[R-sig-ME] AICc and lmer

[Benjamin Risk]

This question is related to the discussion started by Duncan Gillespie
on glmm AIC/LogLik reliability and Ben Bolker's comments. I am trying
to use lmer to rank 22 log-linear models with unbalanced repeated
sampling of bird density at 11 sites, where all models contain
(~1|site) and models differ in their fixed effects (and for the most
part are not nested). I have been using REML and AICc.  From previous
discussions, it appears I should be using ML instead of REML, and that
AICc may be inappropriate.

I have between 6 and 8 parameters and 60 observations in my candidate
set. I am doing two analyses, one examining the effect of habitat
covariates on bird density, the second examining the effect of habitat
covariates on bird richness density (species/hectare). In both
analyses, the AICc's are somewhat different from the AICs, roughly 1-2
units, and ranking with AIC would change the ordering somewhat. At the
end of the analysis, I make inferences about the role of different
water depths and depth diversity on bird density (first analysis) and
on bird richness density (second analysis). Water depth diversity
comes out as more supported than various measures of water depth in
both analyses. For the shorebird density analysis, the delta AICs are
not that large, and I have been playing around using model averaging
and bootstrapping model-averaged estimates. For the richness density
analysis, a model containing depth diversity and a second model
containing depth diversity and a quadratic of depth diversity are
similarly supported, but models containing water depth variables have
delta AICc's>5. I've left out many of the details in the interest of
trying to present the crux of the problem--hopefully this makes sense!
Is it inappropriate to use AICc in these models with fairly small
sample sizes?


Thank you,
Ben Risk
Master's Student
Beissinger Lab, Environmental Science, Policy, and Management at UC Berkeley