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Simulation-Extrapolation with Latent Heteroskedastic Error Variance

Published online by Cambridge University Press:  01 January 2025

J. R. Lockwood  and
Daniel F. McCaffrey
J. R. Lockwood*
Affiliation:
Educational Testing Service
Daniel F. McCaffrey
Affiliation:
Educational Testing Service
*
ajrlockwood@ets.org
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Abstract

This article considers the application of the simulation-extrapolation (SIMEX) method for measurement error correction when the error variance is a function of the latent variable being measured. Heteroskedasticity of this form arises in educational and psychological applications with ability estimates from item response theory models. We conclude that there is no simple solution for applying SIMEX that generally will yield consistent estimators in this setting. However, we demonstrate that several approximate SIMEX methods can provide useful estimators, leading to recommendations for analysts dealing with this form of error in settings where SIMEX may be the most practical option.

Keywords

achievement test scoresmeasurement erroritem response theorycovariate adjustmentnonlinear models
Type
Original paper
Information
Psychometrika , Volume 82 , Issue 3 , September 2017 , pp. 717 - 736
Copyright
Copyright © 2017 The Psychometric Society

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Footnotes

Electronic supplementary material The online version of this article (doi:10.1007/s11336-017-9556-y) contains supplementary material, which is available to authorized users.

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