Publications & Resources

Modeling Heterogeneity in Relationships Between Initial Status and Rates of Change: Latent Variable Regression in a Three-Level Hierarchical Model

Mar 2005

Kilchan Choi and Michael Seltzer

In studies of change in education and numerous other fields, interest often centers on how differences in the status of individuals at the start of a time period of substantive interest relate to differences in subsequent change. In this report we present a fully Bayesian approach to estimating three-level hierarchical models in which latent variable regression coefficients capturing the relationship between initial status and rates of change within each of J schools (Bwj, j = 1, …, J) are treated as varying across schools. Through analyses of data from the Longitudinal Study of American Youth, we show how modeling differences in Bwj as a function of school characteristics can broaden the kinds of questions we can address in school effects research. We illustrate the possibility of conducting sensitivity analyses employing t distributional assumptions at each level of such models (termed LVR-HM3s) and present results from a simulation study that focuses on the coverage properties of marginal posterior intervals for fixed effects in LVR-HM3s. We outline extensions of LVR-HM3s to settings in which growth is nonlinear, and discuss the use of LVR-HM3s in other types of research including multisite evaluation studies in which time-series data are collected during a pre-intervention period, and cross-sectional studies in which within-cluster latent variable regression slopes are treated as varying across clusters.

Choi, K., & Seltzer, M. (2005). Modeling heterogeneity in relationships between initial status and rates of change: Latent variable regression in a three-level hierarchical model (CSE Report 647). Los Angeles: University of California, Los Angeles, National Center for Research on Evaluation, Standards, and Student Testing (CRESST).