Cross-Validation in Penalized Linear Mixed Models: Addressing Common Implementation Pitfalls

Abstract: In this paper, we develop an implementation of cross-validation for penalized linear mixed models. While these models have been proposed for correlated high-dimensional data, the current literature implicitly assumes that tuning parameter selection procedures developed for independent data will also work well in this context. We argue that such naive assumptions make analysis prone to pitfalls, several of which we will describe. Here we present a correct implementation of cross-validation for penalized linear mixed models, addressing these common pitfalls. We support our methods with mathematical proof, simulation study, and real data analysis.