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Kernel Smoothing Approaches to Nonparametric Item Characteristic Curve Estimation

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, 1205 Dr. Penfield Ave., Montreal, Quebec, CANADA H3A 1B1.
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Abstract

The option characteristic curve, the relation between ability and probability of choosing a particular option for a test item, can be estimated by nonparametric smoothing techniques. What is smoothed is the relation between some function of estimated examinee ability rankings and the binary variable indicating whether or not the option was chosen. This paper explores the use of kernel smoothing, which is particularly well suited to this application. Examples show that, with some help from the fast Fourier transform, estimates can be computed about 500 times as rapidly as when using commonly used parametric approaches such as maximum marginal likelihood estimation using the three-parameter logistic distribution. Simulations suggest that there is no loss of efficiency even when the population curves are three-parameter logistic. The approach lends itself to several interesting extensions.

Keywords

fast Fourier transformpolytomous responsebootstrappingoption characteristic curvetrace line
Type
Original Paper
Information
Psychometrika , Volume 56 , Issue 4 , December 1991 , pp. 611 - 630
Copyright
Copyright © 1991 The Psychometric Society

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Footnotes

The author wishes to acknowledge the support of the National Sciences and Engineering Research Council of Canada through grant A320 and the support of Educational Testing Service during his leave there.

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