A revised theorem is presented concerning uniqueness of minimum rank solutions in common factor analysis. (Author)

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 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…

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)

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)

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)

Two Statistical Analysis System (SAS) macros are presented that perform the modified principal components approach of L. R. Tucker (1966) to modeling generalized learning curves analysis up to a rotation of the components. Three SAS macros are described that rotate the factor patterns to have characteristics Tucker considered desirable. (SLD)

Data reduction techniques seek to combine variables that account for patterns of variation in observed dependent variables in such a way that a simpler model is available for analysis. Factor analysis is a data reduction technique that attempts to model or explain a set of variables in terms of their associations. To understand why this technique…

Most researchers using factor analysis extract factors from a matrix of Pearson product-moment correlation coefficients. A method is presented for extracting factors in a non-parametric way, by extracting factors from a matrix of Spearman rho (rank correlation) coefficients. It is possible to factor analyze a matrix of association such that…

Results of empirical comparisons of an inferential model of order analysis with factor analytic models were reported for two sets of data. On the prestructured data set both order and factor analytic models returned its dimensions of length, width and height, but on the random data set the factor analytic models indicated the presence of…

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)

A group of factor analytic rotation procedures are developed which yield both hyperplane fittings and oblique Procrustean analyses as special cases. It is generally supposed that these techniques are rather different in approach. Illustrations are presented and discussed. (Author/JKS)