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The implementation Common Core State Standards and other rigorous standards now demand more authentic assessment. These assessments will require new item types that will likely include ordered scoring. This study presents a novel model, the cross-classified explanatory partial credit model, for describing and measuring item difficulty and person trait level. The cross-classified model extends explanatory item response models by including crossed-random effects for both items and persons and applying it to ordered polytomous data. This study compares the cross-classified model to the rating scale model, the partial credit model, and a more restrictive explanatory partial credit model using a verbal aggression dataset. Findings provide evidence for the use of the cross-classified explanatory partial credit model.