According to some researchers canonical correlation results should be interpreted in part by consulting redundancy coefficients (Rd). This paper, however, makes the case that Rd coefficients generally should not be interpreted. Rd coefficients are not multivariate. Furthermore, it makes little sense to interpret coefficients not optimized as part…

Covariance and correlation structure analytic techniques can be used to test whether a specified correlation structure is an adequate model of the population correlation structure. These procedures include: (1) normal theory (NT) and asymptotically distribution free (ADF) covariance structure analysis techniques; and (2) NT and ADF correlation…

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)

This paper presents an overview of repeated measures designs, designs that measure one group over time, also called within-subjects designs. Both univariate and multivariate designs are discussed, and advantages and disadvantages of each of these designs are considered. The sphericity assumption is examined, and methods are presented to correct…

This paper reviews graphical and nongraphical methods for estimating multivariate normality. Prior to exploring this methodology, a foundation is established by presenting ways to assess univariate and bivariate normality. A data set of three variables used by J. Stevens (1986) is analyzed using Q-Q plots, stem and leaf plots, histograms,…

The rotation process can be very useful in discriminant analysis and multivariate analysis of variance. (CK)

Two multivariate probability distributions, a generalized beta distribution and a generalized F distribution, are derived. Formulas for the moments of these distributions are given and an example of the bivariate generalized beta is presented. (Author/JKS)

Miller and Farr's algorithm for the index of redundancy is shown to be incorrect by means of a counterexample. The consequences of this error for other conclusions drawn by the authors are discussed. (Author/JKS)

The notion of multidimensional structure is discussed within the framework of an additive component model of multidimensional scaling, where a configuration is considered to be composed of disjoint subspaces, each one of which reflects variation due to a specific stimulus component. Empirical examples are given. (Author/BW)

Methods to compare population means in the univariate case and population mean vectors in the multivariate case are presented in terms of hypotheses tested by various procedures. Tests relevant to each hypothesis are described and compared in terms of maximizing power while controlling Type I error rates over the widest variety of conditions. (SLD)

Outlines the multivariate latent distribution specification and the corresponding interpretation issues. Also shows the univariate formulation and some alternative parameterizations that are useful in the estimation phase. Illustrates the procedures through an application to student ratings data. (SLD)

A k-dimensional multivariate normal distribution is made discrete by partitioning the k-dimensional Euclidean space with rectangular grids. The probability integrals over the partitioned cubes forms a k-dimensional contingency table with ordered categories. A loglinear model with main effects plus two-way interactions provides an approximation for…

Proposes a Bayesian analysis of the multivariate linear model with polytomous variables. Shows how a Gibbs sampler algorithm is implemented to produce the Bayesian estimates. Illustrates the proposed methodology through examples using multivariate linear regression and multivariate two-way analysis of variance with real data. (SLD)

Studied a multiple group model with ordinal categorical observed variables that are manifestations of underlying normal variables. Proposed to apply across-group stochastic constraints on thresholds to identify the model and used a Bayesian approach to analyze the model. Simulation findings and the analysis of a real data set show the usefulness…

Developed methods for testing whether or not patterns of incomplete data represent samples from a single population. Results from a simulation study show that the generalized least squares test of homogeneity of means performed close to an ideal Type I error rate for most of the conditions. The generalized least squares test of homogeneity of…