Matching Estimators for Causal Inference with Error-Prone Covariates

• Activity Number: 3
• Type: Invited
• Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Social Statistics Section
• Author(s): J.R. Lockwood*+ and Daniel McCaffrey
• Companies: Educational Testing Service and Educational Testing Service
• Keywords: propensity scores ; balancing scores ; surrogates ; latent variables ; measurement error

Abstract

This paper considers the problem of constructing a matching estimator when there is misalignment between the observed covariates and the covariates required for strong ignorability of treatment assignment. This is the case, for example, when covariates related to outcomes and treatment assignment are measured with error by surrogates. We establish necessary and sufficient conditions for both weighting and matching with functions of observed covariates to yield valid causal effect estimators. We then provide theorems and arguments indicating that while constructing valid weighting estimators from surrogates is often possible, it is generally not possible to construct valid matching estimators from surrogates. We also demonstrate that constructing valid matching estimators using imputed values of latent covariates given the observed data will generally require the outcome to be used in the imputation model, undermining one of the main advantages of matching estimators. The results apply to common measurement error settings including continuous variables with continuous measurement error, discrete variables with misclassification, and factor and item response theory models.