Multilevel Structural equation models are most often estimated from a frequentist framework via maximum likelihood. However, as shown in this article, frequentist results are not always accurate. Alternatively, one can apply a Bayesian approach using Markov chain Monte Carlo estimation methods. This simulation study compared estimation quality using Bayesian and frequentist approaches in the context of a multilevel latent covariate model. Continuous and dichotomous variables were examined because it is not yet known how different types of outcomes-most notably categorical-affect parameter recovery in this modeling context. Within the Bayesian estimation framework, the impact of diffuse, weakly informative, and informative prior distributions were compared. Findings indicated that Bayesian estimation may be used to overcome convergence problems and improve parameter estimate bias. Results highlight the differences in estimation quality between dichotomous and continuous variable models and the importance of prior distribution choice for cluster-level random effects.

The aim of the current article is to provide a brief introduction to Bayesian statistics within the field of health psychology. Bayesian methods are increasing in prevalence in applied fields, and they have been shown in simulation research to improve the estimation accuracy of structural equation models, latent growth curve (and mixture) models, and hierarchical linear models. Likewise, Bayesian methods can be used with small sample sizes since they do not rely on large sample theory. In this article, we discuss several important components of Bayesian statistics as they relate to health-based inquiries. We discuss the incorporation and impact of prior knowledge into the estimation process and the different components of the analysis that should be reported in an article. We present an example implementing Bayesian estimation in the context of blood pressure changes after participants experienced an acute stressor. We conclude with final thoughts on the implementation of Bayesian statistics in health psychology, including suggestions for reviewing Bayesian manuscripts and grant proposals. We have also included an extensive amount of online supplementary material to complement the content presented here, including Bayesian examples using many different software programmes and an extensive sensitivity analysis examining the impact of priors.

A review of the software Just Another Gibbs Sampler (JAGS) is provided. We cover aspects related to history and development and the elements a user needs to know to get started with the program, including (a) definition of the data, (b) definition of the model, (c) compilation of the model, and (d) initialization of the model. An example using a latent class model with large-scale education data is provided to illustrate how easily JAGS can be implemented in R. We also cover details surrounding the many programs implementing JAGS. We conclude with a discussion of the newest features and upcoming developments. JAGS is constantly evolving and is developing into a flexible, user-friendly program with many benefits for Bayesian inference.

The present study investigated (1) how social relationships with teachers and peers and self-esteem of students with social–emotional and behavioral difficulties (SEBD) in inclusive regular education (regular schools) and students with SEBD in exclusive special education (special schools) develop over time in comparison with each other and in comparison with their typically developing peers and (2) whether factors—present before students with SEBD received special education services—predicted social–emotional development in either educational setting. Thirty-six students with SEBD in regular schools, 15 students with SEBD in special schools, and 1,270 typically developing peers participated. We collected data when students with SEBD resided in regular education without additional support, and we followed the development of students with SEBD for 1.5 years with three additional measurements in either school setting. Data of typically developing peers were collected when they resided in a classroom of a participating student with SEBD. Using Bayesian statistics, we found that students with SEBD in special schools had more conflictual relationships with their teachers than typically developing peers, but these relationships improved over time. Students with SEBD in regular schools were less accepted among peers than typically developing students and peer acceptance was stable over time for all three groups. Self-esteem and development in self-esteem over time did not differ between groups. The current study shows that students with SEBD show different developmental trajectories in regular or special schools and that it is difficult to predict their social–emotional development by factors present before students with SEBD received special education services.

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