Presented By: Department of Statistics Dissertation Defenses
Methods for Causal Inference in Settings with Clustered Data Subject to Missingness and Measurement Error
Joshua Wasserman
Educational programs, healthcare policies, and economic shocks frequently act upon intact clusters rather than isolated individuals. Evaluations of such interventions can adjust for baseline differences between clusters with matching, then address persisting imbalances through regression adjustment. The Peters-Belson (PB)/Oaxaca-Blinder (OB) estimator fits a regression to predict outcomes individuals would have had if they were in the control condition, and adjusts for imbalances in predicted outcomes by comparing individuals’ differences between observed and predicted outcomes.
This dissertation begins by showing that in studies that enroll or match only a small number of clusters, the regression fit contributes non-negligibly to variability of the PB/OB estimator both across studies and across treatment allocations within studies. It makes two proposals in response: first, incorporating auxiliary clusters—those that are not retained in the initial cluster match—into the regression fit, and second, defining the regression coefficients and the PB/OB estimator as M-estimators of regression. The first proposal exhibits promising gains in precision in simulations and an empirical application, while the second exhibits improved estimation of sampling variability over variance estimators that ignore variation from the coefficient estimates, particularly when paired with a novel jackknife-type bias correction.
The CR2 adjustment is a widely used bias correction for cluster-robust variance estimates, but it may be computationally infeasible in studies with large clusters given existing routines’ reliance on obtaining spectral decompositions of estimated cluster-specific covariance matrices. Chapter 4 provides exact representations of CR2 that obviate this step of the computations, reducing walltime of CR2 estimates from over a day to just over a minute in settings previously deemed too computationally burdensome.
The concluding chapter focuses on the initial cluster-level match, proposing two propensity score (PS) estimators that balance latent confounders when only noisy measurements are available, if they are available at all. These PS estimators improve matching feasibility and reduce the MSE of treatment effect estimators compared to propensity scores generated from a logistic regression fit to the noisy measurements.
This dissertation begins by showing that in studies that enroll or match only a small number of clusters, the regression fit contributes non-negligibly to variability of the PB/OB estimator both across studies and across treatment allocations within studies. It makes two proposals in response: first, incorporating auxiliary clusters—those that are not retained in the initial cluster match—into the regression fit, and second, defining the regression coefficients and the PB/OB estimator as M-estimators of regression. The first proposal exhibits promising gains in precision in simulations and an empirical application, while the second exhibits improved estimation of sampling variability over variance estimators that ignore variation from the coefficient estimates, particularly when paired with a novel jackknife-type bias correction.
The CR2 adjustment is a widely used bias correction for cluster-robust variance estimates, but it may be computationally infeasible in studies with large clusters given existing routines’ reliance on obtaining spectral decompositions of estimated cluster-specific covariance matrices. Chapter 4 provides exact representations of CR2 that obviate this step of the computations, reducing walltime of CR2 estimates from over a day to just over a minute in settings previously deemed too computationally burdensome.
The concluding chapter focuses on the initial cluster-level match, proposing two propensity score (PS) estimators that balance latent confounders when only noisy measurements are available, if they are available at all. These PS estimators improve matching feasibility and reduce the MSE of treatment effect estimators compared to propensity scores generated from a logistic regression fit to the noisy measurements.
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