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

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.