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.…

Multiple group factor analysis is described and illustrated through a simulation involving 5,000 examinees. The estimation process of the group factors were implemented using the TESTFACT program of Wilson and others (1987). Group factor analysis is described as a special case of confirmatory factor analysis. Group factors can be computed based on…

Real test data of unknown structure were analyzed using both a unidimensional and a multidimensional latent trait model in an attempt to determine the underlying components of the test. The models used were the three-parameter logistic model and a multidimensional extension of the two-parameter logistic model. The basic design for the analysis of…

Guttman's facet theory is described as a method for quantifying information concerning attitudes. It is stated that attitude items are not negatively correlated for usual populations. An attitude is defined as a delimited totality of behavior with respect to something and its components are elements of a set. The first step in facet research…

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…

Latent trait model calibration procedures were used on data obtained from a group testing program. The one-parameter model of Wright and Panchapakesan and the three-parameter logistic model of Wingersky, Wood, and Lord were selected for comparison. These models and their corresponding estimation procedures were compared, using actual and simulated…

This paper discussed methods currently under study for use with multiple-response data. Besides using Bonferroni inequality methods to control type one error rate over a set of inferences involving multiple response data, a recently proposed methodology of plotting the p-values resulting from multiple significance tests was explored. Proficiency…

Four problems faced by the staff of the California Assessment Program (CAP) were solved by applying Rasch scaling techniques: (1) item cultural bias in the Entry Level Test (ELT) given to all first grade pupils; (2) nonlinear regression analysis of the third grade Reading Test scores; (3) comparison of school growth from grades two to three, using…