[R-sig-ME] about graphical checking on glmm and contradiction between parsimony and AIC values

[glenda mendieta]

Dear list members,
I am running GLMMs with count data, Laplace approximation, poisson 
family, using glmer {lme4}, the last version of R and R studio in 
windows platform.
When fitting my final models, I run an anova to look at the 
"significance" of a term inclusion (random effect term), of course, this 
does not apply for random effects, but at least it gives me differences 
in DFs and whether the models are significantly different or not.
It basically tells me that the least parsimonious model is the one with 
the lowest AIC value. As you can see below the difference in AIC values 
is pretty big.

 > anova(g,gwi)
Data: db.e
Models:
gwi: abundance ~ census * avail.surface + (1 | tree) + (1 | spp)
g: abundance ~ census * avail.surface + (1 | tree) + (1 | spp) +   (1 | 
spp:tree)
         Df     AIC     BIC   logLik Chisq Chi Df Pr(>Chisq)
gwi  12 22342.0 22442.9 -11159.0
g      13  9702.5  9811.8  -4838.3 12641      1 < 2.2e-16 ***

Then I run a qqplot on residuals vs. fitted values for each model and I 
can see that the more parsimonious model (*gwi*) is the one with the 
better fit (the points are pretty well alined across a straight line); 
whereas in the other model (*g*) the points are in a curved line.
Would this be because random crossed effects should not be included as 
an interaction term (like in the last model [g]) (Johnson & Omland, 
2004)? or I am overfiting?

My intuition tells me I should go for the most parsimonious model, since 
the graphical checking works. But, I wonder if there any advise you can 
give me to improve the fit of this model?. There is still a lot of 
variance unexplained there, the model with the random effect interaction 
term "spp:tree" has a variance of 59.87 sd. 7.73, in comparison to the 
model with only tree and spp (2.45 sd. 1.55 & 3.5 sd. 1.90).

Greetings and thanks in advance for your time,

Glenda Mendieta-Leiva
PhD candidate
University of Oldenburg

PS.  Johnson, J. B. and Omland, K. S. 2004. Model selection in ecology 
and evolution. Trends Ecol. Evol. 19: 101-108.