Using Shrinkage in Multilevel Models to Understand Intersectionality: A Simulation Study and a Guide for Best Practice

Multilevel models have recently been used to empirically investigate the idea that social characteristics are intersectional such as age, sex, ethnicity, and socioeconomic position interact with each other to drive outcomes. Some argue this approach solves the multiple-testing problem found in standard dummy-variable (fixed-effects) regression, because intersectional effects are automatically shrunk toward their mean. The hope is intersections appearing statistically significant by chance in a fixed-effects regression will not appear so in a multilevel model. However, this requires assumptions that are likely to be broken. We use simulations to show the effect of breaking these assumptions: when there are true main effects/interactions, unmodeled in the fixed part of the model. We show, while the multilevel approach outperforms the fixed-effects approach, shrinkage is less than is desired, and some intersectional effects are likely to appear erroneously statistically significant by chance. We conclude with advice to make this promising method work robustly.