A strategy for the pairwise assessment which may be used to evaluate the nature of both "prerequisite" and "transference" relations existing among a set of traits is presented. Both confirmatory and exploratory strategies are presented. An example of how the strategy would be used is presented in the exploratory context.…

A natural parameterization and formalization of the problem of measuring change in dichotomous data is developed. Mathematically-exact definitions of specific objectivity are presented, and the basic structures of the linear logistic test model and the linear logistic model with relaxed assumptions are clarified. (SLD)

A study was conducted to evaluate six goodness-of-fit procedures using data simulation techniques. The procedures evaluated included the weighted average absolute deviation (WAAD), the mean absolute deviation (MAD), Bock's chi-square (BCHI), Yen's chi-square (YCHI), Wright and Mead's chi-square (WCHI), and the likelihood ratio chi-square (LCHI)…

A Rasch measurement model can be constructed to meet the requirements of rank ordered data. If multiple rankings of the same objects are available, then the parameters of the objects can be estimated, along with their standard errors and also with statistics summarizing the fit of the data to the measurement model. This paper summarizes the…

The usefulness of the general Rasch model for multidimensional data, from the most simple formulations to the more complex versions of the model, is explored. Also investigated was whether the parameters of the models could be readily interpreted. Models investigated included: (1) the vector model; (2) the product term model; (3) the vector and…

The first step of the data analysis with respect to the eventual application of the various new methods in latent trait theory is here initiated. The data are a set of approximately 500 item responses of each of 7,439 examinees to the Iowa Tests of Basic Skills, Form 6, on one of three difficulty levels, which correspond to the ages of 11, 12 and…

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…

A detailed description of five latent structure models of achievement measurement is presented. The first project paper, by David L. McArthur, analyzes the history of mental testing to show how conventional item analysis procedures were developed, and how dissatisfaction with them has led to fragmentation. The range of distinct conceptual and…

This study examines the application of the marginal maximum likelihood (MML) EM algorithm to the parameter estimation problem of the three-parameter normal ogive and logistic polychotomous item response models. A three-parameter normal ogive model, the Graded Response model, has been developed on the basis of Samejima's two-parameter graded…

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…