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Cross-Classified Random Effects Modeling for Moderated Item Calibration

In the research reported here, we propose a new method for scale alignment and test scoring in the context of supporting students with disabilities. In educational assessment, students from these special populations take modified tests because of a demonstrated disability that requires more assistance than standard testing accommodation. Updated federal education legislation and guidance require that these students be assessed and included in state education accountability systems, and their achievement reported with respect to the same rigorous content and achievement standards that the state adopted. Routine item calibration and linking methods are not feasible because the size of these special populations tends to be small. We develop a unified cross-classified random effects model that utilizes item response data from the general population as well as judge-provided data from subject matter experts in order to obtain revised item parameter estimates for use in scoring modified tests. We extend the Metropolis–Hastings Robbins–Monro algorithm to estimate the parameters of this model. The proposed method is applied to Braille test forms in a large operational multistate English language proficiency assessment program. Our work not only allows a broader range of modifications that is routinely considered in large-scale educational assessments but also directly incorporates the input from subject matter experts who work directly with the students needing support. Their structured and informed feedback deserves more attention from the psychometric community.