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…

Motivational constructs and students' engagements have great impacts on students' mathematics achievements, yet they have not been theoretically investigated using international large-scale assessment data. This study utilized the mathematics data of the Trends in International Mathematics and Science Study 2011 to conduct a comparative and…