Clarifications on the intersectional MAIHDA approach: A conceptual guide and response to Wilkes and Karimi (2024)

Intersectional Multilevel Analysis of Individual Heterogeneity and Discriminatory Accuracy (MAIHDA) has been welcomed as a new gold standard for quantitative evaluation of intersectional inequalities, and it is being rapidly adopted across the health and social sciences. In their commentary "What does the MAIHDA method explain?", Wilkes and Karimi (2024) raise methodological concerns with this approach, leading them to advocate for the continued use of conventional single-level linear regression models with fixed-effects interaction parameters for quantitative intersectional analysis. In this response, we systematically address these concerns, and ultimately find them to be unfounded, arising from a series of subtle but important misunderstandings of the MAIHDA approach and literature. Since readers new to MAIHDA may share confusion on these points, we take this opportunity to provide clarifications. Our response is organized around four important clarifications: (1) At what level are the additive main effect variables defined in intersectional MAIHDA models? (2) Do MAIHDA models have problems with collinearity? (3) Why does the Variance Partitioning Coefficient (VPC) tend to be small, and the Proportional Change in Variance (PCV) tend to be large in MAIHDA? and (4) What are the goals of MAIHDA analysis?