[R-sig-ME] Model selection for multivariate mixed models

[Yi-Hsiu Chen]

Dear List members,


I am trying to figure out what is sensible model/variable selection procedure for multivariate mixed model, especially with MCMCglmm. It seems to be a fundamental question but unfortunately I couldn’t find much discussion on this topic. I was wondering if I could have some help here.    

My major question is: is there a difference between model selection procedure for univariate mixed model and for multivariate mixed model?  

More specifically, I meant, when fitting a univariate mixed model, it has been suggested that (such as in Bolker et al. 2009 <https://www.sciencedirect.com/science/article/pii/S0169534709000196> and Zuur et al 2009 <https://www.springer.com/gp/book/9780387874579>  a 2-step model selection procedure should be performed to avoid biased estimates; 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.

For multivariate mixed models, I was just wondering if the same model selection procedure (i.e. starting with a full model) should be followed? Or it is less of a concern for multivariate mixed models, especially with Bayesian-based MCMCglmm?  

Thank you very much in advance. 

Best wishes
Yi-Hsiu
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