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…

Applied early adolescent researchers often sample students (Level 1) from within classrooms (Level 2) that are nested within schools (Level 3), resulting in data that requires multilevel modeling analysis to avoid Type 1 errors. Although several articles have been published to assist researchers with analyzing sample data nested at two levels, few…

Intraclass correlations are used to summarize the variance decomposition in populations with multilevel hierarchical structure. There has recently been considerable interest in estimating intraclass correlations from surveys or designed experiments to provide design parameters for planning future large-scale randomized experiments. The large…