
455
14
Multivariate Analysis I
Reducing Dimensionality
14.1 MULTIVARIATE ANALYSIS: EIGEN-DECOMPOSITION
In this chapter and the next, we will work with several or many variables X
i
. First, we will not
necessarily assume that some of the variables are independent variables X
i
, inuencing one or
more dependent, or response variable Y. Instead, we try to uncover relationships among all the
variables and ways of reducing the dimensionality of the dataset. In this chapter, we will cover
the methods of principal component analysis (PCA), factor analysis (FA), and correspondence
analysis (CA).
All of these methods are based on the eigenvalues and eigen