Statistical Significance in High-dimensional Linear Mixed Models

This paper develops an inferential framework for high-dimensional linear mixed effect models. Such models are suitable, e.g., when collecting n repeated measurements for M subjects. We consider a scenario where the number of fixed effects p is large (and may be larger than M), but the number of random effects q is small. Our framework is inspired by a recent line of work that proposes de-biasing penalized estimators to perform inference for high-dimensional linear models with fixed effects only. In particular, we demonstrate how to correct a 'naive' ridge estimator to build asymptotically valid confidence intervals for mixed effect models. We validate our theoretical results with numerical experiments that show that our method can successfully account for the correlation induced by the random effects. For a practical demonstration we consider a riboflavin production dataset that exhibits group structure, and show that conclusions drawn using our method are consistent with those obtained on a similar dataset without group structure.