Reconsidering Multilevel Latent Class Models: Can Level-2 Latent Classes Affect Item Response Probabilities?

Multilevel latent class analysis (MLCA) has been increasingly used to investigate unobserved population heterogeneity while taking into account data dependency. Nonparametric MLCA has gained much popularity due to the advantage of classifying both individuals and clusters into latent classes. This study demonstrated the need to relax the assumption in specifying the nonparametric MLCA: item response probabilities varied only across level-1 latent classes, but not level-2 latent classes. An empirical demonstration with data from the Trends in International Mathematics and Science Study (TIMSS) 2011 showed that item response probabilities could vary across both level-1 and level-2 latent classes. This relaxed MLCA yielded better model fit and provided more nuanced understanding of the heterogeneous response patterns. Monte Carlo simulation was conducted to evaluate class enumeration and assignment accuracy of the relaxed MLCA. Based on the simulation results, we recommended the use of AIC in class enumeration and highlighted the benefits of having larger cluster size.