YR ~ trait-1 +
at.level(trait,1):tp +
at.level(trait,1):social.style*tp +
at.level(trait,1):social.style,
random=~us(trait):ANIMAL_ID,
rcov=~us(trait):units,
prior=prior_overdisp,
data=rm,
family="zipoisson",
verbose=FALSE,
burnin = 15000,
pl = TRUE,
singular.ok=TRUE,
nitt=40000,
thin = 20)

with prior as follows:

prior_overdisp <- list(R=list(V=diag(c(1,1)),nu=0.002,
fix=2),G=list(list(V=diag(c(1,1e-6)),nu=0.002, fix=2)))
as described by Bolker et al (2012) in their Owl example paper.

Originally, another variable was included in both these models, which was
continuous (year of life). Both models ran with no issues when this
variable was included - the model converged and chains mixed well. I no
longer wish to include the continuous variable though, and without it
neither model runs. I get the error message:

Mixed model equations singular: use a (stronger) prior

I don't know what to make of this, and am loathe to mess around with my
prior specification without fully understanding what it is I am doing. I
would be very grateful for any help and direction in the matter!

Many thanks,
Beki (master's student extremely new to bayesian stats)

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