Estimating a Three-Level Latent Variable Regression Model With Cross-Classified Multiple Membership Data

The current study proposed a new model, termed the cross-classified multiple membership latent variable regression (CCMM-LVR) model that provides an extension to the three-level latent variable regression (HM3-LVR) model that can be used with cross-classified multiple membership data, for example, in the presence of student mobility across schools. The HM3-LVR model is beneficial for testing more flexible hypotheses about growth trajectory parameters and handles pure clustering of participants within higher-level (level-3) units. However, the HM3-LVR model involves the assumption that students remain in the same cluster (school) throughout the duration of the time period of interest. The CCMM-LVR model appropriately models the participants’ changing clusters over time. The impact of ignoring mobility in the real data was investigated by comparing parameter estimates, standard error estimates, and model fit indices for the model (CCMM-LVR) that appropriately modeled the cross-classified multiple membership structure with results when this structure was ignored (HM3-LVR).