Latent causal inference using the propensity score from latent class regression model

Abstract

Unlike randomized trial, statistical strategies for inferring the unbiased causal relationship are required in the observational studies. The matching with the propensity score is one of the most popular methods to control the confounders in order to evaluate the effect of the treatment on the outcome variable. Recently, new methods for the causal inference in latent class analysis (LCA) have been proposed to estimate the average causal effect (ACE) of the treatment on the latent discrete variable. They have focused on the application study for the real dataset to estimate the ACE in LCA. In practice, however, the true values of the ACE are not known, and it is difficult to evaluate the performance of the estimated the ACE. In this study, we propose a method to generate a synthetic data using the propensity score in the framework of LCA, where treatment and outcome variables are latent. We then propose a new method for estimating the ACE in LCA and evaluate its performance via simulation studies. Furthermore we present an empirical analysis based on data form the 'National Longitudinal Study of Adolescents Health,' where puberty as a latent treatment and substance use as a latent outcome variable.