Fourth, the intercept of the simulation model A3 (~PRS+Env+Incomplete Phenotypic PC) regression line is higher when confounder correlations are higher. Again, we present average change in Model A3 in four bins for the proportion of confounding data that is measured in the correction: (1) 10% - 25%, (2) 26% - 50%, (3) 51% - 75%, and (4) 76% - 99%. When rGE=0.1 and confounder correlations range between 0.8-0.9 the model A3 PRS effect increases by 58%, 78%, 89%, and 94%. When rGE=0.5 and confounder correlations range between 0.8-0.9 the model A3 effect increases by 253%, 367%, 435%, and 472%. The correction performs better with less of the confounding data included in the PCA relative to the results reported above with confounder correlations between 0.05-0.1. This suggests that required assumptions about the proportion of confounding data that is measured and the correlation structure of the confounding data are complementary. If a larger proportion of the confounders is measured, the required assumptions about the correlation structure of the confounders are relaxed. If the confounders are highly correlated, the assumptions about the proportion
