Cross-Classified Item Response Theory Modeling With an Application to Student Evaluation of Teaching

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 item-level data with cross-classified structure. An example of such data structure is the routinely collected student evaluation of teaching (SET) data. Motivated by the lack of research on multilevel IRT modeling with crossed random effects and the need of an approach that can properly handle SET data, this study proposed a cross-classified IRT model, which takes into account both the cross-classified data structure and properties of multiple items in an assessment instrument. A new variant of the Metropolis–Hastings Robbins–Monro (MH-RM) algorithm was introduced to address the computational complexities in estimating the proposed model. A preliminary simulation study was conducted to evaluate the performance of the algorithm for fitting the proposed model to data. The results indicated that model parameters were well recovered. The proposed model was also applied to SET data collected at a large public university to answer empirical research questions. Limitations and future research directions were discussed.