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Abstract:
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Estimating treatment effect is important in causal inference. In randomized experiments, a commonly used estimator is the difference in means of the outcomes in treatment and control groups. However, when there are some pretreatment covariates, it is often possible to improve the precision of causal estimation by carefully using the covariate information. For example, linear and logistic models are popularly used to take into consideration the covariate information with continuous or binary outcomes. However, these models may be misspecified which may result in less efficient estimators and even invalid inference. Previous literature has shown that with careful design of the linear model, the estimation precision will always be improved even if the observation does not satisfy the linear model, and the corresponding inference can be corrected using variance estimator robust to Heteroscedasticity. We extend this result to generalized linear models (GLMs). We propose a new estimator based on GLM, prove its improved precision, and provide large-sample valid inference, all of which are robust to misspecification of the GLMs.
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