Multilevel Latent Class Analysis for Cross-Classified Data Structures

• In Event: Recent Developments in Multiple-Group, Multilevel, and Longitudinal Mixture Modeling

Abstract

Latent class analysis (LCA) has become increasingly widespread in educational research settings. However, despite the ubiquity of multilevel data in these same settings, multilevel modeling techniques for LCA are still in their infancy, with the initial educational applications of multilevel LCA occurring only within the last 10 years (e.g., Henry & Muthén, 2010). Thus, it is no surprise that one of the more complicated multilevel modeling extensions involving cross-classified data structures (Beretvas, 2008), has never been applied to LCA. The purpose of this paper is to demonstrate the specification and estimation of a cross-classified multilevel LCA model using data on students nested within schools and neighborhoods. We further explore, with an empirical example, the consequences of ignoring the cross-classified data structure for measurement and structural parameter estimates as well as for individual classification.
Data for this study are from Wave 1 (1994-1995) of the National Longitudinal Study of Adolescent Health (Add Health; Harris, 2013). Following the Collins and Lanza (2013) empirical example of latent class analysis of adolescent delinquency, we used six dichotomized student questionnaire items about past-year delinquent behavior as indicators of a 4-class latent multinomial variable. Student sex (binary) and age (continuous) were considered as student-level predictors of latent class membership. Our analysis is based on the same analytic sample as Dunn, Richmond, Milliren, and Subramanian (2015): 16,070 youth who attended 128 schools and lived in 2111 census tracks, therefore resulting in youths cross-classified by school and neighborhood.
To begin, we use a cross-classified random effects extension of the multilevel LCA assuming cluster effects can be adequately represented by latent class random effects, i.e., randomly-varying multinomial intercepts for the distribution of the latent class variable with fixed thresholds for the latent class indicators. Let be the latent class membership for student i in school j1 and neighborhood j2. Using a multinomial logistic regression specification, the log odds of latent class membership in Class k is given by

where and represent the random effects of school and neighborhood, respectively.
We consider four unconditional latent class models: 1) one-level latent class model, ignoring student clustering; 2) two-level latent class model with students nested within schools, ignoring neighborhood clustering; 3) two-level latent class model with students nested within neighborhoods, ignoring school clustering; and 4) cross-classified multilevel latent class model with students cross-classified by schools and neighborhoods. We compare these four models with regards to the model-estimated class-specific item endorsement probabilities, model-estimated class proportions, and student-specific modal latent classification.
We consider four conditional latent class models: All four of the unconditional latent class models with fixed effects of the student-level predictors of class membership. We compare these four models with regards to the fixed effect point estimates and credible intervals.
Preliminary findings suggest that failure to account for the cross-classified data structure in a multilevel LCA produce biased variance estimates for the random multinomial intercepts, consistent with previous work on cross-classified modeling (Luo & Kwok, 2009; Meyers & Beretvas, 2006). Furthermore, latent class composition at the student level is distorted.

Authors

• Audrey J. Leroux, Georgia State University

• Katherine E. Masyn, Georgia State University