Multiple Group Item Response Models
R. Darrell Bock, Robert D. Gibbons · 2021
Multiple group item response theory (IRT) draws connections between IRT and multivariate generalizations of probit analysis of multivariate binary data that has grown out of statistical and biostatistical applications. This chapter considers several different approaches to the treatment of multiple groups in IRT models and their applications. There are many similarities between generalized mixed-effects regression models and IRT models. The chapter describes results for the Rasch model and the two-parameter logistic model for binary outcomes; however, the ordinal logistic regression model and polytomous IRT models share the same relation. Beyond providing a better understanding between the correspondence between IRT and mixed models, the mixed model formulation of the IRT model has several additional benefits. First, it provides a direct approach to adding covariates and grouping structures to the IRT model. The chapter also considers four cases: a nonparametric approximation, a normal model, a resolution into Gaussian components, and a beta-binomial model.