Many national and international educational data collection programs offer researchers opportunities to investigate contextual effects related to student performance. In those programs, schools are often used in the first-stage sampling process and students are randomly drawn from selected schools. However, the "incidental" dependence of…

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…

Item response theory (IRT) models are the main psychometric approach for the development, evaluation, and refinement of multi-item instruments and scaling of latent traits, whereas multilevel models are the primary statistical method when considering the dependence between person responses when primary units (e.g., students) are nested within…