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. This report presents 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 (Bw[sub]j, j = 1..., J) are treated as varying across schools. Through analyses of data from the Longitudinal Study of American Youth, show how modeling differences in Bw[sub]j as a function of school characteristics can broaden the kinds of questions we can address in school effects research. The possibility of conducting sensitivity analyses employing "t" distributional assumptions at each level of such models (termed LVR-HM3s) is illustrated, and presented results from a simulation study that focuses on the coverage properties of marginal posterior intervals for fixed effects in LVR-HM3s. The article outlines extensions of LVR-HM3s to settings in which growth is nonlinear, and discusses 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.