Residual permutation tests for feature importance in machine learning

Psychological research has traditionally relied on linear models to test scientific hypotheses. However, the emergence of machine learning (ML) algorithms has opened new opportunities for exploring variable relationships beyond linear constraints. To interpret the outcomes of these 'black-box' algorithms, various tools for assessing feature importance have been developed. However, most of these tools are descriptive and do not facilitate statistical inference. To address this gap, our study introduces two versions of residual permutation tests (RPTs), designed to assess the significance of a target feature in predicting the label. The first variant, RPT on Y (RPT-Y), permutes the residuals of the label conditioned on features other than the target. The second variant, RPT on X (RPT-X), permutes the residuals of the target feature conditioned on the other features. Through a comprehensive simulation study, we show that RPT-X maintains empirical Type I error rates under the nominal level across a wide range of ML algorithms and demonstrates appropriate statistical power in both regression and classification contexts. These findings suggest the utility of RPT-X for hypothesis testing in ML applications.