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)

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)

An index of factorial simplicity, employing a quartimax transformational criteria, is developed. This index is both for each row separately and for a factor pattern matrix as a whole. The index varies between zero and one. The problem of calibrating the index is discussed. (Author/RC)

A class of oblique rotation procedures is proposed to rotate a pattern matrix so that it optimally resembles a matrix that has an exact simple pattern. It is demonstrated that the method can recover relatively complex simple structures where other simple structure rotation techniques fail. (SLD)

It is shown that common factors are not subject to indeterminancy to the extent that has been claimed (Guttman, 1955), because the measure of indeterminancy that has been adopted is ill-founded. (Author/RC)

Discusses Guttman's index of indeterminacy in light of alternative solutions which are equally likely to be correct and alternative solutions for the factor which are not equally likely to be chosen. Offers index which measures a different aspect of the same indeterminacy problem. (ROF)

Examples are presented in which it is either necessary or desirable to transform two sets of orthogonal axes to simple structure positions by means of the same transformation matrix. A solution is outlined which represents a two-matrix extension of the general "orthomax" orthogonal rotation criterion. (Author/RC)

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)

Five techniques that combine the ideals of rotation of matrices of factor loadings to optimal agreement and rotation to simple structure are compared on the basis of empirical and contrived data. Combining a generalized Procrustes analysis with Varimax on the main of the matched loading matrices performed well on all criteria. (SLD)

Provides normative data about the distribution of one measure of similarity of factor loadings, the congruence coefficient, through a Monte Carlo Technique. Matching of "chance" factor patterns was done by the method of Tucker. Statistical tests of the results, based on similarities of the method to canonical and multiple correlation,…

The relationship between the factor structure of a convariance matrix and the factor structure of a partial convariance matrix when one or more variables are partialled out of the original matrix is given in this brief note. (JKS)

Applications to the Promax Rotation are discussed, and it is shown that these procedures solve Thurstone's hitherto intractable "invariant" box problem as well as other more common problems based on real data. (Author/RC)