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…

This study investigates the relationships among factor correlations, inter-item correlations, and the reliability estimates of subscores, providing a guideline with respect to psychometric properties of useful subscores. In addition, it compares subscore estimation methods with respect to reliability and distinctness. The subscore estimation…

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,…

When using IRT models in Educational Achievement Testing, the model is as a rule too simple to catch all the relevant dimensions in the test. It is argued that a simple model may nevertheless be useful but that it can be complemented with additional analyses. Such an analysis, called profile analysis, is proposed and applied to the reading data of…

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,…

In this paper, we propose a cluster-MDS model for two-way one-mode continuous rating dissimilarity data. The model aims at partitioning the objects into classes and simultaneously representing the cluster centers in a low-dimensional space. Under the normal distribution assumption, a latent class model is developed in terms of the set of…

After a test is developed, most content validation analyses shift from ascertaining domain definition to studying domain representation and relevance because the domain is assumed to be set once a test exists. We present an approach that allows for the examination of alternative domain structures based on extant test items. In our example based on…

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…

The problem of dimensionality with respect to Raven's Advanced Progressive Matrices (APM) specifically and, more generally, "g" or fluid intelligence, has been a long-standing issue. The present article reports two studies examining the dimensionality of both the original Set II of the APM (n = 506) and a short form (n = 644), using principal…