I would like to perform a multivariate mixed model but am a bit confused about model selection for such models. I wonder if I could get some help here.
When fitting a univariate mixed model, to avoid biased estimates, people (such as in Bolker et al. 2009 and Zuur et al 2009) usually suggest using a 2-step model selection procedure; that is, starting with a full model but varying random effect to determine an optimal random effect structure first, and then varying the fixed effects included with the optimal random effects to find the best fixed-effect structure. Both the optimal random- and fixed-effects structure and be determined by comparing AIC.
But for multivariate mixed model fitting, I didn't find much discussion on the model selection procedure. I was therefore wondering:
When fitting a multivariate mixed model, should we follow the same 2-step model selection procedure as we usually do for a univariate mixed model, to avoid biased estimates?
If no, for Question 1, how to proceed sensible model selection for multivariate mixed models to determine the optimal random and fixed effects, especially with a package like MCMCglmm?