Various models have been proposed for analyzing dichotomous test or questionnaire items which were constructed to reflect an assumed underlying structure (e.g., hierarchical). This paper shows that many such models are special cases of latent class analysis and discusses a currently available computer program to analyze them. (Author/JKS)

Both the binomial and beta-binomial models are applied to various problems occurring in mental test theory. The paper reviews and critiques these models. The emphasis is on the extensions of the models that have been proposed in recent years, and that might not be familiar to many educators. (Author)

Deciding whether sets of test data are consistent with any of a large class of item response models is considered. The assumption of local independence is weakened to a new condition, local nonnegative dependence (LND). Necessary and sufficient conditions are derived for a LND item response model. (Author/JKS)

A latent class model for rating data is presented which provides an alternative to the latent trait approach of analyzing test data. It is the analog of Andrich's binomial Rasch model for Lazarsfeld's latent class analysis (LCA). Response probabilities for rating categories follow a binomial distribution and depend on class-specific item…

The purpose of this paper is to present a generalization of the concept of item difficulty to test items that measure more than one dimension. Three common definitions of item difficulty were considered: the proportion of correct responses for a group of individuals; the probability of a correct response to an item for a specific person; and the…

The Rasch model is generalized to a multicomponent model, so that observations of component events are not needed to apply the model. It is shown that the generalized model maintains the property of specific objectivity of the Rasch model. An application to a mathematics test is provided. (Author/JKS)

The purpose of the present study was to examine the accuracy of indirect trait estimates, i.e., estimates of some primary trait obtained from a second measure which have been equated to the first. The California Achievement Test in Reading was the primary measure and the Prescriptive Reading Inventory was the indirect measure. Four kinds of…

Three item selection methods for criterion-referenced tests are examined: the classical theory of item difficulty and item-test correlation; the latent trait theory of item characteristic curves; and a decision-theoretic approach for optimal item selection. Item contribution to the standardized expected utility of mastery testing is discussed. (CM)

Significant to a latent trait or item response theory analysis of a mental test is the determination of exactly what is being quantified. The following are practical problems to be considered in the formulation of a good theory: (1) deciding whether two tests measure the same trait or traits; (2) analyzing the relative contributions of a pair of…

A method is proposed for providing an absolute, in contrast to comparative, evaluation of how well two tests are equated by transforming their raw scores into a particular common scale. The method is direct, not requiring creation of a standard for comparison; expresses its results in scaled rather than raw scores, and allows examination of the…

The progress of modern mental test theory depends very much on the techniques of maximum likelihood estimation, and many popular applications make use of likelihoods induced by logistic item response models. While, in reality, item responses are nonreplicate within a single examinee and the logistic models are only ideal, practitioners make…

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…

To assess the effects of correlated abilities on test characteristics, and to explore the effects of correlated abilities on the use of a multidimensional item response theory model which does not explicitly account for such a correlation, two tests were constructed. One had two relatively unidimensional subsets of items, the other had all…

A method of estimating the operating characteristics of a new test item added to an established test without assuming a prior model has been proposed by the author. In this paper, the author extends this logic by proposing a different hypothesized distribution of the resulting estimate. The former method used a normal approximation; the present…

Six editions of Scholastic Aptitude Test-Mathematical (SAT-M) were factor analyzed using confirmatory and exploratory methods. Confirmatory factor analyses (using the LISREL VI program) were conducted on correlation matrices among item parcels--sums of scores on a small subset of items. Item parcels were constructed to yield correlation matrices…