Scores estimated from multidimensional item response theory (IRT) models are not necessarily comparable across dimensions. In this article, the concept of aligned dimensions is formalized in the context of Rasch models, and two methods are described--delta dimensional alignment (DDA) and logistic regression alignment (LRA)--to transform estimated…

The main purposes of this study were to develop bi-factor multidimensional item response theory (BF-MIRT) observed-score equating procedures for mixed-format tests and to investigate relative appropriateness of the proposed procedures. Using data from a large-scale testing program, three types of pseudo data sets were formulated: matched samples,…

In Ramsay curve item response theory (RC-IRT, Woods & Thissen, 2006) modeling, the shape of the latent trait distribution is estimated simultaneously with the item parameters. In its original implementation, RC-IRT is estimated via Bock and Aitkin's (1981) EM algorithm, which yields maximum marginal likelihood estimates. This method, however,…

Although there are many methods available for dimensionality assessment for items with monotone item response functions, there are few methods available for unfolding item response theory models. In this study, a modification of Yen's Q3 statistic is proposed for the case of these nonmonotone item response models. Through a simulation study, the…

Empirical results from two studies--a simulation study and an experimental one--indicated that, in achievement data of the problem-solving type where a specific subject matter area is being tested, the greater the variety of the algorithms used, the higher the dimensionality of the test data. (Author/PN)