Confounder Analysis Of Counterfactual Models

Counterfactual model is an important tool of statistical causal inference by importing potential and hypothetical results. If we can get two results of observa-tion according to two different conditions-the same individual is disposed and not disposed, we can use the difference between the two results of observation, that is, individual causal inference, to assess the causal effect of disposal on the individual. However, every individual is in only one condition of disposal. That means the same individual is either disposed or not disposed. Therefore, we can only get one result of observation, and the other result is called hypothetical result.In this paper, we mainly come up with the concept of coarse-subpopulation consecutive nonconfounding, and give the necessity and sufficiency for the coarse-subpopulation consecutive nonconfounding. And we conclude that the following statements are equivalent under the assumption of subpopulation nonconfounding:(1) coarse-subpopulation uniform nonconfounding;(2) coarse-subpopulation pair-wise nonconfounding;(3) coarse-subpopulation consecutive nonconfounding;(4) De‖C|E=e, or C‖E.And we propose the collapsibility of association measures and under the third discrete variable. We give the concept of pair-wise and consecutive collapsibility, and get the necessity and sufficiency for pair-wise and consecutive collapsibility of separately, and the necessity and sufficiency for consecutive collapsibility of...