Two-step multilevel latent class analysis in the presence of measurement non-equivalence

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.