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Multicategorical Spline Model for Item Response Theory

Published online by Cambridge University Press:  01 January 2025

Michal Abrahamowicz  and
James O. Ramsay
Michal Abrahamowicz*
Affiliation:
McGill University
James O. Ramsay
Affiliation:
McGill University
*
Requests for reprints should be sent to Michal Abrahamowicz, Division of Clinical Epidemiology, Montreal General Hospital, 1650 Cedar Ave., Montreal, PQ, CANADA H3G lA4.
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Abstract

Additional information contained in incorrect responses calls for a multicategorical rather than a binary analysis of multiple choice data. A nonparametric divided-by-total model for joint maximum likelihood estimation of probability-of-choice functions (for particular responses) and of latent ability is proposed. The model approximates probability functions by rational splines. Some illustrative examples of real test data analysis and the results of a Monte Carlo study are presented.

Keywords

rational splinemultiple choice datapolytomous regressionnonparametric regressionjoint maximum likelihood estimationitem analysisability estimation
Type
Original Paper
Information
Psychometrika , Volume 57 , Issue 1 , March 1992 , pp. 5 - 27
Copyright
Copyright © 1992 The Psychometric Society

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Footnotes

The research in this paper was supported by the National Sciences and Engineering Research Council of Canada Grants OGP0105521 and APA 320 awarded to the first and the second author, respectively. The authors are indebted to R. Melzack and A. Baker for making available the data analyzed in this paper. We would also like to thank J. McKenna and B. Cont for their assistance in editing this paper.

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