A multiple covariance approach to PLS regression with several predictor groups: Structural Equation Exploratory Regression

TL;DR

This paper introduces SEER, a novel PLS-based method for simultaneous dimension reduction and linear modeling across multiple predictor groups with a focus on their multidimensional structures.

Contribution

It extends PLS regression to handle multiple predictor groups using a new covariance criterion, enabling joint dimension reduction and model exploration.

Findings

SEER effectively reduces dimensions in multiple predictor groups.

The method uncovers linear relationships between components across groups.

Application demonstrates practical utility in complex multigroup data analysis.

Abstract

A variable group Y is assumed to depend upon R thematic variable groups X 1, >..., X R . We assume that components in Y depend linearly upon components in the Xr's. In this work, we propose a multiple covariance criterion which extends that of PLS regression to this multiple predictor groups situation. On this criterion, we build a PLS-type exploratory method - Structural Equation Exploratory Regression (SEER) - that allows to simultaneously perform dimension reduction in groups and investigate the linear model of the components. SEER uses the multidimensional structure of each group. An application example is given.