Two regression models were tested to assess the impact of item-level invariance. First, quitting smoking was regressed on the FTND latent variable in baseline models that did not account for item invariance and compared to adjusted models that accounted for model invariance (Figure S2)1. Second, a similar procedure was conducted to evaluate the impact of measurement non-invariance on the association between FTND and Rs16969968. The regression coefficients were compared between baseline and adjusted models. All regression analyses, included sex (male or female), race (European American or African American), and study sample (AAND, COGEND, COHRA1, COPDGene, or UW-TTURC) as covariates. All statistical testing was two-tailed with p<.05 used to declare statistical significance.