# Two-Step Multilevel Latent Class Analysis in the Presence of Measurement Non-Equivalence

## TL;DR

This paper introduces a two-step method for analyzing clustered data when measurement items are not equivalent across groups.

## Contribution

The novelty is extending two-step estimation to handle measurement non-equivalence in latent class models.

## Key findings

- The proposed method correctly accounts for non-equivalence in measurement models.
- Simulation studies validate the properties of the two-step estimators.
- An applied example demonstrates the method's practical utility.

## Abstract

We consider estimation of two-level latent class models for clustered data, when the measurement model for the observed measurement items includes non-equivalence of measurement with respect to some observed covariates. The parameters of interest are coefficients in structural models for the latent classes given covariates. We propose a two-step method of estimation. This extends previously proposed methods of two-step estimation for models without non-equivalence of measurement by specifying the model used in the first step in such a way that it correctly accounts for non-equivalence. The properties of these two-step estimators are examined using simulation studies and an applied example.