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)

In this paper, the author gives a review of the literature on complex multivariate distributions. Some new results on these distributions are also given. Finally, the author discusses the applications of the complex multivariate distributions in the area of the inference on multiple time series. (Author)

Recent results of Bloomfield and Watson and Knott are used to derive a class of union-intersection tests for sphericity from likelihood ratio tests of independence of two sets of variates. It is shown that the ordinary likelihood ratio test for sphericity has a natural union-intersection interpretation. (Author/RC)

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 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)

Recent work (EJ 208 813) showing that generalized eigenvalue problems in which both matrices are singular can be solved by reducing them to similar problems of smaller order is discussed. Possible extensions of the work are indicated. (Author/JKS)

A generalization of the Procrustes problem (concerning solutions for least squares problems) in which the errors are weighted from the right, left, or both is provided. Mathematical derivations and an illustration are provided. (Author/JKS)

A discussion of how a tensor theory can be adapted to provide a fully quantitative analysis of a social system. A social tensor is developed from the physical analogue and used to analyze the structure of an education course. (Author/HB)

It is shown that common factors are not subject to indeterminancy to the extent that has been claimed (Guttman, 1955), because the measure of indeterminancy that has been adopted is ill-founded. (Author/RC)

A Monte Carlo investigation of Markov chain matrices was conducted to create empirical distributions for two statistics created from the transition matrices. Curve fitting techniques developed by Karl Pearson were used to deduce if theoretical equations could be fit to the two sets of distributions. The set of distributions which describe the…

Standard errors for maximum likelihood estimates of factor loadings are expressed in terms of the inverse of an augmented information matrix. This formulation arises naturally by viewing the problem as one in constrained maximum likelihood estimation. The constraints correspond to the form of rotation used. Results are given for canonical rotation…

The distribution of the likelihood ratio test for testing the reality of the covariance matrix of a complete multivariate normal distribution is investigated. (Author/RC)

Demonstrates the value of spreadsheets for teaching sociology using Lotus 1 2 3 as an example. Shows how a Cholesky factorization, an eigenstructure solution, a correlation analysis, and a discriminant analysis may be performed using a spreadsheet or a BASIC program (included). (BSR)

Order analysis, a technique to isolate unidimensional hierarchies representing multidimensional structure of binary data, is reviewed. Several theoretical flaws inherent in the probalistic version are presented. Suggestions of possible directions for future research are offered. (Author)

A general model is developed for the analysis of multivariate multilevel data structures. Special cases of this model include: repeated measures designs; multiple matrix samples; multilevel latent variable models; multiple time series and variance and covariance component models. (Author)