Recent advances in item analysis have provided greater capabilities for the analysis of tests, but have also significantly increased the gap between the theory and practice of item analysis. This paper traces the lines of development in item analysis under latent trait theory. (MV)

A general model for the homogeneous case of the continuous response is proposed. The model is an expansion and generalization of the one proposed by the author in 1974, in which the open response situation is dealt with. In this generalized model, the closed response situation is dealt with, and it includes the model for the open response…

A probabilistic approach is introduced to classify and diagnose erroneous rules of operation resulting from a variety of misconceptions ("bugs") in a procedural domain of arithmetic. The model is contrasted with the deterministic approach which has commonly been used in the field of artificial intelligence, and the advantage of treating the…

The Pearson and likelihood ratio statistics are frequently used for assessing the absolute fit of probability models. Researchers are often interested in comparing fits provided by different models which may have a subsuming or non-subsuming relation. A subsuming relation exists when the parameters of the reduced model form a subset of those…

A mathematical setting based on a statistical sampling probability mechanism is described. In this setting, a mathematical meaning is given for the information function; and it becomes possible to study the relative merits of various ability-estimating procedures. The maximum likelihood estimation procedure under the one-, two-, three-parameter…

It has often been argued that all techniques of standard setting are arbitrary and likely to yield different results for different techniques or persons. This paper deals with a related but hitherto ignored aspect of standard setting, namely, the possibility that Angoff or Nedelsky judges misspecify the probabilities of the borderline student's…

Using conventional mental test theory, item parameters of an aptitude or achievement test vary with each group of examinees, and as such are somewhat limited in their use and interpretation. Within the last 25 years, measurement models have emerged in which item parameters are considered to be invariant. Generically referred to as latent trait…

The restrictions on item difficulties that must be met when binomial models are applied to domain-referenced testing are examined. Both a deterministic and a stochastic conception of item responses are discussed with respect to difficulty and Guttman-type items. (Author/BH)

Because it is a true score model employing item parameters which are independent of the examined sample, item characteristic curve theory (ICC) offers several advantages over classical measurement theory. In this paper an approach to biased item identification using ICC theory is described and applied. The ICC theory approach is attractive in that…

Macready and Dayton introduced two probabilistic models for mastery assessment based on an idealistic all-or-none conception of mastery. Alternatively, an application of latent trait theory to mastery testing is proposed (a three parameter logistic model) as a more plausible model for test theory. (Author/CTM)

On well-constructed multiple-choice tests, the most serious threat to measurement is not variation in item discrimination, but the guessing behavior that may be adopted by some students. Ways of ameliorating the effects of guessing are discussed, especially for problems in latent trait models. A new item response model, including an item parameter…

A general approach is proposed for modeling the structure of a two-way contingency table, and for drawing inferences about the marginal and interaction effects, cell parameters, and conditional probabilities. The prior distribution expresses uncertainty in a simple reduced model, in particular the independence model. The posterior estimates of the…

A probabilistic item response theory (IRT) model is developed for pair-comparison design in which the unfolding principle governing the choice process uses a discriminant process analogous to Thurstone's Law of Comparative Judgment. A simulation study demonstrates the feasibility of estimation, and two examples illustrate the implications for…

This document contains three papers from the Methodology Project of the Center for the Study of Evaluation. Methods for characterizing test accuracy are reported in the first two papers. "Bounds on the K Out of N Reliability of a Test, and an Exact Test for Hierarchically Related Items" describes and illustrates how an extension of a…

The analysis of fit of data to a measurement model for graded responses is described. The model is an extension of Rasch's dichotomous model to formats which provide more than two levels of response to items. The model contains one parameter for each person and one parameter for each "step" in an item. A dichotomously-scored item…