Aside from distribution theory, projections and the singular value decomposition (SVD) are the two most important concepts for understanding the basic mechanism of multivariate analysis. The former underlies the least squares estimation in regression analysis, which is essentially a projection of one subspace onto another, and the latter underlies principal component analysis, which seeks to find a subspace that captures the largest variability in the original space. This book is about projections and SVD. A thorough discussion of generalized inverse (g-inverse) matrices is also given because...

In multivariate data analysis, regression techniques predict one set of variables from another while principal component analysis (PCA) finds a subspace of minimal dimensionality that captures the largest variability in the data.

• How can regression analysis and PCA be combined in a beneficial way?
• Why and when is it a good idea to combine them?
• What kind of benefits are we getting from them?

Addressing these questions, Constrained Principal Component Analysis and Related Techniques shows how constrained PCA (CPCA) offers a unified...

This valuable reference on projectors, generalized inverses, and SVD covers concepts numerous cutting-edge concepts and provides systematic and in-depth accounts of these ideas from the viewpoint of linear transformations of finite dimensional vector spaces.

Winner of the 2015 Sugiyama Meiko Award (Publication Award) of the Behaviormetric Society of Japan

Developed by the authors, generalized structured component analysis is an alternative to two longstanding approaches to structural equation modeling: covariance structure analysis and partial least squares path modeling. Generalized structured component analysis allows researchers to evaluate the adequacy of a model as a whole, compare a model to alternative specifications, and conduct complex analyses in a straightforward manner.

Generalized Structured...