Model selection for Bayesian linear mixed models with longitudinal data: Sensitivity to the choice of priors

We explore the performance of three popular Bayesian model-selection criteria when vague priors are used for the covariance parameters of the random effects in a linear mixed-effects model (LMM) using an extensive simulation study. In a previous paper, we have shown that the conditional selection criteria perform worse than their marginal counterparts. It is known that for some ?vague? priors, their impact on the estimated model parameters can be non-negligible, e.g., for the priors of the covariance matrix of the random effects in a longitudinal LMM. We evaluate here the impact of vague priors for the covariance matrix of the random effects on selecting the correct LMM using classical Bayesian selection criteria. We consider marginal and conditional criteria. For the random intercept case, we assign different vague priors to the variance parameters. With two or more random effects, we considered five different specifications of inverse-Wishart (IW) prior, five different separation priors and a joint prior. The results show again the better performance of the marginal over the conditional criteria and the superiority of joint and separation priors over IW in all settings. We also illustrate the performance of the selection criteria on a practical dataset.