Model-free causal inference of binary experimental data

Abstract

For binary experimental data, we discuss randomization-based inferential procedures that do not need to invoke any modeling assumptions. In addition to the classical method of moments, we also introduce model-free likelihood and Bayesian methods based solely on the physical randomization without any hypothetical super population assumptions about the potential outcomes. These estimators have some properties superior to moment-based ones such as only giving estimates in regions of feasible support. Due to the lack of identification of the causal model, we also propose a sensitivity analysis approach that allows for the characterization of the impact of the association between the potential outcomes on statistical inference.