ObjectivesIntersectionality conceptualises how different parts of our identity compound, creating unique and multifaceted experiences of oppression. Our objective was to explore and compare several quantitative analytical approaches to measure interactions among four sociodemographic variables and interpret the relative impact of axes of marginalisation on self-reported health, to visualise the potential elevated impact of intersectionality on health outcomes.DesignSecondary analysis of National Epidemiologic Survey on Alcohol and Related Conditions-III, a nationally representative cross-sectional study of 36 309 non-institutionalised US citizens aged 18 years or older.Primary outcome measuresWe assessed the effect of interactions among race/ethnicity, disability status, sexual orientation and income level on a self-reported health outcome with three approaches: non-intersectional multivariate regression, intersectional multivariate regression with a single multicategorical predictor variable and intersectional multivariate regression with two-way interactions.ResultsMultivariate regression with a single multicategorical predictor variable allows for more flexibility in a logistic regression problem. In the fully fitted model, compared with individuals who were white, above the poverty level, had no disability and were heterosexual (referent), only those who were white, above the poverty level, had no disability and were gay/lesbian/bisexual/not sure (LGBQ+) demonstrated no significant difference in the odds of reporting excellent/very good health (aOR=0.90, 95% CI=0.71 to 1.13, p=0.36). Multivariate regression with two-way interactions modelled the extent that the relationship between each predictor and outcome depended on the value of a third predictor variable, allowing social position variation at several intersections. For example, compared with heterosexual individuals, LGBQ+ individuals had lower odds of reporting better health among whites (aOR=0.94, 95% CI=0.93 to 0.95) but higher odds of reporting better health among Black Indigenous People of Color (BIPOC) individuals (aOR=1.13, 95% CI=1.11 to 1.15).ConclusionThese quantitative approaches help us to understand compounding intersectional experiences within healthcare, to plan interventions and policies that address multiple needs simultaneously.