In large-scale educational surveys, a latent regression model is used to compensate for the shortage of cognitive information. Conventionally, the covariates in the latent regression model are principal components extracted from background data. This operational method has several important disadvantages, such as the handling of missing data and…

Maximally reliable composites found in canonical reliability when expressed in the form of a canonical factor analysis solution are shown to have highly desirable data reduction properties. Theoretical relationships among canonical factor analysis, principal components analysis and canonical reliability analysis are emphasized. (Author/JKS)

Univariate procedures proposed by M. Brown and A. Forsythe (1974) and the multivariate procedures from D. Nel and C. van der Merwe (1986) were generalized to form five new multivariate alternatives to one-way multivariate analysis of variance (MANOVA) for use when dispersion matrices are heteroscedastic. These alternatives are evaluated for Type I…

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)

Theta is a statistic which measures the degree to which a designated pattern successfully partitions a matrix of pre- and post-treatment ratings into regions typical of each of two treatments. In this paper, theta is extended to multivariate and multigroup cases. (Author/BW)

Provided is a description of three methods for testing certain types of a priori hypotheses about differences among covariance matrices. Briefly outlined are procedures for using two computer programs, COFAMM and LISREL, for testing such hypotheses. Also provided are examples of application of the methods to a meaningful data set. (Author/BW)

The basic notion of variability is generalized from a univariate context to a multivariate context using two matrix functions, a determinant, and a trace, yielding a number of alternative multivariate indices of shared variation. Some problems in the interpretation of tests of multivariate hypotheses are reviewed. (Author/BW)

The test proposed by Brien, Venables, and Mayo (1984), endorsed by Silver and Dunlap, and supported by computer software that they developed is not a proper test for multivariate independence. A revised appraisal is suggested for the Silver and Dunlap results. (SLD)