In this paper, we study the identification of a particular case of the 3PL model, namely when the discrimination parameters are all constant and equal to 1. We term this model, 1PL-G model. The identification analysis is performed under three different specifications. The first specification considers the abilities as unknown parameters. It is…

An item response theory model for dealing with test speededness is proposed. The model consists of two random processes, a problem solving process and a random guessing process, with the random guessing gradually taking over from the problem solving process. The involved change point and change rate are considered random parameters in order to…

According to the recent Nation's Report Card, 12th-graders failed to produce gains on the 2005 National Assessment of Educational Progress (NAEP) despite earning better grades on average. One possible explanation is that 12th-graders were not motivated taking the NAEP, which is a low-stakes test. We develop three Bayesian IRT mixture models to…

An alternative derivation is given for a generalization of the Rasch model which incorporates a guessing parameter. The probability of a correct response to the problem is a projective transformation of the problem difficulty. The ability and difficulty parameters separate into additive components. (Author/JKS)

Estimating ability parameters in latent trait models in general, and in the Rasch model in particular is almost always hampered by noise in the data. In this study several alternative formulations which attempt to deal with these problems without a reparameterization are tested through a Monte Carlo simulation. (Author/JKS)

The theory of projective transformation is applied to the Rasch model for representing test performances. (Author/RC)

Parameter estimation for Keats generalization of the Rasch model that takes account of guessing behavior is investigated. It is shown that no minimal sufficient statistics for the ability parameters independent of the difficulty parameters exist. (Author/JKS)

The problem of characterizing the manifest probabilities of a latent trait model is considered. The approach taken here differs from the standard approach in that a population of examinees is being considered as opposed to a single examinee. Particular attention is given to the Rasch model. (Author/JKS)

The three-parameter logistic model by Birnbaum for the multiple-choice item in the latent trait theory is considered with respect to the item response information function and the unique maximum condition. (Editor/RK)

In studies involving judgments of similarity or dissimilarity, a variety of other variables may also be measured. In such cases, there are important advantages to joint analyses of the dissimilarity and collateral variables. A variety of models are described for relating these and algorithms are described for fitting these to data. (Author/JKS)

A two-stage testing procedure, a routing test followed by one of several alternative second-stage tests, is studied in the situation where the purpose is measurement, not classification. Models are developed, examined, and compared with conventional tests and up-and-down procedures. (DG)

A model is proposed that describes subject behavior on repeat paired comparison preference tests. The model extends prior work in this area in that it explicitly allows for abstentions and permits the derivation of individual true scores of discrimination ability as well as conditional estimates of proportionate preference. (Author/TJH)

For (0, 1) scored multiple-choice tests, a formula giving test reliability as a function of the number of item options is derived, assuming the "knowledge or random guessing model," the parallelism of the new and old tests (apart from the guessing probability), and the assumptions of classical test theory. It is shown that the formula is a more…

A modified beta binomial model is presented for use in analyzing random guessing multiple choice tests and taste tests. Detection probabilities for each item are distributed beta across the population subjects. Properties for the observable distribution of correct responses are derived. Two concepts of true score estimates are presented.…

On distractor-identification tests students mark as many distractors as possible on each test item. A grading scale is developed for this type testing. The score is optimal in that it yields an unbiased estimate of the student's score as if no guessing had occurred. (Author/JKS)