Abstract
This chapter describes various matrix methods and their applications to factor analysis. The chapter discusses the identifiability conditions, the communality problems, analysis of image and anti-image variables, estimation of factor scores, and the equivalence conditions on canonical factor analysis. In particular, the conditions under which the squared multiple correlation (SMC) of a variable is equal to the communality of the variable are developed in the chapter, and some equivalent conditions under which the eigenvalues resulting from the canonical factor analysis are either 1 or 0 are discussed. Methods for estimating factor score matrices when the unique variance matrix is singular are also introduced. The chapter emphasizes the use of g-inverse and projection matrices, which are useful in explicating some intricate concepts underlying factor analysis models as well as other multivariate data analysis techniques.
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