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 Snapshot highlights key findings from a study that used Bayesian stabilization to improve the reliability (long-term stability) of subgroup proficiency measures that the Pennsylvania Department of Education (PDE) uses to identify schools for Targeted Support and Improvement (TSI) or Additional Targeted Support and Improvement (ATSI). The…

The traditional approach to estimating the consistency of school effects across subject areas and the stability of school effects across time is to fit separate value-added multilevel models to each subject or cohort and to correlate the resulting empirical Bayes predictions. We show that this gives biased correlations and these biases cannot be…

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…

This pedagogical article is intended to explain the similarities and differences between the parameterizations of two multilevel measurement model (MMM) frameworks. The conventional two-level MMM that includes item indicators and models item scores (Level 1) clustered within examinees (Level 2) and the two-level cross-classified MMM (in which item…

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…