Interaction Testing: Residuals-Based Permutations and Parametric Bootstrap in Continuous, Count, and Binary Data

Abstract To obtain statistical inference about interaction hypotheses without making strong distributional assumptions, permutation tests based on permuting the outcomes are often being used. It was shown that in continuous and binary data these tests might not be even approximately valid and parametric bootstrap was suggested as a viable alternative, outperforming such permutation tests. We describe an alternative permutation test, permuting the null hypothesis residuals rather than the outcome. Using simulations, we compare accuracy across the permutation tests and parametric bootstrap, studying continuous, binary, and additionally count data. Finally, we address power.