Measurement Invariance is Necessary but Not Sufficient: Intersectional Validity in Developing and Adapting Measures

Objective: Measurement invariance is usually tested one demographic axis at a time. This article shows that invariance on each axis does not entail invariance across the strata those axes jointly define, and gives a procedure for testing it. Method: Simulated data with differential item functioning planted in an interaction pattern demonstrate the logic, and a Monte Carlo study of 9,000 replications across 23 conditions estimates when the two verdicts diverge. An applied example tests the two-factor PHQ-9 across eight sex-by-race/ethnicity strata in NHANES 2005–2016 (N = 31,180 adults; mean age 47.5 years, SD = 18.8; 50.8% women; 42.9% White, 26.1% Hispanic, 21.7% Black, 9.3% other). Results: Under a pure interaction, marginal comparisons returned equivalence in 95% to 100% of replications while the joint comparison tracked the planted effect. In NHANES, joint invariance held. Conclusions: Invariance evidence licenses the comparison it was gathered for.