Nested logit item response models for multiple-choice data are presented. Relative to previous models, the new models are suggested to provide a better approximation to multiple-choice items where the application of a solution strategy precedes consideration of response options. In practice, the models also accommodate collapsibility across all…

This paper describes and evaluates the use of measurement decision theory (MDT) to classify examinees based on their item response patterns. The model has a simple framework that starts with the conditional probabilities of examinees in each category or mastery state responding correctly to each item. The presented evaluation investigates: (1) the…

Recent changes to federal guidelines for the collection of data on race and ethnicity allow respondents to select multiple race categories. Redefining race subgroups in this manner poses problems for research spanning both sets of definitions. NAEP long-term trends have used the single-race subgroup definitions for over thirty years. Little is…

Spearman's factor-analytic model has been proposed as a unidimensional linear item response theory (IRT) model for continuous item responses. This article first proposes a reexpression of the model that leads to a form similar to that of standard IRT models for binary responses and discusses the item indices of difficulty discrimination and…

A coordinate-free definition of complex-structure multidimensional item response theory (MIRT) for dichotomously scored items is presented. The point of view taken emphasizes the possibilities and subtleties of understanding MIRT as a multidimensional extension of the classical unidimensional item response theory models. The main theorem of the…

This study linked nonlinear profile analysis (NPA) of dichotomous responses with an existing family of item response theory models and generalized latent variable models (GLVM). The NPA method offers several benefits over previous internal profile analysis methods: (a) NPA is estimated with maximum likelihood in a GLVM framework rather than…

The method of maximum-likelihood is typically applied to item response theory (IRT) models when the ability parameter is estimated while conditioning on the true item parameters. In practice, the item parameters are unknown and need to be estimated first from a calibration sample. Lewis (1985) and Zhang and Lu (2007) proposed the expected response…

The standard error of the maximum likelihood ability estimator is commonly estimated by evaluating the test information function at an examinee's current maximum likelihood estimate (a point estimate) of ability. Because the test information function evaluated at the point estimate may differ from the test information function evaluated at an…

The mixture index of fit (T. Rudas et al, 1994) is used to estimate the fraction of a population for which differential item functioning (DIF) occurs, and this approach is compared to the Mantel Haenszel test of DIF. The proposed noniterative procedure provides information about data portions contributing to DIF. (SLD)

The usefulness of joint and conditional maximum-likelihood is considered for the Rasch model under realistic testing conditions in which the number of examinees is very large and the number is items is relatively large. Conditions for consistency and asymptotic normality are explored, effects of model error are investigated, measures of prediction…

Continuation ratio logits are used to model the possibilities of obtaining ordered categories in a polytomously scored item. This model is an alternative to other models for ordered category items such as the graded response model and the generalized partial credit model. The discussion includes a theoretical development of the model, a…

The success of applications of item response theory (IRT) depends upon the properties of the estimates of model parameters. Many theoretical properties of these estimates have been extensively studied. However, the properties of estimates obtained empirically from real data depend not only on the theoretical results, but also on the data and the…

In this paper it is shown that various violations of the two parameter logistic (2PL) model can be evaluated using the Lagrange multiplier test (J. Aitchison and S. Silvey, 1958) or the equivalent difference score test. The tests focus on violation of local stochastic independence and insufficient capture of the form of the item characteristic…

Multinomial-response models are available that correspond implicitly to tests in which a total score is computed as the sum of polytomous item scores. For these models, joint and conditional estimation may be considered in much the same way as for the Rasch model for right-scored tests. As in the Rasch model, joint estimation is only attractive if…

This article organizes models for categorical item response data into three distinct classes. "Difference models" are appropriate for ordered responses, "divide-by-total" models for either ordered or nominal responses, and "left-side added" models for multiple-choice responses with guessing. Details of the taxonomy…