This paper developed and illustrated a technique to analyze categorical data when subjects can appear in any number of categories for multigroup designs. Post hoc procedures to be used in conjunction with the presented statistical test are also developed. The technique is a large sample technique whose small sample properties are as yet unknown.…

A class of multidimensional latent trait models is described. The properties of the model parameters, and initial results on the accuracy of a maximum likelihood procedure for estimating the model parameters are discussed. The model presented is a special case of the general model described by Rasch (1961), with close similarities to the models…

Several special cases of the general Rasch model, varying in complexity, were investigated to determine whether they could successfully model realistic multidimensional item response data. Whether the parameters of the model could be readily interpreted was also investigated. The models investigated included: (1) the vector model; (2) the product…

This paper develops and illustrates a latent trait approach to constructing an item bank when responses are scored in several ordered categories. This approach is an extension of the methodology developed by Choppin, Wright and Stone, and Wright and Bell for the construction and maintenance of banks of dichotomously scored items. (Author/PN)

The effects of varying degrees of correlation between abilities and of various correlation configurations between item parameters on ability and item parameter estimation using the three parameter logistic model were examined. Ten two-trait configurations and one unidimensional test configuration for 30 item tests were simulated. Each…

A strategy is described for dealing with measurement situations in which certain categories of responses are null, that is, persons do not respond in certain categories to certain items. The method is described for the partial credit model while maintaining the integrity of the original response framework. (SLD)

Equating tests from different calibrations under item response theory (IRT) requires calculation of the slope and intercept of the appropriate linear transformation. Two methods have been proposed recently for equating graded response items under IRT, a test characteristic curve method and a minimum chi-square method. These two methods are…

A latent trait model is described that is appropriate for use with tests that measure more than one dimension, and its application to both real and simulated test data is demonstrated. Procedures for estimating the parameters of the model are presented. The research objectives are to determine whether the two-parameter logistic model more…

The general goal of this paper is to help researchers conduct appropriately designed goodness of fit studies for item response model applications. The specific purposes are to describe: (1) an up-to-date set of promising and useful methods for addressing a variety of goodness of fit questions; and (2) current research studies to advance this set…

Work on item response theory was extended to two areas not extensively researched previously, including models for: (1) test items that require more than one ability for a correct response (MIRT); and (2) interaction between modules of instruction that have a hierarchical relationship (HST). In order to develop the MIRT and HST models, the author…

Two extensions of the Mantel Haenszel procedure that may be useful in assessing differential item functioning (DIF) are explored. Simulation results showed that, for both inferential procedures, the studied item should be included in the matching variable, as in the dichotomous case. (SLD)

This report summarizes the results of research designed to study the psychometric and technological feasibility of adaptive testing to assess spatial ability. Data was collected from high school students on two types of spatial items: three-dimensional cubes and hidden figure items. The analysis of the three-dimensional cubes focused on the fit of…

A previous study of pre-equating the Scholastic Aptitude Test (SAT) using item response theory provided unacceptable equating results for SAT-mathematical data. The purpose of this study was to investigate two possible explanations for these unacceptable pre-equating results. Specifically, the calibration process, which made use of the…

The phenomenon of simultaneous differential item functioning (DIF) amplification and cancellation and the role of the SIBTEST computer program in detecting it were studied. A variety of simulated test data was generated for this purpose. In addition, the following real test data were used: (1) American College Testing program data for 2,115 males…

A procedure is presented for examining the influence of instruction on responses to test items by extending item response theory to incorporate variables illustrating different amounts of opportunity to learn. Data from the Second International Mathematics Study (grade 8 scores for about 7,000 students) illustrate the discussion. (SLD)