Regression-based causal inference with factorial experiments: estimands, model specifications and design-based properties
成果类型：
Article
署名作者：
Zhao, Anqi; Ding, Peng
署名单位：
National University of Singapore; University of California System; University of California Berkeley
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/asab051
发表日期：
2022
页码：
799815
关键词：
摘要：
Factorial designs are widely used because of their ability to accommodate multiple factors simultaneously. Factor-based regression with main effects and some interactions is the dominant strategy for downstream analysis, delivering point estimators and standard errors simultaneously via one least-squares fit. Justification of these convenient estimators from the design-based perspective requires quantifying their sampling properties under the assignment mechanism while conditioning on the potential outcomes. To this end, we derive the sampling properties of the regression estimators under a wide range of specifications, and establish the appropriateness of the corresponding robust standard errors for Wald-type inference. The results help to clarify the causal interpretation of the coefficients in these factor-based regressions, and motivate the definition of general factorial effects to unify the definitions of factorial effects in various fields. We also quantify the bias-variance trade-off between the saturated and unsaturated regressions from the design-based perspective.