Information functions of the generalized partial credit model

The concept of information functions developed for dichotomous item response models is adapted for the partial credit model. The information func-tion is explained in terms of the model parameters and scoring functions. The relationship between the item information function and the item response function also is discussed. The informa-tion function then is used to investigate the effect of collapsing and recoding categories of polytomously-scored items of the National Assess-ment of Educational Progress (NAEP). The NAEP writing items were calibrated and the item and test information is used to discuss desirable properties of polytomous items. Index terms: information function, item response model, National Assessment of Educational Progress (NAEP), partial credit model, polytomous item response model. Tests are constructed to measure examinee trait levels. Because the information function (from item response theory) provides valuable information about the precision of measurement at a speci-fied trait level, the information function has been widely used for various applications that are cen-tral to the field of measurement (Hambleton & Swaminathan, 1985). The applications of the information function for dichotomously scored test items have been studied extensively, but applica-tions of the information function for polytomous item response models have not been fully explored. The partial credit model (PCM) is frequently used to analyze polytomous cognitive and affective response data (Masters, 1982; Muraki, 1992; Wright & Masters, 1982). In this paper, the advantages of the PCM are demonstrated and compared to the dichotomous item response model using infor-mation functions. Some cautions about the uncritical application of the PCM also are provided. The Generalized PCM The generalized PCM (GPCM; Muraki, 1992) is formulated on the assumption that the probability of selecting the kth category over the k- 1st category in a multicategory item is governed by the logistic dichotomous response model; that is, where k = 2, 3,..., mj, and mj is the number of response categories. The GPCM then is written a