Inference in Generalized Linear Models with Robustness to Misspecified Variances

Journal of the American Statistical Association, vol. 120, pp. 2762–2771

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.

Authors 5

1. Riccardo De Santis corresponding

   University of Padua

   Affiliation as printed

   University of Padova

2. Jelle J. Goeman Aachen

   Leiden University Medical Center

   Affiliation as printed

   Leiden University Medical Center

3. Jesse Hemerik

   University of California San Diego · Erasmus University Rotterdam

   Affiliation as printed

   Erasmus University Rotterdam

   University of California San Diego

4. Samuel Davenport

   University of California San Diego · Erasmus University Rotterdam

   Affiliation as printed

   University of California San Diego

   Erasmus University Rotterdam

5. Livio Finos

   University of Padua

   Affiliation as printed

   University of Padova