Bayesian mediation analysis for partially clustered designs

Partially clustered design is common in medicine, social sciences, intervention and psychological research. With some participants clustered and others not, the structure of partially clustering data is not parallel. Despite its common occurrence in practice, limited attention has been given regarding the evaluation of intervention effects in partially clustered data. Mediation analysis is used to identify the mechanism underlying the relationship between an independent variable and a dependent variable via a mediator variable. While most of the literature is focused on conventional frequentist mediation models, no research has studied a Bayesian mediation model in the context of a partially clustered design yet. Therefore, the primary objectives of this paper are to address conceptual considerations in estimating the mediation effects in the partially clustered randomized designs, and to examine the performances of the proposed model using both simulated data and real data from the Early Childhood Longitudinal Study, Kindergarten Class of 1998-99 (ECLS-K). A small-scale simulation study was also conducted and the results indicate that under large sample sizes, negligible relative parameter bias was found in the Bayesian estimates of the indirect effects and of covariance between the components of the indirect effect. Coverage rates for the 95% credible interval for these two estimates were found to be close to the nominal level. These results supported use of the proposed Bayesian model for partially clustered mediation in conditions when the sample size is moderately large.