# Alternatives to default shrinkage methods can improve prediction accuracy, calibration, and coverage: A methods comparison study

## TL;DR

This paper compares alternative shrinkage methods to default ones, showing they can improve prediction accuracy, calibration, and confidence interval coverage in regression models.

## Contribution

The study demonstrates that alternative shrinkage methods, such as differential penalties and Bayesian hierarchical modeling, outperform standard approaches in predictive performance.

## Key findings

- Differential ridge penalties for covariate groups improve prediction accuracy in linear regression.
- Bayesian hierarchical modeling enhances calibration and coverage by allowing local shrinkage.
- Local shrinkage in logistic regression outperforms global shrinkage and Firth’s correction in calibration and accuracy.

## Abstract

While shrinkage is essential in high-dimensional settings, its use for low-dimensional regression-based prediction has been debated. It reduces variance, often leading to improved prediction accuracy. However, it also inevitably introduces bias, which may harm two other measures of predictive performance: calibration and coverage of confidence intervals. Here, the latter evaluates whether the amount of uncertainty is correctly quantified. Much of the criticism stems from the usage of standard shrinkage methods, such as lasso and ridge with a single, cross-validated penalty. Our aim is to show that readily available alternatives may improve predictive performance, in terms of accuracy, calibration or coverage. We study linear and logistic regression. For linear regression, we use small sample splits of a large, fairly typical epidemiological data set to illustrate that usage of differential ridge penalties for covariate groups may enhance prediction accuracy, while calibration and coverage benefit from additional shrinkage of the penalties. Bayesian hierarchical modeling facilitates the latter, including local shrinkage. In the logistic regression setting, we apply an external simulation to illustrate that local shrinkage may improve calibration with respect to global shrinkage, while providing better prediction accuracy than other solutions, like Firth’s correction. The potential benefits of the alternative shrinkage methods are easily accessible via example implementations in R, including the estimation of multiple penalties. A synthetic copy of the large data set is shared for reproducibility.