Structural indeterminacy among the multilevel discrete latent variables in the multilevel latent class model (MLCM) is discussed in this paper. Three scenarios - non-full-rank, independent, and permutation indeterminacy - are presented with theoretical explanations and proofs of each structural indeterminate case. Numerical examples are also included to provide intuitive and conceptual understanding of structural indeterminacy. The awareness of the structural indeterminacy in applying the MLCM to data is highlighted in the discussions. Researchers are giving examples and directions to check for problematic structures to ensure their final model has a theoretically sound latent structure when modeling data with multilevel discrete latent variables.
주제어: Multilevel Latent Class Model, Model Indeterminacy, Model Identification