[R-sig-ME] lmer, poisson family and offset variable

[Ivar Herfindal]

Dear Mixed-Models-list

In poisson models, it can often be convenient with an offset variable, 
in order to account for known linear relationships that influence the 
counts (number of occurrences), e.g. observation time or patch size. In 
glm, (and, I hope, lmer), this is simply added as e.g. 
offset(log(exposure.time)) in the formula. This seems to work fine for 
me, and the parameter estimates, se and z-statistics seems reasonable. 
However, when I try the mcmcsamp to look at the distribution of the 
estimates, it looks horrible. Adding exposure time as fixed factor (i.e. 
log(exposure.time)) in the model instead of as an offset gives 
distributions that are reasonable and as expected. Do anyone know if 
offset is compatible with lmer and/or mcmcsamp, or can explain why the 
distribution become so weird when using exposure time as offset variable 
compared to as a fixed variable? Am I doing something completely wrong 
here?

I provide a short example below (the data is perhaps not very realistic 
in terms of values, but provide a a design close to the one I am using. 
It works as an example to show you how the distribution looks like with 
exposure time as offset or fixed variable).

Otherwise, the lme4 package works wonderful and is the package I use 
most frequent in R. Thanks a lot to the developer(s).

Sincerely

Ivar Herfindal

##
set.seed(100)
testdata <- cbind.data.frame(
    Obs=rpois(50, 20),
    gr=rep(1:10, 5),
    fixed=rnorm(50))
testdata$exp.time <- testdata$Obs - (rnorm(50, 1,1))
mod.offset <- lmer(Obs ~ offset(log(exp.time)) + fixed + (1|gr), 
data=testdata, family=poisson)
mod.offset.mcmcsamp <- mcmcsamp(mod.offset, 10000)
mod.no.offset <- lmer(Obs ~ (log(exp.time)) + fixed + (1|gr), 
data=testdata, family=poisson)
mod.no.offset.mcmcsamp <- mcmcsamp(mod.no.offset, 10000)

# histogram of parameter distribution with offset
windows()
par(mfrow=c(2,2))
for(i in 1:3)
hist(mod.offset.mcmcsamp[,i], col="gray", 
main=colnames(mod.offset.mcmcsamp)[i])

# histogram of parameter distribution without offset
windows()
par(mfrow=c(2,2))
for(i in 1:4)
hist(mod.no.offset.mcmcsamp[,i], col="gray", 
main=colnames(mod.no.offset.mcmcsamp)[i])

##
sessionInfo()
R version 2.4.1 (2006-12-18)
i386-pc-mingw32
attached base packages:
[1] "stats"     "graphics"  "grDevices" "utils"     "datasets"  
"methods"   "base"    

other attached packages:
       lme4      Matrix     lattice
"0.9975-11"  "0.9975-8"   "0.14-16"