to the centroid of the white group. The hyperellipsoid was continuously expanded, updating the centroid and variance-covariance matrix every time another subject was added to the white group inside the hyperellipsoid. Expansion continued until further expansion started to bring in primarily subjects who were previously thought to be non-white on the basis of self-report. Thus, the white group was defined partly by self-report and partly by clustering in a principal-component space. The process resulted in a sample of 7702 putatively white individuals, including 101 for whom we did not have self-reported ethnicity and 46 who had originally self-reported as something other than white. Ten principal components were then computed on the newly defined white group and they were also used as covariates in all analyses to correct for any spurious effects arising from population stratification.
