Principal Component Regression (PCR) and Partial Least Squares Regression (PLSR) are linear and non-linear methods respectively.

Author: Wang Huiwen, Wu Zaibin, Meng Jie
Publisher:
Publish Date: 2006-09-01
Features: Partial Least Squares Regression (PLSR) is a novel multivariate data analysis method proposed from applied fields. Over the past 20 years, it has undergone rapid development in both theory and application. PLSR is primarily applicable for regression modeling with multiple dependent variables on multiple independent variables and can effectively solve many problems that cannot be addressed using ordinary multivariate regression, such as overcoming the adverse effects of multicollinearity of variables in system modeling and conducting regression modeling when the sample size is smaller than the number of variables. Additionally, it can organically integrate the fundamental functionalities of regression modeling, principal component analysis, and canonical correlation analysis. In 1999, with the support of the National Defense Science and Technology Publishing Fund, one of the authors, Professor Wang Huiwen, published the monograph Partial Least Squares Regression Methods and Applications. This book builds upon that monograph, more comprehensively reflecting the cutting-edge developments in the theory and application of PLSR, and provides detailed introductions to various linear and nonlinear PLSR methods, including the research work of the authors in this field in recent years. The book first briefly introduces the basic knowledge of multivariate linear regression, principal component analysis, and canonical correlation analysis, with a focus on discussing the harmful effects of multicollinearity of variables in regression modeling. On this basis, the book elaborates in detail on both linear and nonlinear PLSR methods, including partial least squares regression linear models, partial least squares path analysis, hierarchical partial least squares regression models, modeling methods and application techniques for component data regression, nonlinear PLSR based on functional transformation, and partial least squares logistic regression, among others. Furthermore, the book explores some related theories of PLSR in greater depth, providing a more profound insight into its theoretical connotations and development potential. To facilitate readers in applying PLSR methods more conveniently, the book also introduces the basic functionalities of the specialized PLSR software SIMCA-P. The target readers of this book are researchers in the fields of economics, management, social sciences, and engineering, as well as graduate students and senior undergraduate students in relevant disciplines at universities and colleges.