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

Abstract

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.

Keywords:

• Information criteria
• latent class analysis
• model selection
• multilevel
• nonparametric

Notes

1 This study focuses on nonparametric MLCA. Readers that are interested in parametric MLCA are referred to Henry and Muthén (2010).

2 Note that entropy in the population varies across simulation conditions because it is a function of class-specific response probabilities, number of level-1 latent classes, number of level-2 latent classes, number of clusters, and cluster size which are the simulation factors in this study. Tables of entropy values by condition are available upon request.

3 Data can be replicated if the data generation is reinitiated with the same seed. Such replicability of data is recommended in case data are lost or damaged. For more details on the use of seed for data generation, please refer to Bandalos and Leite (2013). Also note that different data were generated across conditions with the same seed, because population models used to generate data were different with respect to the number of classes at level-1 and level-2, the number of clusters, cluster size, and mixing proportions.