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Weighted Likelihood Estimation of Ability in Item Response Theory

Published online by Cambridge University Press:  01 January 2025

Thomas A. Warm
Thomas A. Warm*
Affiliation:
FAA Academy
*
Requests for reprints should be sent to Thomas A. Warm, FAA Academy AAC-934, Mike Monroney Aeronautical Center, PO Box 25082, Oklahoma City, OK 73125.
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Abstract

Applications of item response theory, which depend upon its parameter invariance property, require that parameter estimates be unbiased. A new method, weighted likelihood estimation (WLE), is derived, and proved to be less biased than maximum likelihood estimation (MLE) with the same asymptotic variance and normal distribution. WLE removes the first order bias term from MLE. Two Monte Carlo studies compare WLE with MLE and Bayesian modal estimation (BME) of ability in conventional tests and tailored tests, assuming the item parameters are known constants. The Monte Carlo studies favor WLE over MLE and BME on several criteria over a wide range of the ability scale.

Keywords

maximum likelihood estimationunbiased estimationstatistical biasBayesian modal estimationitem response theorytailored testingadaptive testing
Type
Original Paper
Information
Psychometrika , Volume 54 , Issue 3 , September 1989 , pp. 427 - 450
Copyright
Copyright © 1989 The Psychometric Society

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