ABSTRACT
In Chapter 3, factor analysis was defined as solving the equation Z = F P' for both F and P with only the Z known. Without knowledge of either the F or the P, the problem is mathematically indeterminate because an infinite number of F's and P's could exist to satisfy the equation. All of the F and P combinations reproduce Z with the same number of factors and the same degree of accuracy. Chapters 5, 6, and 7 gave methods of extracting the factors to meet certain specifications. The specifications were generally sufficient so that F and P were uniquely defined. For example, for the principal factor variants, the solution was restricted so that each factor maximally reproduced the elements of the matrix from which it was extracted, a restriction that generally leads to a unique solution. After the factors have been extracted, it is not necessary to retain the initial restrictions. In the principal factor solution, for example, the requirement that each successive factor must account for the maximum variance possible can be relaxed and other solutions found by rotation. Although the size of each factor may shift, the set of new factors will retain the same ability to reproduce the original data matrix as was found for the set of principal factors. Hence, both the rotated and the unrotated factors will reproduce the same correlations with the same degree of accuracy.
