Multiblock latent root regression. Application to epidemiological data
type: Item
instance of: scholarly article
title: Multiblock latent root regression. Application to epidemiological data
zbMATH Open document ID: 1196.62101
author: Stéphanie Bougeard
author: Mohamed Hanafi
author: El Mostafa Qannari
published in: Computational Statistics
publication date: 2010-04-22T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62J99
Mathematics Subject Classification ID: 62P10
Mathematics Subject Classification ID: 92D30
zbMATH DE Number: 5697286
zbMATH Keywords: latent variables
zbMATH Keywords: partial least squares regression
zbMATH Keywords: cross-validation
describes a project that uses: Multi-block Toolbox
MaRDI profile type: Publication
full work available at URL: s00180-007-0036-1
OpenAlex ID: W2044800641
cites work: Q3339960
cites work: Q5511808
cites work: Q4066417
cites work: Latent Root Regression Analysis
cites work: Q3965546
DOI: 10.1007/S00180-007-0036-1
description: scientific article; zbMATH DE number 5697286