The purpose of this paper is to present a generalization of the concept of item difficulty to test items that measure more than one dimension. Three common definitions of item difficulty were considered: the proportion of correct responses for a group of individuals; the probability of a correct response to an item for a specific person; and the…

Cliff's Index "c" derived from an item dominance matrix is utilized in a clustering approach, termed extracting Reliable Guttman Orders (ERGO), to isolate Guttman-type item hierarchies. A comparison of factor analysis to the ERGO is made on social distance data involving multiple ethnic groups. (Author/BW)

Multidimensional item response theory (IRT) models have been proposed for better understanding the dimensional structure of data or to define diagnostic profiles of student learning. A compensatory multidimensional two-parameter partial credit model (M-2PPC) for constructed-response items is presented that is a generalization of those proposed to…