To assess association between rows of proximity matrices, H. de Vries (1993) introduces weighted average and row-wise average variants for Pearson's product-moment correlation, Spearman's rank correlation, and Kendall's rank correlation. For all three, the absolute value of the first variant is greater than or equal to the second. (SLD)

A completing-the-squares type approach to the varimax rotation problem is presented. This approach yields a direct proof of global optimality of a solution for optimal rotation in a plane. (Author/LMO)

The triangular decomposition method is suggested as a general technique for obtaining the various measures of an ill-conditioned matrix. The advantages of using triangular decomposition are computing nicety, cost, and parsimony. (Author/PN)

A factor replication procedure (FACTOREP) was evaluated using four psychometrically equivalent synthetic correlation matrices containing an imposed three-subscale structure. Comparisons of the structure revealed by two, three, four, and nine-factor rotations using the FACTOREP showed that only the three factor solutions were replicable across all…

A generalized congruence maximization procedure for the case of m matrices is presented. The orthogonal rotation procedure simultaneously maximizes the sums of all coefficients of congruence between corresponding factors of m factor matrices. (NSF)

The logic and procedures underlying a disturbance term regression test of logical consistency for structural models are reviewed for recursive and nonrecursive designs. It is shown that in a simple three-variable, complete mediational case the test procedure is mathematically equivalent to a part correlation. (Author/LMO)

In order to make parallel analysis more accessible to researchers employing principal component techniques, regression equations are presented for the logarithms of the latent roots of random data correlation matrices with unities on the diagonal. (Author/LMO)

Two applications of Kristof's theorem on traces of matrix products are presented in order to highlight their utility for psychometric theory and studies. (Author/JKS)

The purpose of this paper is to examine the validity of regression estimates when skewed dichotomous scales are used as independent variables. When Pearson product-moment correlations are used to measure zero-order associations involving dichotomous variables, the resulting coefficients underestimate the true associations. As a result, using…

Principal component analysis, image component analysis, and maximum likelihood factor analysis were compared to assess the effects of variable sampling. Results with respect to degree of saturation and average number of variables per factor were clear and dramatic. Differential effects on boundary cases and nonconvergence problems were also found.…

The extension of regression estimation and poststratification to factor analysis is considered. These methods may be used either to improve the efficiency of estimation or to adjust for the effects of nonrandom selection. The estimation procedure may be formulated in a LISTREL framework. (Author/LMO)

It is shown that for equal parameters explicit formulas exist, facilitating the application of the Newton-Raphson procedure to estimate the parameters in the Rasch model and related models according to the conditional maximum likelihood principle. (Author/LMO)

Multiple-hypothesis testing in the context of a correlation matrix is used to compare the statistical power of the original Bonferroni with six modified Bonferroni procedures that control the overall Type I error rate. Three definitions of statistical power are considered: (1) the ability to detect at least one true relationship; (2) the ability…

The usefulness of path analysis as a means of better understanding various linear models is demonstrated. First, two linear models are presented in matrix form using linear structural relations (LISREL) notation. The two models, regression and factor analysis, are shown to be identical although the research question and data matrix to which these…

The present study compares the performance of phi coefficients and tetrachorics along two dimensions of factor recovery in binary data. These dimensions are (1) accuracy of nontrivial factor identifications; and (2) factor structure recovery given a priori knowledge of the correct number of factors to rotate. (Author/LMO)