Longtime lurker here.
I have a question about determining informative variables in generalized linear mixed models (GLMMs). My background is ecology, and I primarily examine habitat selection under a case-control (or "used-available") framework, typically using a binomial distribution.
Given that conventional GLMs are much easier and faster to fit than GLMMs, why is it not advisable to first determine the optimal fixed-effects structure in a fixed-effects only (conventional GLM) framework, and then determine the appropriate random effects?
My assumption here is that there would never be an informative parameter in a GLMM that is not also informative in an equivalently specified GLM, but not vice versa. Is this not the case?
I have read through Zuur et al. 2009, but they focus more on LMMs and recommend the opposite strategy (determine RE structure first using REML, then FE structure using ML). I've also read here that REML is perhaps poorly defined for GLMMs, so I don't know that their strategy is valid.