Robust Testing in Generalized Linear Models by Sign Flipping Score Contributions

Abstract

Summary Generalized linear models are often misspecified because of overdispersion, heteroscedasticity and ignored nuisance variables. Existing quasi‐likelihood methods for testing in misspecified models often do not provide satisfactory type I error rate control. We provide a novel semiparametric test, based on sign flipping individual score contributions. The parameter tested is allowed to be multi‐dimensional and even high dimensional. Our test is often robust against the mentioned forms of misspecification and provides better type I error control than its competitors. When nuisance parameters are estimated, our basic test becomes conservative. We show how to take nuisance estimation into account to obtain an asymptotically exact test. Our proposed test is asymptotically equivalent to its parametric counterpart.

Permutation testing in high-dimensional linear models: an empirical investigation

“…The test BM from Bühlmann [37] had higher power than the permutation methods in this specific setting, but was anti-conservative for small α. In the simulations underlying Table 9, we did not use sign-flipping, which is known to be robust to heteroscedasticity [12,13]. Surprisingly, our tests nevertheless provided appropriate type I control.…”

“…Permutation tests can be robust to violations of the standard linear model, such as nonnormality and heteroscedasticity [12,13]. The power of parametric methods is often substantially decreased when the residuals have heavy tails.…”

“…Permutation tests for low-dimensional linear models are valuable for two main reasons. First, they are robust to violations of certain standard assumptions, such as normality and homoscedasticity [12,13]. Second, when the outcome is multidimensional, a permutation-based test can be combined with existing permutation-based multiple testing methods, which tend to be relatively powerful, since they take into account the dependence structure of the outcomes [5][6][7]14].…”

Consistency of invariance-based randomization tests

“…A number of invariance-based randomization based tests have been developed for linear and generalized linear models (Freedman and Lane, 1983;Perry and Owen, 2010;Winkler et al, 2014;Hemerik et al, 2020a). The works by Anderson and Legendre (1999); Winkler et al (2014) review and compare a number of previously proposed permutation methods for inference in linear models with nuisance parameters.…”

Computationally efficient familywise error rate control in genome‐wide association studies using score tests for generalized linear models

“…We are not aware of any well‐established approximate methods using permutations in presence of covariates in nonnormal GLMs, but recently Hemerik, Goeman, and Finos (2019) presented a method based on flipping the sign of score contributions.…”