Influence of single observations on the choice of the penalty parameter in ridge regression

Penalized regression methods such as ridge regression heavily rely on the choice of the penalty parameter, which is often computed via cross-validation. Discrepancies in the value of the penalty parameter may lead to substantial differences in regression coefficient estimates and predictions. This paper investigates the effect of single observations on the optimal choice of the penalty parameter, showing how the presence of influential points can change it dramatically. The points are distinguished as ‘expanders’ or ‘shrinkers’ based on their effect on the model complexity. The approach supplies a visual exploratory tool to identify influential points, naturally implementable for high-dimensional data where traditional approaches usually fail. Applications to simulated and real data examples, both low- and high-dimensional, are presented. The visual tool is implemented in the R package <i>influridge</i>.