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Joint Consistency of Nonparametric Item Characteristic Curve and Ability Estimation

Published online by Cambridge University Press:  01 January 2025

Jeff Douglas
Jeff Douglas*
Affiliation:
Department of Biostatistics, University of Wisconsin
*
Please send requests for reprints to Jeff Douglas, Department of Biostatistics, K6/438 Clinical Science Center, 600 Highland Avenue, Madison, WI 53792-4675.
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Abstract

The simultaneous and nonparametric estimation of latent abilities and item characteristic curves is considered. The asymptotic properties of ordinal ability estimation and kernel smoothed nonparametric item characteristic curve estimation are investigated under very general assumptions on the underlying item response theory model as both the test length and the sample size increase. A large deviation probability inequality is stated for ordinal ability estimation. The mean squared error of kernel smoothed item characteristic curve estimates is studied and a strong consistency result is obtained showing that the worst case error in the item characteristic curve estimates over all items and ability levels converges to zero with probability equal to one.

Keywords

item characteristic curvekernel smoothinglarge sample theorynonparametric regression
Type
Original Paper
Information
Psychometrika , Volume 62 , Issue 1 , March 1997 , pp. 7 - 28
Copyright
Copyright © 1997 The Psychometric Society

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Footnotes

The author thanks James O. Ramsay and William F. Stout for helpful discussions of this material.

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