Mediation Analysis with Zero-inflation Using Factored Structural Equation Modeling

Abstract Mediation analysis with zero-inflated count variables often concerns associations with the overall expected count, whereas traditional zero-inflated models yield component-specific interpretations. This article integrates marginalized zero-inflated Poisson (mZIP) modeling with derivative-based mediation within the factored structural equation modeling (FSEM) framework. We formulate conditional indirect effects when either the mediator or the outcome is zero-inflated and incorporate a measurement model for a latent predictor. The measurement and structural submodels are jointly estimated within a Bayesian framework. A simulation study evaluates point estimation and interval coverage with an observed predictor and an mZIP mediator. For nonzero effects, estimation generally became more accurate as sample size increased, with coverage of 95% credible intervals ranging from 91.4% to 95.8%. An application to 952 participants from the Manitoba Follow-up Study examines the indirect association between latent social engagement and functional limitations through mental health. Greater engagement was associated with fewer expected limitations indirectly through better mental health, after adjustment for age. The formulation connects marginal-mean modeling with local, response-scale indirect associations and supports joint analysis of latent constructs and zero-inflated counts.