Beyond the Mean: A Flexible Framework for Studying Causal Effects Using Linear Models.

Area of Science:

• Causal inference
• Graph-based causal models
• Observational data analysis

Background:

• Graph-based causal models are widely used for causal inference from observational data.
• Existing methods primarily focus on estimating causal effects on the mean and variance of outcome variables.
• There is a need for a more comprehensive framework to estimate a wider range of causal quantities.

Purpose of the Study:

• To develop a comprehensive framework for defining, identifying, and estimating a broad class of causal quantities in linearly parametrized graph-based models.
• To extend the scope of causal inference beyond mean and variance effects.
• To introduce the concept of 'probability of treatment success' as a computable causal quantity.

Main Methods:

• Developing a framework to link graph-based causal quantities (using the do-operator) to parameters of the model-implied distribution.
• Utilizing causal effect functions to connect theoretical causal quantities to estimable parameters.
• Proposing consistent and asymptotically efficient estimators for these causal quantities.

Main Results:

• The proposed method allows for the estimation of a broader class of causal quantities in graph-based models.
• Demonstrated computation of the 'probability of treatment success' given an intervention.
• The proposed estimators are consistent and converge at a rate of O(n^-1/2), suitable for typical social science sample sizes.
• Maximum likelihood estimators are asymptotically efficient.

Conclusions:

• The developed framework provides a robust method for causal inference in linearly parametrized graph-based models.
• The approach extends causal inference capabilities beyond traditional mean and variance effects.
• The proposed estimators are statistically sound and practical for empirical research in social and behavioral sciences.