  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. 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 can strongly improve predictive performance, in terms of
accuracy, calibration or coverage. For linear regression, we use small sample
splits of a large, fairly typical epidemiological data set to illustrate this.
We show that usage of differential ridge penalties for covariate groups may
enhance prediction accuracy, while calibration and coverage benefit from
additional shrinkage of the penalties. In the logistic setting, we apply an
external simulation to demonstrate that local shrinkage improves calibration
with respect to global shrinkage, while providing better prediction accuracy
than other solutions, like Firth's correction. The benefits of the alternative
shrinkage methods are easily accessible via example implementations using
\texttt{mgcv} and \texttt{r-stan}, including the estimation of multiple
penalties. A synthetic copy of the large data set is shared for
reproducibility.

Methodology;Applications