Abstract:
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The counterfactual-based causal mediation analysis aims at providing a solid theoretical ground for mediation analysis beyond linear modeling of the outcome and the mediator. However, it has limitations: 1) It is assumption-rich. Some assumptions are debatable or hard to verify in practice. 2) The effect estimates can be biased even when the identification conditions hold as these conditions are not related to how parameters are estimated. 3) The scale of the outcome in some literature is not clearly stated. 4) Counterfactuals are matched but not treated as such. It is invalid to use population models such as unconditional logistic regression on matched data arising from counterfactuals. To address these issues, I introduce a general method for mediation analysis without using counterfactuals. This method is based on the observation that the mediator affects the outcome through its distribution and this distribution depends on the treatment typically through its mean. Identification conditions can be given in terms of likelihood equations. These likelihood equations apply regardless the treatment is continuous or discrete.
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