Three-Step Latent Class Analysis with Inverse Propensity Weighting in the Presence of Differential Item Functioning

The integration of causal inference techniques such as inverse propensity weighting (IPW) with latent class analysis (LCA) allows for estimating the effect of a treatment on class membership even with observational data. In this article, we present an extension of the bias-adjusted three-step LCA with IPW, which allows accounting for differential item function (DIF) caused by the treatment or exposure variable. Following the approach by Vermunt and Magidson, we propose including treatment with its direct effect on the class indicators in the step-one model. In the step-three model we include the IPW and account for the fact that the classification errors differ across treatment groups. DIF caused by the confounders used to create the propensity scores turns out to be less problematic. Our newly proposed approach is illustrated using a synthetic and a real-life data example and is implemented in the program Latent GOLD.