A test for linear trend among a set of eigenvalues of a correlation matrix is described. It is a generalization of G. Anderson's (1965) test for the equality of eigenvalues and extends the present authors' previous work on linear trends in eigenvalues of a covariance matrix. The linear trend hypothesis is discussed. (SLD)

When conducting an exploratory factor analysis, the decision regarding the number of factors to retain following factor extraction is one that the researcher should consider very carefully, as the decision can have a dramatic effect on results. Although there are numerous strategies that can and should be utilized when making this decision,…

A method is presented of calculating correlation matrices using single subscript rather than double subscript notation. This saves time and space, and permits the calculation of larger matrices in the space available. (Author)

Two generalizations of canonical correlational analysis are developed. The partial, part, and bipartial canonical correlation coefficients are shown to be special cases of the generalization. Illustrative examples are provided. (Author/JKS)

A method is presented for determining the number of components to retain in a principal components or image components analysis which utilizes a matrix of partial correlations. Advantages and uses of the method are discussed and a comparison of the proposed method with existing methods is presented. (JKS)

It is shown that a weaker generalized inverse (Rao's g-inverse; Graybill's c-inverse) can be used in place of the Moore-Penrose generalized inverse to obtain multiple and canonical correlations from singular covariance matrices. Mathematical derivations are provided. (Author/JKS)

Proposes a method for generalized constrained canonical correlation analysis (GCCANO) that incorporates external information on both rows and columns of data matrices. In this method, each set of variables is first decomposed into the sum of several submatrices according to the external information, and then canonical correlation analysis is…

Influence curves of some parameters under various methods of factor analysis depend on the influence curves for either the covariance or the correlation matrix used in the analysis. The differences between the two types of curves are derived, and simple formulas for the differences are presented. (SLD)

At United States Military Academy, a unit on biological modeling applications forms the culminating component of the first semester core mathematics course for freshmen. The course emphasizes the use of problem-solving strategies and modeling to solve complex and ill-defined problems. Topic areas include functions and their shapes, data fitting,…

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)

Derives the asymptotic standard errors and intercorrelations for several matrix correlations assuming multivariate normality for manifest variables and derives the asymptotic standard errors of the matrix correlations for two factor-loading matrices. (SLD)

Higher order factor analysis is an extension of factor analysis that is little used, but which offers the potential to model the hierarchical order often seen in natural (including psychological) phenomena more accurately. The process of higher order factor analysis is reviewed briefly, and various interpretive aids, including the Schmid-Leiman…

The program can compute a great number of different correlation and other statistical measures. The user is free to select among the measures and also among the variables that are read by the program. When a particular set of variables has been treated in the prescribed way, a new set may follow together with new measure definitions. (Author)