Nested logit models have been presented as an alternative to multinomial logistic models for multiple-choice test items (Suh and Bolt in "Psychometrika" 75:454-473, 2010) and possess a mathematical structure that naturally lends itself to evaluating the incremental information provided by attending to distractor selection in scoring. One potential…

A comprehensive analysis of difficulty for multiple-choice items requires information at different levels: the test, the items, and the alternatives. This paper introduces a new parameterization of the nominal categories model (NCM) for analyzing difficulty at these three levels. The new parameterization is referred to as the NE-NCM and is…

Nested logit item response models for multiple-choice data are presented. Relative to previous models, the new models are suggested to provide a better approximation to multiple-choice items where the application of a solution strategy precedes consideration of response options. In practice, the models also accommodate collapsibility across all…

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

On a multiple-choice test in which each item has k alternative responses, the test taker is permitted to choose any subset which he believes contains the one correct answer. A scoring system is devised. (Author/CTM)

A modification of the method of reciprocal averages for scaling multiple choice data is proposed. The proposed method handles the data in a piecewise fashion and allows for faster convergence to a solution. (Author/JKS)

In Guttman-type quantification of contingency tables and multiple-choice data (incidence data), the trivial solution because of marginal constraints is typically removed before quantification. Relevant formulas are presented for cases affected by the trivial solution and those that are not. (SLD)

This study formulates a property of a quantification method, the principle of equivalent partitioning. When used with Guttman's principle of internal consistency, the combination allows the analysis of correlational data in terms of the variate(s) chosen by the investigator. Applications to multiple-choice, rank-order, and paired comparison data…

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)

Proposes a parametric approach that involves a modification of standard Item Response Theory models that explicitly accounts for the nesting of items within the same testlets and that can be applied to multiple-choice sections comprising a mixture of independent items and testlets. (Author/SLD)

Proposed and evaluated two new methods of improving the measurement precision of a general test factor. One provides a multidimensional item response theory estimate based on administrations of multiple-choice test items that span general and nuisance dimensions, and the other chooses items adaptively to maximize the precision of the general…

Presents a latent variable representation for multiple-choice items and option characteristic curves, and proposes a criterion for distractors based on distractor selection ratios. Results allow for testing the criterion from observable data without specifying a parametric form for the characteristic curves. (Author/SLD)

Complete response vectors of all answer options in multiple-choice items can be used to estimate ability. The rising selection ratios criterion is necessary for scoring individuals because it implies that estimated ability always increases when the correct alternative is selected. This paper introduces the generalized DLT model, which assumes…

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.…