To evaluate potential sources of confounding for expression and genetic ancestry, we first correlated the technical and RNA quality variables available from the downloaded R variables and removed highly correlated variables (Pearson r > 0.95) present in two or more brain regions. After this, we retained variables common across the four brain regions. In addition to these variables, we also accounted for hidden variables using the downloaded qSVA (Supplementary Fig. 35 and equation (1), k = 13, 6, 9 and 14, for the caudate nucleus, dentate gyrus, DLPFC and hippocampus, respectively). We found that qSVs were also accurately correct for observed variables like batch effect and cell type composition12,20:1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{array}{l}E\left(Y\right)={\beta }_{0}+{\beta }_{1}{\mathrm{ancestry}}+{\beta }_{2}{\mathrm{sex}}+{\beta }_{3}{\mathrm{age}}+{\beta }_{4}{{\mathrm{mito}}\,{\mathrm{rate}}}+{\beta }_{5}{{\mathrm{rRNA}}\,{\mathrm{rate}}}\\\qquad+\,{\beta }_{6}{{\mathrm{total}}\,{\mathrm{assigned}}\,{\mathrm{genes}}}+{\beta }_{7}{{\mathrm{overall}}\,{\mathrm{mapping}}\,{\mathrm{rate}}}+\mathop{\sum }\limits_{i=1}^{k}{\gamma }_{i}{qS}{V}_{i}\end{array}$$\end{document}EY=β0+β1ancestry+β2sex+β3age+β4mitorate+β5rRNArate+β6totalassignedgenes+β7overallmappingrate+∑i=1kγiqSVi
