The results in Panel A illustrate a general implication of the measurement-error correction for mediation analyses: the correction deflates estimates of how much covariates mediate the effect of the PGI. There have been several mediation analyses in which researchers study how much the coefficient on a PGI is reduced when control variables—which are usually positively correlated with both the PGI and the dependent variable—are added to the regression37–39. Going from column (1) to (2), the drop in the coefficient on the PGI would lead a researcher to conclude that parental education mediates (0.844 – 0.619) / 0.844 = 27% of the effect of the PGI. Going from column (3) to (4) shows the corrected estimate of mediation is only (1.318 – 1.104) / 1.318 = 16%. The drop is larger for the uncorrected regressions because in those regressions, the control variables are proxying for part of the additive SNP factor that is not well captured by the PGI. Therefore, studies that do not correct for measurement error will tend to overestimate the extent to which the control variables mediate the effect of the PGI.
