# Counterfactual Mediation Analysis with a Latent Class Exposure

## TL;DR

The paper introduces a new method called uPCD to better analyze how latent classes affect outcomes in counterfactual mediation models.

## Contribution

The novel contribution is the development of the updated pseudo class draws (uPCD) method for counterfactual mediation analysis with latent classes.

## Key findings

- uPCD shows minimal bias in estimating counterfactual mediation effects across all entropy levels.
- uPCD performs similarly to existing recommended methods but offers greater flexibility.
- The method can be used with any commonly-used counterfactual mediation approach.

## Abstract

Latent classes are a useful tool in developmental research, however there are challenges associated with embedding them within a counterfactual mediation model. We develop and test a new method “updated pseudo class draws (uPCD)” to examine the association between a latent class exposure and distal outcome that could easily be extended to allow the use of any counterfactual mediation method. UPCD extends an existing group of methods (based on pseudo class draws) that assume that the true values of the latent class variable are missing, and need to be multiply imputed using class membership probabilities. We simulate data based on the Avon Longitudinal Study of Parents and Children, examine performance for existing techniques to relate a latent class exposure to a distal outcome (“one-step,” “bias-adjusted three-step,” “modal class assignment,” “non-inclusive pseudo class draws,” and “inclusive pseudo class draws”) and compare bias in parameter estimates and their precision to uPCD when estimating counterfactual mediation effects. We found that uPCD shows minimal bias when estimating counterfactual mediation effects across all levels of entropy. UPCD performs similarly to recommended methods (one-step and bias-adjusted three-step), but provides greater flexibility and scope for incorporating the latent grouping within any commonly-used counterfactual mediation approach.