A Generalized Levene's Scale Test for Variance Heterogeneity in the Presence of Sample Correlation and Group Uncertainty

TL;DR

This paper extends Levene's test to handle complex data with sample correlation and group uncertainty, ensuring accurate variance heterogeneity detection in such settings.

Contribution

It introduces a generalized scale test using least absolute deviation regression within a two-stage framework, applicable to correlated samples and uncertain group memberships.

Findings

The gS test follows a chi-squared distribution under null hypothesis.

The gS test is independent of the location test under null.

The method performs well in simulations and genetic studies.

Abstract

We generalize Levene's test for variance (scale) heterogeneity between $k$ groups for more complex data, which includes sample correlation and group membership uncertainty. Following a two-stage regression framework, we show that least absolute deviation regression must be used in the stage 1 analysis to ensure a correct asymptotic $\chi^2_{k-1}/(k-1)$ distribution of the generalized scale ($gS$) test statistic. We then show that the proposed $gS$ test is independent of the generalized location test, under the joint null hypothesis of no mean and no variance heterogeneity. Consequently, we generalize the recently proposed joint location-scale ($gJLS$) test valuable in settings where there is an interaction effect, but one interacting variable is not available. We evaluate the proposed method via an extensive simulation study, and two genetic association application studies.