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…

Rank ordering examinees is an easier task for judges than is awarding numerical ratings. A measurement model for rankings based on Rasch's objectivity axioms provides linear, sample-independent and judge-independent measures. Estimates of examinee measures are obtained from the data set of rankings, along with standard errors and fit statistics.…

A general linear model (GLM), using least-squares techniques, was used to develop a criterion measure to replace freshman year grade point average (GPA) in college admission predictive validity studies. Problems with the use of GPA include those associated with the combination of grades from different courses and disciplines into a single measure,…

The current status of item response theory (IRT) is discussed. Several IRT methods exist for assessing whether an item is biased. Focus is on methods proposed by L. M. Rudner (1975), F. M. Lord (1977), D. Thissen et al. (1988) and R. L. Linn and D. Harnisch (1981). Rudner suggested a measure of the area lying between the two item characteristic…

In order to determine the effectiveness of multidimensional scaling (MDS) in recovering the dimensionality of a set of dichotomously-scored items, data were simulated in one, two, and three dimensions for a variety of correlations with the underlying latent trait. Similarity matrices were constructed from these data using three margin-sensitive…

Two modification formulas are presented for the test information function in order to provide better measures of local accuracies of the estimation of "theta" when maximum likelihood estimation is used to provide the estimate of ability "theta." A minimum bound of any estimator, biased or unbiased, is considered; and Formula 1…

Three strategies for augmenting the interpretation of significance test results are illustrated. Determining the most suitable indices to use in evaluating empirical results is a matter of considerable debate among researchers. Researchers increasingly recognize that significance tests are very limited in their potential to inform the…

Attitude measures frequently produce distributions of item scores that attenuate interitem correlations and thus also distort findings regarding the factor structure underlying the items. An actual data set involving 260 adult subjects' responses to 55 items on the Love Relationships Scale is employed to illustrate empirical methods for…

A variety of locally dependent models are introduced having individual difference parameters that may be interpreted as reflecting effective learning abilities. One version is a univariate extension of the Rasch model with a Markov property: the probability that a given individual will pass an item depends on previous items only through the…

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…

The decision making processes of children in a probabilistic environment were studied within the context of the theory of signal detection (TSD). The relationship between the age of the child and his ability to revise decision criteria was examined, as well as the appropriateness of TSD measures and methodology with children. It was hypothesized…

A more familiar and efficient method for estimating the parameters of Cason and Cason's model was examined. Using a two-step analysis based on linear regression, rather than the direct search interative procedure, gave about equally good results while providing a 33 to 1 computer processing time advantage, across 14 cohorts of junior medical…

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…

Methods for examining the viability of assumptions underlying generalized linear models are considered. By appealing to the likelihood, a natural generalization of the raw residual plot for normal theory models is derived and is applied to investigating potential misspecification of the linear predictor. A smooth version of the plot is also…

This paper deals with test fairness regarding a test consisting of two parts: (1) a "common" section, taken by all students; and (2) a "variable" section, in which some students may answer a different set of questions from other students. For example, a test taken by several thousand students each year contains a common multiple-choice portion and…