Matrices can be diagonalized by singular vectors or, when they are symmetric, by eigenvectors. Pairs of square matrices often admit simultaneous diagonalization, and always admit block wise simultaneous diagonalization. Generalizing these possibilities to more than two (non-square) matrices leads to methods of simplifying three-way arrays by…

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)

An experimental procedure involving interaction between subject and computer was used to determine an opitmum subset of stimuli for multidimensional scaling (MDS). A computer program evaluated this procedure compared with MDS based on (a) all pairs of stimuli, and (b) on one-third of the possible pairs. The new method was better. (Author/HG)

A formula for the ratio of the variance of the pooled transformed data under departure from the binomial assumption to the variance of the pooled transformed data when the binomial assumption holds is given. (Authors)

A class of monotonic transformations which generalize the power transformation is fit to the independent and dependent variables in multiple regression so that the resulting additive relationship is optimized. Examples of analysis of real and artificial data are presented. (Author/JKS)

Four types of metric scales are distinguished: absolute, ratio, difference, and interval. A general coefficient of association for two variables of the same scale type is developed which reduces to specific coefficients of association for each scale type. (NSF)

Examples are presented in which it is either necessary or desirable to transform two sets of orthogonal axes to simple structure positions by means of the same transformation matrix. A solution is outlined which represents a two-matrix extension of the general "orthomax" orthogonal rotation criterion. (Author/RC)

A procedure is outlined showing how the axiom of local independence for latent structure models can be weakened. (CK)

Relations between maximum likelihood factor analysis and factor indeterminacy are discussed. (CK)

The distance approach to nonlinear multivariate analysis proposed by J. J. Meulman (1986) is reviewed. Several generalizations are discussed by combining features from the conventional multivariate analysis approach, which seeks weighted sums of variables, with the alternative approach, which seeks to fit distances. (SLD)

In the family of correlation suggested by Janson and Vegilius, some coefficients are generalized squared product-moment correlations and some are not. This paper advocates a family of correlations for variables of mixed scale types in which all members are generalized squared product-moment correlations. Practical advantages are explained.…

A Monte Carlo simulation and applications to eight sets of proximity data are presented to support the practical utility of a network scaling algorithm (NETSCAL)--NETwork SCALing. The algorithm determines which vertices within a network are directly connected by an arc and estimates the length of each arc. (TJH)