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Maximum Marginal Likelihood Estimation for Semiparametric Item Analysis

Published online by Cambridge University Press:  01 January 2025

J. O. Ramsay  and
S. Winsberg
J. O. Ramsay*
Affiliation:
McGill University
S. Winsberg
Affiliation:
IRCAM
*
Requests for reprints should be sent to J. O. Ramsay, Department of Psychology, 1205 Dr. Penfield Ave., Montreal, Quebec, CANADA H3A 1B1.
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Abstract

The item characteristic curve (ICC), defining the relation between ability and the probability of choosing a particular option for a test item, can be estimated by using polynomial regression splines. These provide a more flexible family of functions than is given by the three-parameter logistic family. The estimation of spline ICCs is described by maximizing the marginal likelihood formed by integrating ability over a beta prior distribution. Some simulation results compare this approach with the joint estimation of ability and item parameters.

Keywords

I-splinesmonotone splinesregression splinesbeta Gaussian quadrature
Type
Original Paper
Information
Psychometrika , Volume 56 , Issue 3 , September 1991 , pp. 365 - 379
Copyright
Copyright © 1991 The Psychometric Society

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Footnotes

The research reported in this paper was supported by Grants APA320 and A4035 from the Natural Sciences and Engineering Research Council of Canada. It was also supported by Contract No. F41689-82-C-10020 from the Air Force Human Resources Laboratory to Educational Testing Service. The author wishes to thank M. Abrahamowicz for his assistance and R. Darrell Bock for providing the parameters for the items used in the simulations.

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