Three-step latent class analysis with inverse propensity weighting in the presence of differential item functioning

Bias-adjusted three-step latent class analysis (LCA) is a popular tool to relate external variables to latent class membership. The integration of causal inference techniques such as inverse propensity weighting (IPW) with LCA allows for addressing causal questions about the relationship between these external variables and the latent classes even when data is collected in an observational design. However, LCA’s key assumption of conditional independence between external variables and latent class indicators is often violated in practice. This is the case when external variables have direct effects on (some of) the latent class indicators, i.e., when a (nominal) covariate represents subgroups showing measurement non-invariance (MNI) or differential item functioning (DIF). Following the approach by Vermunt and Magidson (2021), we propose a modification of the bias-adjusted three-step LCA with IPW to account for DIF. Covariates causing DIF, specifically the treatment or exposure variable, should be included in the first step, that is, the estimation of the measurement model. Furthermore, in the third step, that is, the estimation of the structural model which includes IPW, the step-three classification error adjustment needs to be allowed to differ across the values of the DIF covariates. Additionally, we propose a modelbuilding strategy to identify if the treatment or exposure variable shows MNI or DIF. Our newly proposed approach is illustrated using a synthetic and a real-life data example and is implemented in the program Latent GOLD.