Chapter 5: Multilevel Cross-Classified Testlet Model for Complex Item and Person Clustering in Item Response Data Analysis

This chapter proposes a multilevel cross-classified testlet model that incorporates two sources of dependency in items resulting from two cross-classifying item clustering factors, such as testlets and content areas, in addition to a person clustering factor. The proposed model was built upon previously proposed models in the literature, and their background and rationale are described in the first part of this chapter. They were all formulated within the hierarchical generalized linear modeling (HGLM) framework. In the following section, the proposed model was presented, and an application of the model was demonstrated through an analysis of the 2006 PISA science assessment data. Model parameters were estimated using the Markov Chain Monte Carlo (MCMC) estimation method in OpenBUGS. Model selection and model fit were evaluated based on multiple information-based fit indexes.