The fundamental assumption in any latent variable model is that observations are independent of one another, given the latent status. However, this assumption is often inadequate when observations are nested within higher-level units because such nested data structures induce dependencies in data. The nonparametric version of the multilevel latent class model (MLCM) is an extension of latent class model (LCM) in which the dependencies in data are accounted for by discrete latent variables in the model. To date, such a modeling framework has been used in a wide variety of empirical applications. This paper aims to review models with discrete latent variables and introduce the MLCM which integrates LCM and random effect models. The model selection issue in the MLCM is also discussed with an empirical example.

키워드 :　Latent class analysis, Clustering, Multilevel modeling