Handling parametric assumptions in principal causal effect estimation using Gaussian mixtures.

Area of Science:

• Causal Inference
• Statistical Modeling
• Econometrics

Background:

• Principal stratification models with continuous outcomes often use Gaussian mixture models.
• However, parametric mixture modeling is typically avoided for identifying principal effects when nonparametric identification is not assured.
• Assessing the quality of principal effect estimates is challenging under parametric assumptions.

Purpose of the Study:

• To re-evaluate the utility of parametric mixture modeling in principal stratification.
• To propose a method for assessing the quality of principal effect estimates derived from parametric mixture models.
• To explore the potential of parametric mixture modeling as an accessible tool for causal inference.

Main Methods:

• Utilizing Gaussian mixture models within a parametric estimation framework.
• Employing parametric mixture modeling with and without the guarantee of nonparametric identification to assess estimation quality.
• Implementing the moving exclusion restriction assumption, a variation of the standard exclusion restriction.

Main Results:

• Parametric mixture modeling can be a viable approach for principal stratification, even without nonparametric identification.
• The proposed method allows for the assessment of principal effect estimate quality.
• The moving exclusion restriction aids in evaluating estimates from parametric mixture models.

Conclusions:

• Parametric mixture modeling shows promise as an accessible tool for causal inference in principal stratification.
• This approach can overcome previous limitations and expand possibilities in the field.
• Further research can build upon these findings to refine causal inference methods.