Item Response Theory for Scores on Tests Including Polytomous Items with Ordered Responses

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 pro-vide 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.