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)

A simpler and more complete version of Kaiser's method for finding a set of derived orthogonal variables which correlate maximally with a set of original variables is presented. The method is compared to related factor analytic transformations. (Author/JKS)

A scale-invariant simple structure function of previously studied function components for principal component analysis and factor analysis is defined. First and second partial derivatives are obtained, and Newton-Raphson iterations are utilized. The resulting solutions are locally optimal and subjectively pleasing. (Author/JKS)

A scale-invariant index of factorial simplicity is proposed as a summary statistic for principal components and factor analysis. The index ranges from zero to one, and attains its maximum when all variables are simple rather than factorially complex. (Author/JKS)

Conditions for removing the indeterminancy due to rotation are given for both the oblique and orthogonal factor analysis models. The conditions indicate why published counterexamples to conditions discussed by Joreskog are not identifiable. (Author)

A form of Browne's (1967) solution of finding a least squares fit to a specified factor structure is given which does not involve solution of an eigenvalue problem. It suggests the possible existence of a singularity, and a simple modification of Browne's computational procedure is proposed. (Author/RC)

Three properties of the binormamin criterion for analytic transformation in factor analysis are discussed. Particular reference is made to Carroll's oblimin class of criteria. (Author)

In oblique rotation of factor analyses, a variety of methods is possible. The direct oblimin method is one such rotation. The direct oblimin method requires setting a value for a parameter called gamma. This article explores problems with choosing gamma values and clarifies the results obtained at various gamma levels. (JKS)

Procrustean analysis is a form of factor analysis where a target matrix of results is specified and then approximated. Procrustean analysis is extended here to the case where matrices have different row order. (Author/JKS)

Some methods that analyze three-way arrays of data (including INDSCAL and CANDECOMP/PARAFAC) provide solutions that are not subject to arbitrary rotation. This property is studied in this paper by means of the "triple product" (A, B, C) of three matrices. (Author)

A simplified procedure for obtaining a weighted procrustes factor analysis rotation is presented in this brief note. Implications are discussed. (See also EJ 180 443). (JKS)

In Korth and Tucker (EJ 131 795), the matrices T1 and T2 are defined as transformations for matching two factor patterns in a common space. Contrary to the statement of this article, however, T1 and T2 are not the matrices of eigenvectors from the matrices in (1) and (2) of the article. (Author/CTM)

A general formulation for obtaining conditionally unbiased, univocal common-factor score estimates that have maximum validity for the true orthogonal factor scores is presented. Other similar efforts described in the literature are discussed. (Author/JKS)

Tucker's method of oblique congruence rotation is shown to be equivalent to a procedure by Meredith. This implies that Monte Carlo studies on congruence by Nesselroade, Baltes, and Labouvie and by Korth and Tucker are highly comparable. The problem of rotating two matrices orthogonally to maximal congruence is considered. (Author/CTM)

A rigorous definition for a factor analysis model and a complete solution of the factor score indeterminacy problem are presented in this technical paper. The meaning and application of these results are discussed. (Author/JKS)