Jolliffe I. Principal Component Analysis (2ed., Springer, 2002)(518s)

7.2. Estimation of the Factor Model 155Figure 7.1. Factor loadings for two factors with respect to original andorthogonally rotated factors.were designed to give quick computationally feasible results. Such methodsdo a reasonable job of getting a crude factor model, but have little or nofirm mathematical basis for doing so. This, among other aspects of factoranalysis, gave it a ‘bad name’ among mathematicians and statisticians.Chatfield and Collins (1989, Chapter 5), for example, treat the topic ratherdismissively, ending with the recommendation that factor analysis ‘shouldnot be used in most practical situations.’There are more ‘statistically respectable’ approaches, such as theBayesian approach outlined by Press (1972, Section 10.6.2) and the widelyimplemented idea of maximum likelihood estimation of Ψ and Λ, assumingmultivariate normality of f and e. Finding maximum likelihood estimatesof Ψ and Λ leads to an iterative procedure involving a moderate amountof algebra, which will not be repeated here (see, for example, Lawley andMaxwell (1971)).