Test Equating under the Multiple-Choice Model

Jee-Seon Kim, University of Illinois
Bradley A. Hanson, ACT, Inc.

Paper presented at the Annual Meeting of the American Educational Research Association (New Orleans, April, 2000)

Revised: May 12, 2000

Abstract: This paper presents a characteristic curve procedure for computing transformations of the item response theory (IRT) ability scale assuming the multiple-choice model (Thissen & Steinberg, 1984). The multiple-choice model provides a realistic and informative approach to analyzing multiple-choice items in two important ways. First, the probability of guessing is a decreasing function of ability rather than a constant across different ability levels as in the three-parameter logistic model. Second, the model utilizes information from incorrect answers as well as from correct answers. The multiple-choice model includes many well-known IRT models as special cases, such as Bock's (1972) nominal response model. Formulas needed to implement a characteristic curve method for scale transformation are presented for the multiple-choice model. Two moment methods of estimating a scale transformation for the multiple-choice model (the mean/mean and mean/sigma methods) are also presented. The use of the characteristic curve method for the multiple-choice model is illustrated in an example equating ACT mathematics tests, and is compared to the results from the mean/mean and mean/sigma methods. In the process of deriving the scale transformation procedure for the multiple-choice model, corrections were made in some of the formulas presented by Baker (1993) for computing a scale transformation for the nominal response model.

Programs: The programs used in this paper to compute the equating results for the examples are available for downloading.

PDF Download paper in PDF format (380 KB). Version 3.0 or later of Adobe Acrobat Reader (which is available for free) is needed to view this paper.

Return to Papers by Brad Hanson

Return to Brad Hanson's Home Page

Return to OpenIRT Home Page

Last updated: November 16, 2014.