Matching Methods for Causal Inference
Matching and weighting methods are commonly used to reduce confounding bias in observational studies. Many existing methods are sensitive to user-provided inputs, provide little formal guidance in selecting these inputs, and do not necessarily return a balanced subset of the data. The proposed method adapts the support vector machine classifier in order to provide a fully automated, nonparametric procedure for identifying the largest balanced subset of the data. The method allows for a sensitivity analysis and an assessment of the common support assumption. Two applications, a simulation study and a benchmark dataset, illustrate the method's use and efficacy.
Balancing within the Margin: Causal Effect Estimation with Support Vector Machines
Marginal structural models (MSMs) are becoming increasingly popular as a tool to make causal inference from longitudinal data. Unlike standard regression models, MSMs can adjust for time-dependent observed confounders while avoiding the bias due to the adjustment for covariates affected by the treatment. Despite their theoretical appeal, a main practical difficulty of MSMs is the required estimation of inverse probability weights. Previous studies have found that MSMs can be highly sensitive to misspecification of treatment assignment model even when the number of time periods is moderate. To address this problem, we generalize the Covariate Balancing Propensity Score (CBPS) methodology of Imai and Ratkovic (2014) to longitudinal analysis settings. The CBPS estimates the inverse probability weights such that the resulting covariate balance is improved. Unlike the standard approach, the proposed methodology incorporates all covariate balancing conditions across multiple time periods. Since the number of these conditions grows exponentially as the number of time period increases, we also propose a low-rank approximation in order to ease the computational burden. Our simulation and empirical studies suggest that the CBPS significantly improves the empirical performance of MSMs by making the treatment assignment model more robust to misspecification. Open-source software is available for implementing the proposed methods.
With Kosuke Imai.
Forthcoming, Journal of the American Statistical Association.
Robust Estimation of Inverse Probability Weights for Marginal Structural Models.
The propensity score plays a central role in a variety of causal inference settings. In particular, matching and weighting methods based on the estimated propensity score have become increasingly common in observational studies. Despite their popularity and theoretical appeal, the main practical difficulty of these methods is that the propensity score must be estimated. Researchers have found that slight misspecification of the propensity score model can result in substantial bias of estimated treatment effects. In this paper, we introduce covariate balancing propensity score (CBPS) methodology, which models treatment assignment while optimizing the covariate balance. This is done by exploiting the dual characteristics of the propensity score as a covariate balancing score and the conditional probability of treatment assignment. The estimation of the CBPS is done within the generalized method of moments or empirical likelihood framework. We find that the CBPS dramatically improves the poor empirical performance of propensity score matching and weighting methods reported in the literature. We also show that the CBPS can be extended to a number of other important settings, including the estimation of the generalized propensity score for non-binary treatments and the generalization of experimental estimates to a target population. Open-source software is available for implementing the proposed methods.
With Kosuke Imai.
Journal of the Royal Statistical Society, Series B (Statistical Methodology), Vol. 76, No. 1 (January), pp. 243-246.
Covariate Balancing Propensity Score
Improving Instrumental Variable Methods
Instrumental variable estimation is a long-established means of reducing endogeneity bias in regression coefficients. Researchers commonly confront two problems when conducting an IV analysis: the instrument may be only weakly predictive of the endogenous variable, and the estimates are valid only for observations that comply with the instrument. We introduce Complier Instrumental Variable (CIV) estimation, a method for estimating who complies with the instrument. CIV uses these compliance probabilities to strengthen the instrument through up-weighting estimated compliers. As compliance is latent, we model each observation's density as a mixture between that of a complier and a non-complier. We derive a Gibbs sampler and Expectation Conditional Maximization algorithm for estimating the CIV model. A set of simulations shows that CIV performs favorably relative to several existing alternative methods, particularly in the presence of small sample sizes and weak instruments. We then illustrate CIV on data from a prominent study estimating the effect of property rights on growth. We show how CIV can strengthen the instrument and generate more reliable results. We also show how characterizing the compliers can help cast insight into the underlying political dynamic.
With Yuki Shiraito.
Strengthening Weak Instruments by Modeling Compliance