This article presents a latent class model for multilevel data to identify latent subgroups and estimate heterogeneous treatment effects. Unlike sequential approaches that partition data first and then estimate average treatment effects (ATEs) within classes, we employ a Bayesian procedure to jointly estimate mixing probability, selection, and…

Understanding whether or not different types of students master various attributes can aid future learning remediation. In this study, two-level diagnostic classification models (DCMs) were developed to represent the probabilistic relationship between external latent classes and attribute mastery patterns. Furthermore, variational Bayesian (VB)…

There is widespread interest in using various statistical inference tools as a part of the evaluations for individual teachers and schools. Evaluation systems typically involve classifying hundreds or even thousands of teachers or schools according to their estimated performance. Many current evaluations are largely based on individual estimates…

Variation is a key concept in the study of statistics and its understanding is a crucial aspect of most statistically related tasks. This study aimed to extend and apply a hierarchy for describing students' understanding of variation that was developed in a sampling context to the context of a natural event in which variation occurs. Students aged…