Hierarchical models are extensively used in pharmacokinetics and longitudinal studies. When the estimation is performed from a Bayesian approach, model comparison is often based on the deviance information criterion (DIC). In hierarchical models with latent variables, there are several versions of this statistic: the conditional DIC (cDIC) that incorporates the latent variables in the focus of the analysis and the marginalized DIC (mDIC) that integrates them out. Regardless of the asymptotic and coherency difficulties of cDIC, this alternative is usually used in Markov chain Monte Carlo (MCMC) methods for hierarchical models because of practical convenience. The mDIC criterion is more appropriate in most cases but requires integration of the likelihood, which is computationally demanding and not implemented in Bayesian software. Therefore, we consider a method to compute mDIC by generating replicate samples of the latent variables that need to be integrated out. This alternative can be easily conducted from the MCMC output of Bayesian packages and is widely applicable to hierarchical models in general. Additionally, we propose some approximations in order to reduce the computational complexity for large-sample situations. The method is illustrated with simulated data sets and 2 medical studies, evidencing that cDIC may be misleading whilst mDIC appears pertinent.

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.

AimWe aimed to investigate whether the 12-item Multidimensional Scale of Perceived Social Support (MSPSS) constitutes a valid and reliable measure of social support for the general adult Australian population.MethodsData were from Australia’s National Survey of Adult Oral Health 2004–2006 and included 3899 participants aged 18 years old and over. The psychometric properties were evaluated with Bayesian confirmatory factor analysis. One-, two-, and three-factor (Significant Other, Family and Friends) structures were tested. Model fit was assessed with the posterior predictive p-value (PPPχ2), Bayesian root mean square error of approximation (BRMSEA), and Bayesian comparative fit index (BCFI). Dimensionality was tested by comparing competing factorial structures with the Bayes factor (BF). Reliability was evaluated with the Bayesian ΩH. Convergent validity was investigated with the Perceived Stress Scale (PSS) and discriminant validity with the Perceived Dental Control scale (PDC-3).ResultsThe theoretical three-factor model (Significant Other, Family, and Friends) provided a good fit to the data [PPPχ2 < 0.001, BRMSEA = 0.089-95% credible interval (CrI) (0.088, 0.089); BCFI = 0.963-95% CrI (0.963, 0.964)]. The BF provided decisive support for the three-factor structure in relation to the other structures. The SO [BΩH = 0.95 - 95% CrI (0.90, 0.99)], FA (BΩH = 0.92 - 95% CrI (0.87, 0.97), and FR (BΩH = 0.92 - 95% CrI (0.88, 0.97)] subscales displayed excellent reliability. The MSPSS displayed initial evidence of convergent and discriminant validity.ConclusionThe MSPSS demonstrated good psychometric properties and excellent reliability in a large Australian sample. This instrument can be applied in national surveys and provide evidence of the role of social support in the Australian population.

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.