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Inverse probability weighting with error-prone covariates

Author

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  • Daniel F. McCaffrey
  • J. R. Lockwood
  • Claude M. Setodji

Abstract

Inverse probability-weighted estimators are widely used in applications where data are missing due to nonresponse or censoring and in the estimation of causal effects from observational studies. Current estimators rely on ignorability assumptions for response indicators or treatment assignment and outcomes being conditional on observed covariates which are assumed to be measured without error. However, measurement error is common for the variables collected in many applications. For example, in studies of educational interventions, student achievement as measured by standardized tests is almost always used as the key covariate for removing hidden biases, but standardized test scores may have substantial measurement errors. We provide several expressions for a weighting function that can yield a consistent estimator for population means using incomplete data and covariates measured with error. We propose a method to estimate the weighting function from data. The results of a simulation study show that the estimator is consistent and has no bias and small variance. Copyright 2013, Oxford University Press.

Suggested Citation

  • Daniel F. McCaffrey & J. R. Lockwood & Claude M. Setodji, 2013. "Inverse probability weighting with error-prone covariates," Biometrika, Biometrika Trust, vol. 100(3), pages 671-680.
    • Handle: RePEc:oup:biomet:v:100:y:2013:i:3:p:671-680
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    File URL: http://hdl.handle.net/10.1093/biomet/ast022
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    Citations

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    Cited by:

    1. 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.
    2. J. R. Lockwood & D. McCaffrey, 2020. "Using hidden information and performance level boundaries to study student–teacher assignments: implications for estimating teacher causal effects," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(4), pages 1333-1362, October.
    3. Hwanhee Hong & Kara E. Rudolph & Elizabeth A. Stuart, 2017. "Bayesian Approach for Addressing Differential Covariate Measurement Error in Propensity Score Methods," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1078-1096, December.
    4. Hao Dong & Daniel L. Millimet, 2020. "Propensity Score Weighting with Mismeasured Covariates: An Application to Two Financial Literacy Interventions," JRFM, MDPI, vol. 13(11), pages 1-24, November.
    5. Di Shu & Grace Y. Yi, 2018. "Estimation of Causal Effect Measures in the Presence of Measurement Error in Confounders," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(1), pages 233-254, April.
    6. Trang Quynh Nguyen & Elizabeth A. Stuart, 2020. "Propensity Score Analysis With Latent Covariates: Measurement Error Bias Correction Using the Covariate’s Posterior Mean, aka the Inclusive Factor Score," Journal of Educational and Behavioral Statistics, , vol. 45(5), pages 598-636, October.
    7. Nicholas T. Longford, 2015. "Equating Without an Anchor for Nonequivalent Groups of Examinees," Journal of Educational and Behavioral Statistics, , vol. 40(3), pages 227-253, June.
    8. 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.
    9. Marie-Ann Sengewald & Steffi Pohl, 2019. "Compensation and Amplification of Attenuation Bias in Causal Effect Estimates," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 589-610, June.
    10. 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.

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