Linear mixed models (LMMs) are popular to analyze repeated measurements with a Gaussian response. For longitudinal studies, the LMMs consist of a fixed part expressing the effect of covariates on the mean evolution in time and a random part expressing the variation of the individual curves around the mean curve. Selecting the appropriate fixed and random effect parts is an important modeling exercise. In a Bayesian framework, there is little agreement on the appropriate selection criteria. This paper compares the performance of the deviance information criterion (DIC), the pseudo-Bayes factor and the widely applicable information criterion (WAIC) in LMMs, with an extension to LMMs with skew-normal distributions. We focus on the comparison between the conditional criteria (given random effects) versus the marginal criteria (averaged over random effects). In spite of theoretical arguments, there is not much enthusiasm among applied statisticians to make use of the marginal criteria. We show in an extensive simulation study that the three marginal criteria are superior in choosing the appropriate longitudinal model. In addition, the marginal criteria selected most appropriate model for growth curves of Nigerian chicken. A self-written R function can be combined with standard Bayesian software packages to obtain the marginal selection criteria.
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 data set.
We explore the performance of three popular model-selection criteria for generalised linear mixed-effects models (GLMMs) for longitudinal count data (LCD). We focus on evaluating the conditional criteria (given the random effects) versus the marginal criteria (averaging over the random effects) in selecting the appropriate data-generating model. We advocate the use of marginal criteria, since Bayesian statisticians often use the conditional criteria despite previous warnings. We discuss how to compute the marginal criteria for LCD by a replication method and importance sampling algorithm. Besides, we show via simulations to what extent we err when using the conditional criteria instead of the marginal criteria. To promote the usage of the marginal criteria, we developed an R function that computes the marginal criteria for longitudinal models based on samples from the posterior distribution. Finally, we illustrate the advantages of the marginal criteria on a well-known data set of patients who have epilepsy.
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