On Reverse Shrinkage Effects and Shrinkage Overshoot

Given a squared Euclidean norm penalty, we examine some less well-known properties of shrinkage estimates. In particular, we highlight that it is possible for some components of the shrinkage estimator to be placed further away from the prior mean than the original estimate. An analysis of this effect is provided within three different modeling settings—encompassing linear, logistic, and ordinal regression models. Additional simulations show that the outlined effect is not a mathematical artefact, but likely to occur in practice. As a byproduct, they also highlight the possibilities of sign reversals (“overshoots”) for shrinkage estimates. We point out practical consequences and challenges, which might arise from the observed effects with special emphasis on psychometrics. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s11336-022-09872-8.