How to perform three-step latent class analysis in the presence of measurement non-invariance or differential item functioning

The practice of latent class (LC) modeling using a bias-adjusted three-step approach has become widely popular. However, the current three-step approach has one important drawback - its key assumption of conditional independence between external variables and latent class indicators is often violated in practice, such as when a (nominal) covariate represents subgroups showing measurement non-invariance (MNI) or differential item functioning (DIF). In this article, we demonstrate how the current three-step approach should be modified to account for MNI; that is, covariates causing DIF should be included in the step-one model and the step-three classification error adjustment should differ across the values of the DIF covariates. We also propose a model-building strategy that makes the new methodology practically applicable also when it is unknown which of the external variables cause DIF. The new approach, implemented in the program Latent GOLD, is illustrated using a synthetic and a real data example.

Automated summary

This article highlights a drawback in the current three-step approach used in latent class modeling, which is the assumption of conditional independence is often violated. The study proposes a modification to account for measurement non-invariance (MNI) and differential item functioning (DIF), as well as a new model-building strategy to address these issues practically. The new approach is implemented in the Latent GOLD program and demonstrated using synthetic and real data examples.