Finite mixture models provide a flexible framework to study unobserved entities and have arisen in many statistical applications. The flexibility of these models in adapting various complicated structures makes it crucial to establish model identifiability when applying them in practice to ensure study validity and interpretation. However, researches to establish the identifiability of finite mixture model are limited and are usually restricted to a few specific model configurations. Conditions for model identifiability in the general case have not been established. In this paper, we provide conditions for both local identifiability and global identifiability of a finite mixture model. The former is based on Jacobian matrix of the model, and the latter is based on decomposition of three-way contingency table. The results are derived for a general finite mixture model, which allows for continuous, discrete or mix-typed manifest variables, ordinal or nominal latent groups, and flexible inclusion of covariates. We also provide intuitive explanation of the conditions and discuss the effect of including covariates in the model.
Statistical Methodology | Statistical Theory
Wang, Zheyu and Zhou, Xiao-Hua, "Nonparametric Identifiability of Finite Mixture Models with Covariates for Estimating Error Rate without a Gold Standard" (April 2014). UW Biostatistics Working Paper Series. Working Paper 403.