Multilevel Latent Class Enumeration and Cross-Level Measurement Invariance

Introduction: Utilizing latent class analysis (LCA) is becoming more common in school-based research. Previous work utilizing simulated data has explored single level class enumeration (e.g., Nylund, Asparouhov & Muthen, 2007) and has evaluated the performance of different approaches to parameterization of distribution of the multinomial latent class intercepts in a multilevel LCA (e.g., Finch & French, 2014). However, no study to date has specifically explored the impact of nested data on class enumeration or the impact of non-invariance in the latent class structure across levels of nesting to the same extent as has been done for multilevel factor analysis (e.g., Dunn, Masyn, Jones, Subramanian, & Koenen, 2015). The consequence of this inadequate methodological foundation is that studies employing mixture modeling may not have appropriately accounted for the multilevel nature of school-based datasets (cf., Henry & Muthén, 2010). Method: Simulation Study I examines the impact of variation in intraclass correlations (ICCs) on the level one class enumeration. We generate data from population models applying uniform ICCs (small, medium, and large) across all the level one latent class indicators as well as population models wherein the ICCs vary across the indictors. Four analysis models are considered including one that ignores the non-independence of observations. Simulation Study II examines the impact of cross-level non-invariance in latent class structure between level one and level two and the level two class enumeration. We generate data from two populations: 1) the level two latent class variable measured by the random multinomial intercepts of the level one latent class variable; and 2) the level two latent class variable measured by random effects of the level one latent class indicators. Results: For Study I, it is hypothesized that a multilevel model with random multinomial intercepts of the level one latent class variable will be necessary for uniformly high ICCs; a multilevel model with random effects on the latent class indicators will be required for non-uniform ICCs. For Study II, it is hypothesized that the latent class enumeration process will be biased, under- or over-extracting classes, depending on the nature of the mismatch between the analysis and population models. We believe the bias will be attenuated by use of an unstructured level one model. Discussion: The class enumeration process is an incredibly important part of latent class analysis, as such, biases introduced at this junction can lead to further biases in later analyses. As an increased number of researchers utilize multilevel data, the development of proper methodology to handle this data is greatly needed.