Identifiability of causal effects with multiple causes and a binary outcome.

Area of Science:

• Causal inference
• Observational studies
• Econometrics

Background:

• Unobserved confounding is a significant challenge in observational studies.
• Shared confounding, where treatments are independent given a latent confounder, has been proposed as a solution.
• Previous research indicated causal effects are unidentifiable without parametric assumptions under linear Gaussian models.

Purpose of the Study:

• To demonstrate causal effect identifiability in a shared confounding setting with a general binary choice outcome model.
• To overcome the identifiability limitations of prior linear Gaussian models.
• To propose a novel identification strategy leveraging distributional incongruence.

Main Methods:

• Utilizing a general binary choice model for the outcome with a non-probit link.
• Leveraging the incongruence between Gaussianity of treatments/latent confounder and non-Gaussianity of the latent outcome.
• Developing a two-step likelihood-based estimation procedure.

Main Results:

• The causal effect is identifiable under the specified binary outcome model, contrary to previous findings with linear Gaussian models.
• The identification strategy relies on the distributional mismatch between variables.
• A feasible two-step estimation procedure is presented.

Conclusions:

• Causal effects can be identified in shared confounding settings with non-Gaussian outcomes, even when treatments are Gaussian.
• The proposed method offers a way to address unobserved confounding in observational data.
• This research advances causal inference methodologies for complex data structures.