Default Priors for the Intercept Parameter in Logistic Regressions.

Area of Science:

• Statistics
• Machine Learning
• Biostatistics

Background:

• Separation in logistic regression, where predictors perfectly discriminate outcomes, prevents maximum likelihood estimation.
• Bayesian regression with shrinkage priors is a viable alternative, but the intercept's prior is often overlooked.
• Existing methods lack focus on intercept prior's role in handling separation.

Purpose of the Study:

• To propose and evaluate alternative prior distributions for the intercept in Bayesian logistic regression.
• To assess the impact of intercept priors on regression coefficient estimation, particularly under separation.
• To investigate the interplay between intercept and coefficient priors.

Main Methods:

• Development of novel prior distributions for the intercept that downweight extreme parameter values.
• Simulation studies and analysis of exemplar datasets to quantify differences across priors.
• Stratification of results by established measures of data separation.

Main Results:

• Proposed intercept priors yield more efficient regression coefficient estimation in nearly separated datasets compared to diffuse priors.
• Efficiency is maintained in non-separated datasets, suggesting suitability for default use.
• Findings are more sensitive to intercept priors when coefficient priors are weakly informative.

Conclusions:

• The choice of intercept prior significantly impacts Bayesian logistic regression, especially when dealing with separation.
• Proposed priors offer improved efficiency and robustness, making them valuable for practical applications.
• Careful consideration of both intercept and coefficient priors is crucial for reliable regression modeling.