Modeling Possibilities With Multilevel Latent Class Analysis

• In Event: Multilevel Latent Variable Models: The Next Generation

Abstract

Traditional single-level latent class analysis (LCA) assumes that all individuals or observations are independent of each other. This assumption is commonly not met in educational datasets (e.g., students are clustered within a classroom, teachers within a district, schools within a community) and as a result the parameters estimates of the single-level LCA model are often biased when ignoring the clustering units. Taking a Multilevel LCA (MLCA) approach accounts for the clustering nature and assumes that the Level-2 units are drawn from a population of Level-2 units, allowing parameters of the LCA model to be random effects at Level-2. Most commonly only the intercepts of the class probabilities, the variable that determines the relative size of the latent classes, are considered random variables at Level-2. However, models with random measurement intercepts (e.g., random effects on the latent class indicators at Level-1) are possible and will be discussed. Taking a multilevel LCA approach not only reduces bias the parameter estimates, but allows for meaningful substantive research questions to be addressed relating to how the clustering units (e.g., classrooms, communities, etc.) may influence individual probability of being in a particular latent class. Further allowing for random effects on the class indicators may allow for a more accurate measurement of the latent classes at Level-1 while allowing for the Level-2 clustering units to influence the measurement and identification of the latent classes. It is recommended that the variation at Level-2 in the random effects for a MLCA be modeled using a common factor (Vermunt, 2003; Asparouhov & Muthen, 2008), a parametric approach, which assumes that the random means at Level-2 are highly correlated. This is due to a very computationally heavy model, espically when random effects are included for the measurement intercepts. A non-parametric approach can also be taken, where instead of the factor at Level-2, a latent class variable is specified to describe the heterogeneity at Level-2 (Vermunt, 2008, Muthen 2009, Henry and Muthen, 2010). This is considered a non-parametric approach since there is no assumption of normality at Level-2, instead using the multinomial distribution for the Level-2 latent classes. This paper will present the modeling framework in detail, showing the combination of a latent class variable at Level-1 with a factor or latent class variable at Level-2. Modeling possibilities and extensions will be discussed.

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Author

• Karen L. Nylund-Gibson, University of California - Santa Barbara