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A Comparison of Three Simple Test Theory Models

Published online by Cambridge University Press:  01 January 2025

J. O. Ramsay
J. O. Ramsay*
Affiliation:
McGill University
*
Requests for reprints should be sent to J. O, Ramsay, Department of Psychology, Stewart Biological Sciences Building, 1205 Dr. Penfield Avenue, Montreal QC, H3A 1B1 CANADA.
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Abstract

In very simple test theory models such as the Rasch model, a single parameter is used to represent the ability of any examinee or the difficulty of any item. Simple models such as these provide very important points of departure for more detailed modeling when a substantial amount of data are available, and are themselves of real practical value for small or even medium samples. They can also serve a normative role in test design.

As an alternative to the Rasch model, or the Rasch model with a correction for guessing, a simple model is introduced which characterizes strength of response in terms of the ratio of ability and difficulty parameters rather than their difference. This model provides a natural account of guessing, and has other useful things to contribute as well. It also offers an alternative to the Rasch model with the usual correction for guessing. The three models are compared in terms of statistical properties and fits to actual data. The goal of the paper is to widen the range of “minimal” models available to test analysts.

Keywords

difference modelquotient modelBayesian estimationempirical Bayes estimationmaximum likelihood estimationRasch modeljoint estimationmarginal estimation
Type
Original Paper
Information
Psychometrika , Volume 54 , Issue 3 , September 1989 , pp. 487 - 499
Copyright
Copyright © 1989 The Psychometric Society

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Footnotes

This research was supported by grant AP320 from the Natural Sciences and Engineering Research Council of Canada. The author is grateful for discussions with M. Abrahamowicz, I. Molenaar, D. Thissen, and H. Wainer.

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