Some mathematical aspects of minimum trace factor analysis (MTFA) are discussed. The uniqueness of an optimal point of MTFA is proved, and necessary and sufficient conditions for any particular point to be optimal are given. The connection between MTFA and classical minimum rank factor analysis is discussed. (Author/JKS)

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)

In matrix comparison, the performance of four vector matching indices (the coefficient of congruence, the Pearson product moment correlation, the "s"-statistic, and kappa) was evaluated. Advantages and disadvantages of each index are discussed, and the performance of each was assessed within the framework of principal components…

For the confirmatory factor model a series of inequalities is given with respect to the mean square error (MSE) of three main factor score predictors. The eigenvalues of these MSE matrices are a monotonic function of the eigenvalues of the matrix gamma[subscript rho] = theta[superscript 1/2] lambda[subscript rho] 'psi[subscript rho] [superscript…

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)

The Kaiser Measures of Sampling Adequacy (MSA) were derived for a typical six-concept Semantic Differential. The overall indices indicated that both concept and total correlation matrices would lead to comparable decisions regarding the psychometric quality of the sample data sets. The individual MSA's, however, revealed considerable variability…

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)

Component analysis provides an attractive alternative to factor analysis, since component scores are easily determined while factor scores can only be estimated. The correct method of determining component scores is presented as well as several illustrations of how commonly used incorrect methods distort the meaning of the component solution. (RC)

Necessary and sufficient conditions for rotating matrices to maximal agreement in the least-squares sense are discussed. A theorem which solves the case of two matrices is given a more straightforward proof. Other considerations in rotating matrices are discussed. (Author/JKS)

A shortcut formula for the computation of "coefficients of invariance" in the comparison of factor structures is presented. A limitation of the coefficient of invariance is pointed out in the case of comparing two first principal components. (NE)

The extent to which one can reduce the rank of a symmetric matrix by only changing its diagonal entries is discussed. Extension of this work to minimum trace factor analysis is presented. (Author/JKS)