Extending The Range of Application of Permutation Tests: the Expected Permutation p-value Approach

TL;DR

This paper introduces an expected permutation p-value (Eppv) approach that extends permutation tests to cases where exchangeability does not hold, especially in logistic regression, broadening their applicability.

Contribution

It develops an Eppv method for permutation tests in non-exchangeable settings, particularly within generalized linear models like logistic regression.

Findings

Eppv approach successfully applied to logistic regression.

Simulation study demonstrates Eppv's effectiveness.

Real data illustration confirms practical utility.

Abstract

The limitation of permutation tests is that they assume exchangeability. It is shown that in generalized linear models one can construct permutation tests from score statistics in particular cases. When under the null hypothesis the observations are not exchangeable, a representation in terms of Cox-Snell residuals allows to develop an approach based on an expected permutation p-value (Eppv); this is applied to the logistic regression model. A small simulation study and an illustration with real data are given.