Logistic or linear? Estimating causal effects of experimental treatments on binary outcomes using regression analysis

Area of Science:

• Psychology
• Econometrics
• Statistics

Background:

• Psychologists commonly employ nonlinear models like logit or probit for binary outcomes.
• These nonlinear strategies present challenges in estimating causal effects and interpreting results.
• Quantities derived from nonlinear models, such as odds ratios, are often difficult to understand.

Purpose of the Study:

• To demonstrate that linear regression is the superior method for estimating causal effects of treatments on binary outcomes.
• To analytically prove the unbiasedness of linear regression estimates using the Neyman-Rubin causal model.
• To provide practical evidence through simulations and real-world data analysis.

Main Methods:

• Leveraging econometric theory and statistical findings.
• Applying the Neyman-Rubin causal model for analytical proof.
• Conducting simulations and analyzing a large dataset of middle school students.

Main Results:

• Linear regression coefficients offer direct interpretability in terms of probabilities.
• Linear regression remains robust and safer when incorporating interaction terms or fixed effects.
• Simulations and data analysis confirm the effectiveness and unbiasedness of linear regression for causal effect estimation.

Conclusions:

• Linear regression is recommended for psychologists estimating treatment effects on binary outcomes.
• The study advocates for a shift from nonlinear models to linear regression for enhanced clarity and accuracy.
• Findings support the use of linear regression for more reliable causal inference in psychological research.