order to determine how PC covariates perform when only a subset of the total confounding data is measured. This provides a more detailed picture of how the method can work in practice. A PRS variable was generated from a standard normal distribution. We generated a heritable collider environment variable as a function of the PRS and a single PC, which was derived from all 100 confounding variables. The effect of the polygenic risk score on the heritable environment (rGE) was fixed at different values in different iterations of the simulation (0, 0.1, 0.2, 0.3, 0.4, 0.5). We generated a target phenotype as a function of the PRS, the first PC of 100 confounders, and the heritable collider environment. We set the true value of the effect of PRS on the target phenotype to 0.1 . This effect size magnitude is comparable to previous studies that use PRS to predict complex traits in observed data sets (Barr et al., 2020). Observed datasets will generally not include all relevant confounding variables. Therefore, we calculated a second PC from randomly selected subsets of the confounding variable, ranging from 10% (10 variables) to 100% (100 variables) at intervals of 1% in order to model
