[R-sig-ME] Selecting random effects in lme4: ML vs. QAICc

[Richard Feldman]

Hello all,

I am trying to select between two models that differ in their random 
effects. Running a likelihood test gives me a different result than 
using information criteria.

My models:

model.1 <- glmer(Y ~ V1 + V2 + V1:V2 + (V2|SITE), data=Data, family = 
quasipoisson, REML = TRUE)

model.2 <- glmer(Y ~ V1 + V2 + V1:V2 + (1|SITE), data=Data, family = 
quasipoisson, REML = TRUE)

I use quasipoisson because they are highly overdispersed:

lme4:::sigma(model.1)
#5.886659
lme4:::sigma(model.2)
#101.6434

The results of the likelihood test:
(I know that technically one should not use (RE)ML for 
quasi-distributions. However the results are nearly identical whether I 
use quasipoisson or poisson as the family)

anova(model.2, model.1)

#         Df    AIC    BIC   logLik  Chisq Chi Df Pr(>Chisq)
#model.2  9 4648.3 4665.1 -2315.13
#model.1 14  346.8  373.0  -159.39 4311.5      5  < 2.2e-16 ***

Now, I run the same models with a poisson distribution and then adjust 
the AIC by the overdispersion and the number of parameters to obtain 
QAICc. With all these penalties taken into account, model.2 has the 
lowest QAICc. My gut instinct is to go with model.1, however, because 
the overdispersion of model.2 is so high that perhaps it shouldn't even 
be a candidate model. On the other hand, perhaps adjusting the AIC 
really does put the two models on a more level playing field.

Does anyone in the community have any guidance on this matter?

Much appreciated and thanks in advance!

Richard

-- 
Richard Feldman, PhD Candidate
Dept. of Biological Sciences, McGill University
W3/5 Stewart Biology Building
1205 Docteur Penfield
Montreal, QC H3A 1B1
514-212-3466
richard.feldman at mail.mcgill.ca