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 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 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,…

Akaike's information criterion is suggested as a tool for evaluating fit and dimensionality in metric multidimensional scaling that uses least squares methods of estimation. This criterion combines the least squares loss function with the number of estimated parameters. Numerical examples are presented. The results from analyses of both simulation…

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…

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…

For the exploratory analysis of a matrix of proximities or (dis)similarities between objects, one often uses cluster analysis (CA) or multidimensional scaling (MDS). Solutions resulting from such analyses are sometimes interpreted using external information on the objects. Usually the procedures of CA, MDS and using external information are…

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…

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…