Multiblock latent root regression. Application to epidemiological data
Let \(y\) be a response to be predicted by \(x_1\),\dots, \(x_p\). The authors propose a modified latent root regression (LRR) method for dimension reduction of this problem. The method is based on constructing linear combinations \(t^{(i)}=\sum_{p=1}^P w_p^i x_p\) such that \(\| w^{(i)}\| =1\) and \[ \text{cov}^2(y,t^{(i)})+\sum_{p=1}^P\text{cov}^2(x_p,t^{(i)})\to\max, \] where the maximization is unconstrained for \(t^{(1)}\), and \(t^{(i)}\) are taken orthogonal to \(t^{(1)}\),\dots, \(t^{(i-1)}\). A multiple-response and multiblock LRR are also considered. A cross-validation technique is proposed for selection of the number of LRR components for prediction. Links to existing multiblocks techniques are discussed. Applications to real life data are presented.
scientific article; zbMATH DE number 5697286