Customizing Bayesian multivariate generalizability theory to mixed-format tests

Mixed-format tests, which typically include dichotomous items and polytomously scored tasks, are employed to assess a wider range of knowledge and skills. Recent behavioral and educational studies have highlighted their practical importance and methodological developments, particularly within the context of multivariate generalizability theory. However, the diverse response types and complex designs of these tests pose significant analytical challenges when modeling data simultaneously. Current methods often struggle to yield reliable results, either due to the inappropriate treatment of different types of response data separately or the imposition of identical covariates across various response types. Moreover, there are few software packages or programs that offer customized solutions for modeling mixed-format tests, addressing these limitations. This tutorial provides a detailed example of using a Bayesian approach to model data collected from a mixed-format test, comprising multiple-choice questions and free-response tasks. The modeling was conducted using the Stan software within the R programming system, with Stan codes tailored to the structure of the test design, following the principles of multivariate generalizability theory. By further examining the effects of prior distributions in this example, this study demonstrates how the adaptability of Bayesian models to diverse test formats, coupled with their potential for nuanced analysis, can significantly advance the field of psychometric modeling.