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 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)

Whether to factor the image correlation matrix or to use a new model with an alpha factor analysis of it is mentioned, with particular reference to the determinacy problem. It is pointed out that the distribution of the images is sensibly multivariate normal, making for "better" factor analyses. (Author/CTM)

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)

Formulas are presented in this paper for computing scores associated with factors of G, the image covariance matrix, under three conditions. The subject of the paper is restricted to "pure" image analysis. (Author/NE)

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)

The accuracy of the varimax and promax methods of rotation of axes in reproducing known factor matrices was examined. It was found that only when all tests are univocal, or nearly so, could one be reasonably confident that an obtained factor matrix faithfully reproduces a contrived matrix. (Author/JKS)

A generalized matrix procedure is developed for computing the proportionate contribution of a factor, either orthogonal or oblique, to the total common variance of a factor solution. (Author)

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)

Over the years, a number of rationales have been advanced to solve the problem of "blind" oblique factor transformation. By blind transformation is meant the transformation of orthogonal--and often interpretively ineffectual--factors to a position usually dictated by Thurstone's principles of simple structure, but not influenced by a…

A computational algorithm, called the orthotran solution, is developed for determining oblique factor analytic solutions utilizing orthogonal transformation matrices. Selected results from illustrative studies are provided. (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)

Principal components analysis is generalized to the case where any of the variables under consideration can be nominal, ordinal or interval. Hotelling's original formulation is seen to be a special case of this generalization. (JKS)