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Simulation-Extrapolation with Latent Heteroskedastic Error Variance

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  • J. R. Lockwood

    (Educational Testing Service)

  • Daniel F. McCaffrey

    (Educational Testing Service)

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.

Suggested Citation

  • J. R. Lockwood & Daniel F. McCaffrey, 2017. "Simulation-Extrapolation with Latent Heteroskedastic Error Variance," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 717-736, September.
    • Handle: RePEc:spr:psycho:v:82:y:2017:i:3:d:10.1007_s11336-017-9556-y
    DOI: 10.1007/s11336-017-9556-y
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    References listed on IDEAS

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    1. Michela Battauz & Ruggero Bellio, 2011. "Structural Modeling of Measurement Error in Generalized Linear Models with Rasch Measures as Covariates," Psychometrika, Springer;The Psychometric Society, vol. 76(1), pages 40-56, January.
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    7. Michela Battauz & Ruggero Bellio & Enrico Gori, 2008. "Reducing Measurement Error in Student Achievement Estimation," Psychometrika, Springer;The Psychometric Society, vol. 73(2), pages 289-302, June.
    8. Raymond J. Carroll & Yuedong Wang, 2008. "Nonparametric variance estimation in the analysis of microarray data: a measurement error approach," Biometrika, Biometrika Trust, vol. 95(2), pages 437-449.
    9. Brian Junker & Lynne Schofield & Lowell Taylor, 2012. "The use of cognitive ability measures as explanatory variables in regression analysis," IZA Journal of Labor Economics, Springer;Forschungsinstitut zur Zukunft der Arbeit GmbH (IZA), vol. 1(1), pages 1-19, December.
    10. J. R. Lockwood & Daniel F. McCaffrey, 2014. "Correcting for Test Score Measurement Error in ANCOVA Models for Estimating Treatment Effects," Journal of Educational and Behavioral Statistics, , vol. 39(1), pages 22-52, February.
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    2. J. R. Lockwood & Daniel F. McCaffrey, 2019. "Impact Evaluation Using Analysis of Covariance With Error-Prone Covariates That Violate Surrogacy," Evaluation Review, , vol. 43(6), pages 335-369, December.

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