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,…

This study aims to evaluate a multidimensional latent trait model to determine how well the model works in various empirical contexts. Contrary to the assumption of these latent trait models that the traits are normally distributed, situations in which the latent trait is not shaped with a normal distribution may occur (Sass et al, 2008; Woods…

This dissertation is comprised of three papers that propose and apply psychometric models to deal with complexities and challenges in large-scale assessments, focusing on modeling rater effects and complex learning progressions. In particular, three papers investigate extensions and applications of multilevel and multidimensional item response…

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.…

The utility of Orlando and Thissen's ("2000", "2003") S-X[squared] fit index was extended to the model-fit analysis of the graded response model (GRM). The performance of a modified S-X[squared] in assessing item-fit of the GRM was investigated in light of empirical Type I error rates and power with a simulation study having…

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,…

The statistical assessment of dimensionality provides evidence of the underlying constructs measured by a survey or test instrument. This study focuses on educational measurement, specifically tests comprised of items described as multidimensional. That is, items that require examinee proficiency in multiple content areas and/or multiple cognitive…

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,…

Motivated by Gibbons et al.'s (Appl. Psychol. Meas. 31:4-19, "2007") full-information maximum marginal likelihood item bifactor analysis for polytomous data, and Rijmen, Vansteelandt, and De Boeck's (Psychometrika 73:167-182, "2008") work on constructing computationally efficient estimation algorithms for latent variable…

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…

Most researchers agree that psychological/educational tests are sensitive to multiple traits, implying the need for a multidimensional item response theory (MIRT). One limitation of applying a MIRT in practice is the difficulty in establishing equivalent scales of multiple traits. In this study, a new MIRT linking method was proposed and evaluated…