Graph-theoretic Inference for Random Effects in High-dimensional Studies

TL;DR

This paper introduces a non-parametric, graph-theoretic test for detecting random effects in high-dimensional mixed models, which does not require model specification or parameter estimation, and is validated through simulations and real data.

Contribution

It proposes a novel rank-based, graph-theoretic testing method for random effects in high-dimensional settings, avoiding model misspecification and parameter estimation.

Findings

The test is consistent and asymptotically null.

Simulation studies show high power and robustness.

Application to real data demonstrates practical utility.

Abstract

We study the problem of testing for the presence of random effects in mixed models with high-dimensional fixed effects. To this end, we propose a rank-based graph-theoretic approach to test whether a collection of random effects is zero. Our approach is non-parametric and model-free in the sense that we not require correct specification of the mixed model nor estimation of unknown parameters. Instead, the test statistic evaluates whether incorporating group-level correlation meaningfully improves the ability of a potentially high-dimensional covariate vector $X$ to predict a response variable $Y$. We establish the consistency of the proposed test and derive its asymptotic null distribution. Through simulation studies and a real data application, we demonstrate the practical effectiveness of the proposed test.