BAYESIAN MODEL SELECTION FOR LONGITUDINAL RANDOM-EFFECTS MODELS

The popularity of the mixed model can be explained by its flexibility in modelling complex hierarchical data. Since the introduction of the basic mixed models—the linear mixed model (LMM), generalized linear mixed model (GLMM) and non-linear mixed model (NLMM)—a great variety of extensions have been suggested. For longitudinal studies, the mixed model consists of a fixed part expressing the effect of covariates on the mean evolution over time and a random part representing the variation of the individual curves around the mean curve. Selecting the appropriate fixed and random effect parts is an essential modelling exercise when choosing the best mixed model. As such, we considered three Bayesian model selection criteria: the Pseudo-Bayes factor (PSBF), Deviance Information Criteria (DIC) and Watanabe-Akaike Information Criterion (WAIC). Since there is little agreement in the statistical literature on the most suitable choice among these model selection criteria, it a useful exercise to evaluate their performance. The above criteria can be classified according to the way the random effects are handled: given the random effects (conditional likelihood) resulting in conditional model selection criteria; or integrating out the random effects (marginal likelihood), resulting in the marginal model selection criteria. Although the conditional criteria have been criticized in the statistical literature, applied Bayesians still use the conditional criteria since they are built-in standard Bayesian software.\\ The marginal model selection criteria have been advocated, but less attention has been paid to the LMM. Besides, it is surprising that almost no mention is made of the suboptimality of the conditional criteria. Therefore, we compared via extensive simulations the performance of the conditional and marginal versions of DIC, WAIC and PSBF on the classical LMM, to create also awareness of the problem. We also considered extensions of the classical LMM. The results confirm the superiority of the marginal criteria in all settings and scenarios of our simulations. To promote the usage of the marginal criteria among practitioners, we provided an R function capable of computing the three marginal and conditional criteria with a minimal computational cost. We further determined the effect of vague priors on the performance of the above Bayesian model selection criteria. More specifically, we evaluated the impact of vague priors for the covariance matrix of the random effects on selecting the correct LMM. For two or more random effects, we considered five different specifications of the Inverse-Wishart (IW) prior, four different separation techniques, one hierarchical prior and a joint prior. We showed that the choice of a vague prior has a relatively low to minimal impact on the marginal criteria, in contrast to the conditional criteria. But if the conditional criteria are to be used, then it is best to use a separation or a joint prior. Furthermore, we extended our exploration to check the performance of the model selection criteria to GLMMs for longitudinal count data. Since a GLMM does not have a closed-form likelihood like LMM, we, therefore, searched for efficient ways to compute the marginal criteria. Our computational procedure is based on the replication sampling approach in combination with importance sampling. We also provided an R function that computes the marginal model selection criteria for longitudinal Poisson models and their extensions. Finally, we explored the performance of the Bayesian model selection criteria in the context of multilevel mediation models, namely for the 1-1-1 mediation model. We again demonstrated the superiority of the marginal selection criteria over their conditional counterparts in the mediated longitudinal settings through simulation. We also showed that the above R function for LMM needs only little modification for multilevel mediation models. In total, we used four longitudinal clinical data sets and one longitudinal non-clinical data set to further illustrate the performance of the marginal and conditional criteria. These are Jimma infant survival study, Potthoff \& Roy dental study and Nigeria indigenous Chicken data sets for both LMM and priors sensitivities papers. We used Epilepsy seizure data set for GLMM count data paper. For the mediation paper; we made use of data from the LASA (Longitudinal Aging Study of the Amsterdam) study. We made use of the Bayesian software package JAGS in combination with R. The relevant code can found on https://ibiostat.be/online-resources/bayesian and in the supplementary material of the papers.

Jaar van publicatie:2020

Toegankelijkheid:Open