Item response theory for scores on tests including polytomous items with ordered responses

Abstract

Item response theory (IRT) provides procedures for scoring tests including any combination of rated constructed-response and keyed multiple-choice items, in that each response pattern is associated with some modal or expected a posteriori estimate of trait level. However, various considerations that frequently arise in large-scale testing make response-pattern scoring an undesirable solution. Methods are described based on IRT that provide scaled scores, or estimates of trait level, for each summed score for rated responses, or for combinations of rated responses and multiple-choice items. These methods may be used to combine the useful scale properties of IR’r-based scores with the practical virtues of a scale based on a summed score for each examinee. Index terms: graded response model, item response theory, ordered responses, polytomous models, scaled scores.