Longitudinal mediation analysis through generalised linear mixed models: a comparison of maximum-likelihood and Bayesian estimation

The main goal of mediation analysis is to estimate the indirect effect of an exposure on a response variable conveyed by an intermediate variable called mediator. Estimating the standard error and confidence interval of the indirect effect using maximum likelihood is challenging even in the traditional setting where each variable is measured a single time and all models are linear, and the issue is exacerbated for longitudinal non-Normal data. Multilevel models are widely used to address longitudinal data, but have some shortcomings in mediational settings. To overcome these issues, we propose to adopt a Bayesian perspective to derive the posterior distribution of the indirect effect in a multilevel modeling framework using Monte Carlo Markov Chains. We run a simulation study to compare the performance of maximum likelihood and Bayesian estimation approaches for either linear and nonlinear mediation models. In the linear case, the Bayesian approach outperforms maximum likelihood in terms of bias and coverage rate, while results are more nuanced in nonlinear cases. We conclude by presenting an empirical application to data on how family environment influences students’ attitudes.