The previous chapter explored linear algebra and matrix operations. This chapter can best be characterized as concerned with the linear algebra of covariance and correlation matrices. Principal component analysis (PCA) and factor analysis (FA) are two classic methods of identifying structures in the correlations of datasets. Despite the fact that they are concerned with covariances and correlations, many statisticians have very limited experience with these methods, because they make heavy use not only of statistics, but also of linear algebra; therefore, they straddle the realms of both statistics and engineering.
In this chapter, the following topics will be discussed:
A primer on correlation and covariance structures
Principle component analysis
Basic exploratory factor analysis
Advanced exploratory factor analysis