A multidimensional partial credit model with associated item and test statistics: An application to mixed-format tests

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 date along with a compensatory multidimensional three-parameter logistic model for multiple-choice data (M-3PL). Estimation of these models using Markov chain Monte Carlo methods is discussed. To further evaluate these models and characterize item and test functioning, multidimensional representations of statistics such as information, difficulty, and discrimination for the M-3PL and M-2PPC are presented. Many assessment programs have a mixture of item types in which multiple choice and constructed response are administered together. An example is presented in which the dimensional structure of a test containing mixed item types is examined. Goodness-of-fit testing under various model formulations and derived statistics are discussed.