Each violin plot depicts the empirical correlations between the summary-level genetic associations with the outcomes (dark gray) and the posterior mean of the residual correlations estimated byMR2(red) in simulation scenario III undirected pleiotropy averaged over 50 replicates at different levels of the pleiotropy effectthetaA={0.25,0.50,0.75,1.00,1.50,2.00}. Confounding effects on the exposures and outcomes are fixed atthetaXU=2andthetaYU=1, respectively, without correlation between exposures and responses errors and assuming 100% sample overlap in the summary-level genetic associations with the outcomes. For each side of the violin plot, the vertical black thick line displays the interquartile range, while the black line indicates the median. Black dashed line depicts the theoretical value of residual correlation between summary-level outcomes as a function ofthetaAas shown inEquation 8. For more details on the simulation setting, seeTable S2.
