IDP and non-IDP variables are prepared as for the univariate correlation analyses described above, resulting in a brain-IDP matrix of size 5034×2501 (subjects × IDPs) and a non-IDP matrix of size 5034×1100 (subjects × non-IDP variables). The intention is to feed these into CCA in order to identify population modes linking multiple variables from both matrices. However, in order to avoid an over-determined (rank deficient) CCA solution, we first compress both matrices along the respective phenotype dimension to 200 columns (i.e., much smaller than the numbers of subjects). This was done by separately reducing each matrix to the top 200 subject-eigenvectors using PCA. To achieve this while avoiding the problem of missing data, we use the approach detailed recently34 of estimating first a pseudo-covariance matrix ignoring missing data, projecting this onto the nearest valid (positive definite) covariance matrix, and then carry out an eigenvalue decomposition. The two resulting (IDP and non-IDP) matrices of size 5034×200 are then fed into standard CCA (“canoncorr” in Matlab), resulting in 200 CCA modes being estimated. The CCA aims to identify symmetric linear relations between
