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Matching and Weighting With Functions of Error-Prone Covariates for Causal Inference

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  • J. R. Lockwood
  • Daniel F. McCaffrey

Abstract

Matching estimators are commonly used to estimate causal effects in nonexperimental settings. Covariate measurement error can be problematic for matching estimators when observational treatment groups differ on latent quantities observed only through error-prone surrogates. We establish necessary and sufficient conditions for matching and weighting with functions of observed covariates to yield unconfounded causal effect estimators, generalizing results from the standard (i.e., no measurement error) case. We establish that in common covariate measurement error settings, including continuous variables with continuous measurement error, discrete variables with misclassification, and factor and item response theory models, no single function of the observed covariates computed for all units in a study is appropriate for matching. However, we demonstrate that in some circumstances, it is possible to create different functions of the observed covariates for treatment and control units to construct a variable appropriate for matching. We also demonstrate the counterintuitive result that in some settings, it is possible to selectively contaminate the covariates with additional measurement error to construct a variable appropriate for matching. We discuss the implications of our results for the choice between matching and weighting estimators with error-prone covariates. Supplementary materials for this article are available online.

Suggested Citation

  • J. R. Lockwood & Daniel F. McCaffrey, 2016. "Matching and Weighting With Functions of Error-Prone Covariates for Causal Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1831-1839, October.
    • Handle: RePEc:taf:jnlasa:v:111:y:2016:i:516:p:1831-1839
    DOI: 10.1080/01621459.2015.1122601
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    Cited by:

    1. Hongwen Guo & Mo Zhang & Paul Deane & Randy E. Bennett, 2019. "Writing Process Differences in Subgroups Reflected in Keystroke Logs," Journal of Educational and Behavioral Statistics, , vol. 44(5), pages 571-596, October.
    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.
    3. 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.
    4. 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.
    5. 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.
    6. Finn Tarp & Sam Jones & Felix Schilling, 2021. "Doing business while holding public office: Evidence from Mozambique’s firm registry," DERG working paper series 21-08, University of Copenhagen. Department of Economics. Development Economics Research Group (DERG).
    7. 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.

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