Influence curves of some parameters under various methods of factor analysis depend on the influence curves for either the covariance or the correlation matrix used in the analysis. The differences between the two types of curves are derived, and simple formulas for the differences are presented. (SLD)

An illustration of a test for independence was provided with a mixed set of variables. The matrix consisted of 10 tests of interest and four random deviates in which the relationship between sets was demonstrated to be minimal. The result was discussed for a situation in which factoring methods might be considered. (Author)

Methods for rotating factor analysis matrices to a least squares fit with a specified structure are discussed. Existing solutions are shown to be not valid in some cases or to not work when matrices are not of full rank. A general solution is derived, addressing both issues. (Author/JKS)

Some effects of using inappropriate criteria for sufficiency of factors are discussed, and examples from the literature are used to show how procedures leading to the rotation of large numbers of factors may result in fragmentation and difficulty in interpretation. (Author/JKS)

The residual variance is often used as an approximation to the uniqueness in factor analysis. An upper bound approximation to the residual variance is presented for the case when the correlation matrix is singular. (Author/JKS)

A full-fledged matrix derivation of Sherin's matrix formulation of Kaiser's varimax criterion is provided. Matrix differential calculus is used in conjunction with the Hadamard (or Schur) matrix product. Two results on Hadamard products are presented. (Author/JKS)

Procedures for oblique rotation of factors or principal components typically focus on rotating the pattern matrix so that it becomes optimally simple. How the Harris and Kaiser independent cluster (1964) rotation can be modified to obtain a simple weights matrix rather than a simple pattern is described and illustrated. (SLD)

Gives sufficient and necessary conditions for the observability of factors in terms of the parameter matrices and a finite number of variables. Outlines five conditions that rigorously define indeterminacy and shows that (un)observable factors are (in)determinate, and extends L. Guttman's (1955) proof of indeterminacy to Heywood (H. Heywood, 1931)…

Provides a fully flexible approach for orthomax rotation of the core to simple structure with respect to three modes simultaneously. Computationally the approach relies on repeated orthomax rotation applied to supermatrices containing the frontal, lateral, or horizontal slabs, respectively. Exemplary analyses illustrate the procedure. (Author/SLD)

In three-mode principal components analysis, the P x Q x R core matrix "G" can be transformed to simple structure before it is interpreted. This paper shows that, when P=QR-1, G can be transformed to have nearly all the elements equal to values specified a priori. A closed-form solution for this transformation is offered. (SLD)

A sufficient condition in terms of the unique variances of a common factor model is given for the results of factor analysis to come closer to those of principal components analysis. In general, vectors corresponding to loading matrices can be related to each other by a specific measure of closeness, which is illustrated. (SLD)

Higher order factor analysis is an extension of factor analysis that is little used, but which offers the potential to model the hierarchical order often seen in natural (including psychological) phenomena more accurately. The process of higher order factor analysis is reviewed briefly, and various interpretive aids, including the Schmid-Leiman…

A desirable property of the equamax criterion for analytic rotation in factor analysis is presented. (Author)