The cross-classified data structure is ubiquitous in education, psychology, and health outcome sciences. In these areas, assessment instruments that are made up of multiple items are frequently used to measure latent constructs. The presence of both the cross-classified structure and multivariate categorical outcomes leads to the so-called…

Standard item response theory (IRT) models have been extended with testlet effects to account for the nesting of items; these are well known as (Bayesian) testlet models or random effect models for testlets. The testlet modeling framework has several disadvantages. A sufficient number of testlet items are needed to estimate testlet effects, and a…

Valid inferences on teaching drawn from students' test scores require that tests are sensitive to the instruction students received in class. Accordingly, measures of the test items' instructional sensitivity provide empirical support for validity claims about inferences on instruction. In the present study, we first introduce the concepts of…

In educational measurement, responses of students on items are used not only to measure the ability of students, but also to evaluate and compare the performance of schools. Analysis should ideally account for the multilevel structure of the data, and school-level processes not related to ability, such as working climate and administration…