Are repeated measurements, neighbourhoods and intersectional strata exchangeable? On simple means versus random effects in the study of health inequalities

Abstract

Multilevel random-effects (RE) models are standard in social and geographical epidemiology. They rest on the assumption of exchangeability, which means that, before seeing the data, we have no reason to distinguish one group from another: group means become draws from one common distribution. RE models were developed for repeated measurements within individuals where a shared physiology underwrites the assumption, and partial pooling improves prediction. A silent transfer later applied the same machinery to schools, hospitals, neighbourhoods and, recently, to intersectional strata. There exchangeability fails twice: individuals are not repeated measurements of their group, and groups are social positions produced by directional forces such as racism, not draws from a common distribution. We review strict, conditional and tolerant readings of exchangeability and show that they agree: social and intersectional categories are not exchangeable, as this would paradoxically require the absence of the unjustified inequalities which are the very object of study. In many intersectional analyses, shrinkage erases the small and deviating strata, where inequality lives. Modelling injustice as dispersion around a mean domesticates rather than denounces it. For describing realised health inequalities we recommend Simple-Means MAIHDA (S-MAIHDA). Here, each stratum is estimated from its own individuals, and uncertainty is reported openly rather than smoothed. RE models keep their legitimate uses, such as prediction, cluster-randomised trials and the propensity models of causal S-MAIHDA. Exchangeability is not a property of the software. It is a claim about the world, to be justified in every application.

The authors' abstract, as published at the source. Social Science & Medicine, 2026 · DOI ↗