Identification in Causal Models With Hidden Variables.

Area of Science:

• Causal inference
• Statistical modeling
• Graphical models

Background:

• Causal inference relies on counterfactual reasoning and potential outcomes.
• Observed data often requires assumptions to link with counterfactuals via causal models.
• Causal models have evolved from potential outcomes to graphical representations.

Purpose of the Study:

• To review identification theory in causal models with hidden variables.
• To cover common causal inference targets like causal effects and path-specific effects.
• To present a formulation using causal graphical models and the fixing operator.

Main Methods:

• Review of existing causal inference identification theories.
• Formulation of theory using causal graphical models.
• Application of the fixing operator for statistical intervention.

Main Results:

• Identification results for causal inference targets in models with hidden variables are complex.
• The g-formula, manipulated distribution, and truncated factorization are key for identification.
• A simplified theory using causal graphical models and the fixing operator is described.

Conclusions:

• Causal graphical models and the fixing operator offer a framework for causal inference with hidden variables.
• The review provides a foundation for understanding identification in complex causal settings.
• This work facilitates the estimation of various causal effects in the presence of unobserved confounders.