Multiple Membership Data Structures in Multilevel Latent Transition Analysis

• In Event: Methodological Advances in Longitudinal Mixture Modeling

Abstract

Latent class analysis (LCA) and latent profile analysis (LPA) are primarily used with cross-sectional data to identify distinct subgroups (latent classes) of individuals. There are numerous examples of applications of LCA and LPA in educational research. In the case of longitudinal data, latent class membership can be measured at each assessment occasion. If changes in latent class membership occur (sometimes referred to as regime switching, state change, or stage-sequential change), these changes can be modeled using a latent transition analysis (LTA) wherein the probability of class membership at a given time point is conditional on class membership at one or more prior time points.
A nearly ubiquitous feature of educational research studies, be they cross-sectional or longitudinal, is nested data (e.g., students nested within classrooms, classrooms nested within schools, etc.). Nested data poses analytic challenges as the typical assumption of independent observations may be violated but also presents opportunities for empirical examination of contextual effects on the student-level phenomenon under investigation.
Conventional multilevel longitudinal models assume “pure” or “hierarchical” clustering such that students remain nested in the same cluster for the duration of the observation period. However, in multilevel longitudinal research, it is rare for data structures to remain purely clustered during a study. One resulting data structure in this situation is known as a multiple membership structure, where some lower-level units are members of more than one higher-level unit, e.g., students changing schools between longitudinal assessment occasions (Beretvas, 2011; Fielding & Goldstein, 2006). Simulation studies with various latent growth curve models (Choi & Wilson, 2016; Grady, 2010; Leroux & Beretvas, 2018) have found that ignoring multiple membership (due to student mobility) leads to biased estimates of student-level and school-level variance components as well as school-level covariate effects.
Despite the widespread use of mixture models in educational research and the pervasiveness of clustered data structures, there is a scarcity of work on multilevel LTA (c.f., Asparouhov & Muthén, 2008; Cho, Cohen, & Bottge, 2013). The small amount of work that is available on ML-LTA suggests that ignoring the clustering results in incorrect classification of individuals at each time point as well as biased estimates of the transition probabilities for class membership across time (Cho et al., 2013). To date, no work has been done to specify, estimate, or evaluate a multiple membership LTA (MM-LTA) model accounting for student mobility.
The purpose of this paper is to derive and demonstrate the MM-LTA model with a real data example. Results are compared to a ML-LTA (using cluster membership at baseline) and a single-level LTA. We compare these three models with regards to the model-estimated latent class proportions at each assessment, student-specific modal latent classification at each assessment, and the conditional latent transition probabilities across time. The specification of the joint distribution of the latent class random effects across time as well as the individual cluster weights are discussed in detail. By necessity, Bayesian estimation with Markov chain Monte Carlo methods is used to estimate all models.

Authors

• Katherine E. Masyn, Georgia State University

• Audrey J. Leroux, Georgia State University