Abstract:
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We present copula structural equation models that provide a unified mediation analysis for variables of mixed types, including continuous, categorical, count variables. Similar to the classical structural equation model, the proposed copula model allows to specify the triangular relationships where confounders enter via generalized linear models. Based on the resulting joint parametric distributions of outcome variable, mediator and exposure variable of interest, we develop the maximum likelihood estimation and inference to evaluate casual pathways for direct and/or indirect effects of exposure variable on mediator and outcome variables. The proposed model also enables us to identify important mediators with which exposure variable has indirect effects. We examine necessary model assumptions for the identifiability of casual effects and establish asymptotic properties. We compare the performance of the proposed method with other existing methods using simulation studies. We apply the proposed method to assess if, and if so how, timing of the infancy peak may mediate the association of prenatal exposure to endocrine disrupting chemicals (e.g. phthalates) on child growth outcome.
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