Applied Psychological Measurement

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.

Two local methods for observed-score equating are applied to the problem of equating an adaptive test to a linear test. In an empirical study, the methods were evaluated against a method based on the test characteristic function (TCF) of the linear test and traditional equipercentile equating applied to the ability estimates on the adaptive test for a population of test takers. The two local methods were generally best. Surprisingly, the TCF method performed slightly worse than the equipercentile method. Both methods showed strong bias and uniformly large inaccuracy, but the TCF method suffered from extra error due to the lower asymptote of the test characteristic function. It is argued that the worse performances of the two methods are a consequence of the fact that they use a single equating transformation for an entire population of test takers and therefore have to compromise between the individual score distributions.