This article proposes a latent variable regression four-level hierarchical model (LVR-HM4) that uses a fully Bayesian approach. Using multisite multiple-cohort longitudinal data, for example, annual assessment scores over grades for students who are nested within cohorts within schools, the LVR-HM4 attempts to simultaneously model two types of change, arising from individual student over grades, and successive cohorts in the same grade over years. In addition, as an extension of Choi and Seltzer, the LVR coefficients, that is, gap-in-time parameter, capturing the relationships between initial status and rates of changes within each cohort and school, help bring to light the distribution of student growth and differences in the distribution over different cohorts within schools. Advantages associated with the LVR-HM4 can be highlighted in studies on monitoring school performance or evaluations of policies and practices that may target different aspects of student academic performance such as initial status, growth, or gap over time in schools.
Detecting Instruction Effects—Deciding Between Covariance Analytical and Change-Score Approach
