When EDU was added to the model, the standardized coefficient estimates for the PRS decreased by 0.004 (3%) (B1 to B2). PRS Change R2 decreased by 0.001 (5%) (B1 to B2). When the phenotypic PCs were added to the model, the standardized coefficient estimate for the PRS increased by 0.005 (3%) (B2 to B3). PRS Change R2 increased by 0.001 (5%) (B2 to B3). Although these results demonstrate the same general pattern as the example above using TOB as the heritable environment, the small magnitude of beta and change R2 suggest that EDU does not induce a substantial collider bias in this example, possibly due to the modest correlation between PRS and EDU (r = −0.051). Alternatively, confounder correlations with different directions of effect may reduce the magnitude of the observed bias. Importantly, the phenotypic PCs do not appear to increase the PRS effect size in the absence of an indication of robust collider bias.
