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)

The method proposed by Harman and Fukuda to treat the so-called Heywood case in the minres method in factor analysis (i.e., the case where the resulting communalities are greater than one) involves the frequent solution of eigenvalue problems. A simple method to treat this problem is presented. (Author/JKS)

Several algorithms for computing the greatest lower bound to reliability or the constrained minimum-trace communality solution in factor analysis have been developed. The convergence properties of these methods are examined. A uniqueness proof for the desired solution is offered. (Author/JKS)

Thurstone's primary mental abilities (1938/1968) involving 57 tests were factor analyzed to produce a comprehensive hierarchical model. Kaiser's varimax solution for primary mental abilities served as the raw data for this study. (Author/GK)

The notion of scale freeness does not seem to have been well understood in the factor analytic literature. Misconceptions concerning scale-freeness are clarified, and a theorem that ensures scale freeness in the orthogonal factor model is given in this paper. (Author/JKS)

The validity of asymptotic results for the distribution of unrotated and rotated factor loadings is investigated via simulation techniques. In particular, principal component extraction and quartimax rotation are examined on a problem with thirteen variables. The asymptotic results appear to be quite good. (Author/JKS)

The intercorrelations among the twelve subtests of the WISC were analyzed for each of eleven age groups in the standardization sample, using the principal factor method. Both the two and three factor solutions are assessed using the coefficient of congruence. (Author/JKS)

Reanalyzed data matrix of previous study (Ownby and Murray, 1982) of parenting behavior. Results of hierarchical factor analysis of parent behaviors showed 10 primary factors, 5 secondary factors, 2 tertiary factors, and 1 general factor. Showed that hierarchical organization of factors of parent behavior can be demonstrated and can help to…

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)

Used confirmatory factor analysis (CFA), hypothesized factors that were less than the number of variables, and then examined how well the intercorrelations were reproduced. Results help explain that the type of correlation matrix and estimation method affect factor loadings and fit functions. Suggests some alternative approaches. (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)