Asymptotic Distribution of Robust Effect Size Index

TL;DR

This paper develops an asymptotic distribution theory for the Robust Effect Size Index (RESI), enabling faster and more reliable inference in various models without bootstrap, demonstrated through simulations and real data applications.

Contribution

It introduces a general theorem for RESI's asymptotic distribution, reducing computational cost and improving inference reliability across multiple regression models.

Findings

RESI has smaller bias than Cohen's d and f.

Asymptotic CI coverage is more reliable than bootstrap.

Speedup of up to 50-fold over bootstrap methods.

Abstract

The Robust Effect Size Index (RESI) is a recently proposed standardized effect size to quantify association strength across models. However, its confidence interval construction has relied on computationally intensive bootstrap procedures. We establish a general theorem for the asymptotic distribution of the RESI using a Taylor expansion that accommodates a broad class of models. Simulations under various linear and logistic regression settings show that RESI and its CI have smaller bias and more reliable coverage than commonly used effect sizes such as Cohen's d and f. Combining with robust covariance estimation yields valid inference under model misspecification. We use the methods to investigate associations of depression and behavioral problems with sex and diagnosis in Autism spectrum disorders, and demonstrate that the asymptotic approach achieves up to a 50-fold speedup over the bootstrap. Our work provides a scalable and reliable alternative to bootstrap inference, greatly enhancing the applicability of RESI to high-dimensional studies.