Item difficulty and dimensionality often correlate, implying that unidimensional IRT approximations to multidimensional data (i.e., reference composites) can take a curvilinear form in the multidimensional space. Although this issue has been previously discussed in the context of vertical scaling applications, we illustrate how such a phenomenon…

This study investigates the effect of multidimensionality on extraction of latent classes in mixture Rasch models. In this study, two-dimensional data were generated under varying conditions. The two-dimensional data sets were analyzed with one- to five-class mixture Rasch models. Results of the simulation study indicate the mixture Rasch model…

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 dimensionality of a set of items is important for scale development. In practice, tools that make use of eigenvalues are often used to assess dimensionality. Parallel analysis is featured here as it is becoming an increasingly popular method for assessing the number of dimensions, and computational tools have recently been made available which…

This study examines linking relationships among latent test scores and how these latent linking relationships relate to observed-score linkings. Equations are used to describe the effects of correlation between underlying latent dimensions and the similarity or dissimilarity of test composition on linking functions among latent test scores. These…

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,…

The purpose of this study was to examine the impact of dimensionality, common-item set format, and different scale linking methods on preserving equity property with mixed-format test equating. Item response theory (IRT) true-score equating (TSE) and IRT observed-score equating (OSE) methods were used under common-item nonequivalent groups design.…

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,…

Participants with personal and without personal experiences with the Earth as a sphere estimated large-scale distances between six cities located on different continents. Cognitive distances were submitted to a specific multidimensional scaling algorithm in the 3D Euclidean space with the constraint that all cities had to lie on the same sphere. A…

A simulation study compared the performance of robust normal theory maximum likelihood (ML) and robust categorical least squares (cat-LS) methodology for estimating confirmatory factor analysis models with ordinal variables. Data were generated from 2 models with 2-7 categories, 4 sample sizes, 2 latent distributions, and 5 patterns of category…

Numerous assessments contain a mixture of multiple choice (MC) and constructed response (CR) item types and many have been found to measure more than one trait. Thus, there is a need for multidimensional dichotomous and polytomous item response theory (IRT) modeling solutions, including multidimensional linking software. For example,…

A cyclical conditional maximum likelihood estimation procedure is developed for the multidimensional unfolding of two- or three-way dominance data (e.g., preference, choice, consideration) measured on ordered successive category rating scales. The technical description of the proposed model and estimation procedure are discussed, as well as the…

A multidimensional unfolding technique that is not prone to degenerate solutions and is based on multidimensional scaling of a complete data matrix is proposed: distance information about the unfolding data and about the distances both among judges and among objects is included in the complete matrix. The latter information is derived from the…

As item response models gain increased popularity in large-scale educational and measurement testing situations, many studies have been conducted on the development and applications of unidimensional and multidimensional models. Recently, attention has been paid to IRT-based models with an overall ability dimension underlying several ability…

The dynamics model, which is based on L. Talmy's (1988) theory of force dynamics, characterizes causation as a pattern of forces and a position vector. In contrast to counterfactual and probabilistic models, the dynamics model naturally distinguishes between different cause-related concepts and explains the induction of causal relationships from…