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Thissen, David; Pommerich, Mary; Billeaud, Kathleen; Williams, Valerie S. L.
doi: 10.1177/014662169501900105pmid: N/A
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.
doi: 10.1177/014662169501900107pmid: N/A
Data from the California Learning Assessment System are used to examine certain characteristics of tests designed as the composites of items of different modes. The characteristics include rater severity, test information, and definition of the latent variable. Three different assessment modes-multiple-choice, open-ended, and investigation items (the latter two are referred to as performance-based modes)-were combined in a test across three different test forms. Rater severity was investigated by incorporating a rater parameter for each rater in an item response model that then was used to analyze the data. Some rater severities were found to be quite extreme, and the impact of this variation in rater severities on both total scores and trait level estimates was examined. Within-rater variation in rater severity also was examined and was found to have significant variation. The information contribution of the three modes was compared. Performance-based items provided more information than multiple-choice items and also provided greatest precision for higher levels of the latent variable. A projection-like method was applied to investigate the effects of assessment mode on the definition of the latent variable. The multiple-choice items added information to the performance-based variable. The results of the analysis also showed that the projection-like method did not practically differ from the results when the latent trait was defined jointly by both the multiple-choice and the performance-based items. Index terms: equating, linking, multiple assessment modes, polytomous item response models, rater effects.
doi: 10.1177/014662169501900110pmid: N/A
The following types of discrete item responses are distinguished : nominal-dichotomous, ordinal-dichotomous, nominal-polytomous, and ordinal-polytomous. Bock (1972) presented a model for nominal-polytomous item responses that, when applied to dichotomous responses, yields Birnbaum's (1968) two-parameter logistic model. Applying Bock's model to ordinal-polytomous items leads to a conceptual problem. The ordinal nature of the response variable must be preserved; this can be achieved using three different methods. A number of existing models are derived using these three methods. The structure of these models is similar, but they differ in the interpretation and qualities of their parameters. Informa-tion, parameter invariance, log-odds differences invariance, and model violation also are discussed. Information and parameter invariance of dichotomous item response theory (nt'r) also apply to polytomous IRT. Specific objectivity of the Rasch model for dichotomous items is a special case of log-odds differences invariance of polytomous items. Differential item functioning of dichotomous IRT is a special case of measurement model violation of polytomous IRT. Index terms: adjacent categories, continuation ratios, cumulative probabilities, differential item functioning, log-odds differences invariance, measurement model violation, parameter invariance, polytomous IRT models.
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