Bayesian estimation of a longitudinal mediation model with three-level clustered data
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Longitudinal modeling allows researchers to capture changes in variables that take time to exert their effects. Furthermore, incorporating mediation into a longitudinal model allows for researchers to test causal inferences about, for example, how an independent variable might affect growth in an outcome variable through growth in a mediating variable. In scenarios in which multiple variables are measured over time, the parallel process model can be used to model the inter-relationships among the measures’ trajectories where both processes are modeled to have their own separate but related growth parameters. The hierarchical linear modeling (HLM) framework can be used to model a parallel process model and allows for easy extensions to handle multiple levels and non-hierarchical data, such as cross-classified or multiple membership data structures, in clustered data. This study assessed a three-level parallel process model couched in the context of longitudinal mediation where treatment was assigned at the cluster level, matching a longitudinal cluster randomized trial design. The treatment’s effect on growth in an outcome is modeled as mediated by the growth in a mediating variable at the cluster and individual level, resulting in a cross-level and cluster-level mediated effect. A simulation and real data analysis study were conducted using a fully Bayesian analysis. In the simulation study, the following four factors were manipulated to assess the recovery of the parameters of interest: mediated effect size, random effects variance component values, number of measurement occasions, and number of clusters. Overall, relative parameter bias and statistical power improved for higher values for each of the four factors. The cross-level mediated effects were less biased and had greater statistical power than the cluster-level mediated effects. For the mediated effects that were truly zero, coverage rates based on the highest posterior density intervals showed mostly acceptable rates for the cross-level mediated effect and when path b was zero paired with a non-zero path a for the cluster-level effect. For conditions with a true value of zero for the cluster-level mediated effect with a path a of zero, the cluster-level coverage rates provided over-coverage. Results are discussed along with clarification of study limitations and suggestions for future research. Recommendations for applied researchers are also noted.