Automatic Mediation Analysis Under Measurement Error Via Bayesian Machine Learning

This paper considers the problem of causal mediation analysis (CMA) when the outcome, mediator, or both are modeled as latent variables that are measured with error from multiple indicators. Traditional structural equation modeling approaches rely on restrictive parametric assumptions and struggle to capture nonlinear relationships or interactions among covariates, outcomes, and mediators; additionally, accounting for measurement error is difficult when nonlinearities are present. We address these challenges using Bayesian causal mediation forests to model the structural relationships, which were shown by Linero and Zhang to perform well for estimating mediation effects. To infer the latent variables, we consider (a) a full hierarchical Bayesian model and (b) an approximation based on composite scores that is easier to implement. We evaluate our approach through simulation experiments and apply our methodology to data from the Advanced Cognitive Training for Independent and Vital Elderly (ACTIVE) study, which is a publicly available, large-scale, multi-site randomized controlled trial designed to evaluate the effectiveness of cognitive training interventions in order to improve the cognitive abilities of older adults. We find a nonlinear relationship between the ability to perform daily activities (the outcome) and reasoning ability (the mediator), with reasoning training improving the outcome through the mediator.