Exact mediation analysis for ordinal outcome and binary mediator

TL;DR

This paper introduces an exact, model-based method for estimating causal direct and indirect effects in mediation analysis with an ordinal outcome and binary mediator, extending previous approximations.

Contribution

It provides a precise parametric formulation for causal effects in this setting, along with practical R routines for implementation.

Findings

Exact formulas for causal effects are derived.

Method can be implemented with standard software.

Bootstrap methods are used for standard error estimation.

Abstract

With reference to a single mediator context, this brief report presents a model-based strategy to estimate counterfactual direct and indirect effects when the response variable is ordinal and the mediator is binary. Postulating a logistic regression model for the mediator and a cumulative logit model for the outcome, the exact parametric formulation of the causal effects is presented, thereby extending previous work that only contained approximated results. The identification conditions are equivalent to the ones already established in the literature. The effects can be estimated by making use of standard statistical software and standard errors can be computed via a bootstrap algorithm. To make the methodology accessible, routines to implement the proposal in R are presented in the Appendix. A natural effect model coherent with the postulated data generating mechanism is also derived.