Estimating ability parameters in latent trait models in general, and in the Rasch model in particular is almost always hampered by noise in the data. In this study several alternative formulations which attempt to deal with these problems without a reparameterization are tested through a Monte Carlo simulation. (Author/JKS)

Stochastic ordering properties are investigated for a broad class of item response theory (IRT) models for which the monotone likelihood ratio does not hold. A taxonomy is given for nonparametric and parametric models for polytomous models based on the hierarchical relationship between the models. (SLD)

Gives an account of classical test theory that shows how it can be viewed as a mean and variance approximation to a general version of item response theory and then shows how this approach can give insight into predicting the true score of a test and the true scores of tests not necessarily parallel to the given test. (SLD)

Measures of multivariate association, based on Wilks'"lambda" or the Bartlett-Nanda-Pillai trace criterion "V", are compared in terms of properties of univariate R-squared, which they generalize. A unified set of derivations of properties is provided, which is self-contained and not restricted to decompositions in canonical…

The application of a class of Rasch models is discussed for situations in which test items are grouped into subsets and the common attributes of items within the subsets bring into question the usual assumption of conditional independence. Models are expressed as particular cases of the random coefficients multinomial logit model. (SLD)

Presents a three-way, three-mode extension of the two-way, two-mode hierarchical classes model of P. De Boeck and S. Rosenberg (1998) for the analysis of individual differences in binary object x attribute arrays. Illustrates the model with data on psychiatric diagnosis and discusses the relation between the model and other extant models. (SLD)

As examples of models that are not based on normality or its approximation, the logistic positive exponent family of models is discussed. These models include the item task complexity as the third parameter, which determines the single principle of ordering individuals on the ability scale. (SLD)

This book is a compendium of recent item response theory (IRT) research that reviews 27 IRT models. The book contains a historical overview of IRT followed by six sections that deal with the application of a particular IRT model or set of models. (SLD)

The assumptions underlying item response theory (IRT) models may be expressed as a set of equality and inequality constraints on the parameters of a latent class model. It is well known that the same assumptions imply that the parameters of the manifest distribution have to satisfy a more complicated set of inequality constraints which, however,…

A procedure--based on item response theory--for testing the hypothesis of unidimensionality of the latent space is proposed. Use of the procedure is supported by an asymptotic theory and a Monte Carlo simulation study. The procedure tests for unidimensionality in test construction and/or compares two tests. (SLD)

Unlike their monotone counterparts, nonparametric unfolding response models, which assume the item response function is unimodal, have seen little attention in the psychometric literature. This paper studies the nonparametric behavior of unfolding models by building on the work of Post (1992). The paper provides rigorous justification for a class…

We illustrate a class of multidimensional item response theory models in which the items are allowed to have different discriminating power and the latent traits are represented through a vector having a discrete distribution. We also show how the hypothesis of unidimensionality may be tested against a specific bidimensional alternative by using a…

The assumptions of the Rasch model are discussed and the Rasch model is reformulated as a quasi-independence model. Using ordinary contingency table methods, the Rasch model can be tested generally or against less restrictive quasi-loglinear models to investigate specific violations of its assumptions. (Author/BW)

Four types of metric scales are distinguished: absolute, ratio, difference, and interval. A general coefficient of association for two variables of the same scale type is developed which reduces to specific coefficients of association for each scale type. (NSF)