Inference in generalized linear models with robustness to misspecified variances

TL;DR

This paper introduces a semi-parametric testing method for generalized linear models that remains robust against variance misspecification, improving error control especially in small samples and complex data like RNA sequencing.

Contribution

It proposes a novel sign-flipping based test that only requires correct mean model specification, enhancing robustness against variance misspecification in GLMs.

Findings

Asymptotically valid test with strong small-sample performance

Effective in RNA sequencing data with overdispersion

Available in R package flipscores

Abstract

Generalized linear models usually assume a common dispersion parameter, an assumption that is seldom true in practice. Consequently, standard parametric methods may suffer appreciable loss of type I error control. As an alternative, we present a semi-parametric group-invariance method based on sign flipping of score contributions. Our method requires only the correct specification of the mean model, but is robust against any misspecification of the variance. We present tests for single as well as multiple regression coefficients. The test is asymptotically valid but shows excellent performance in small samples. We illustrate the method using RNA sequencing count data, for which it is difficult to model the overdispersion correctly. The method is available in the R library flipscores.