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…

Through simulation, showed that a multivariate test of interactions for aligned ranks in a split-plot design controlled Type I error rates for nonnormal data with nonspherical covariance structures. This method also performed well in the presence of a strong repeated measures main effect and demonstrated more statistical power than parametric…

Cohen's kappa statistic is frequently used to measure agreement between two observers using categorical polytomies. Cohen's statistic is: shown to be inherently multivariate in nature; expanded to analyze ordinal and interval data; and extended to over two observers. A non-asymptotic test of significance is provided for the generalized statistic.…

Monotonically convergent algorithms are described for maximizing sums of quotients of quadratic forms. Six (constrained) functions are investigated. The general formulation of the functions and the algorithms allow for application of the algorithms in various situations in multivariate analysis. (SLD)

Provides an overall test statistic to evaluate significance that yields 100% (1-alpha) confidence intervals for all linear combinations of effect sizes, shows how the stepdown Finite Intersection Test (N. Timm, 1995) may be used to test whether effect sizes are simultaneously different from zero, and illustrates the procedure. (SLD)

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…

Studied variations in the magnitude of self-belief discrepancies among adolescents with different levels of identity development using a sample of 336 male and female adolescents. Multivariate analyses of variance showed that respondents with different identity statuses significantly varied on the magnitude of self-discrepancy experiences,…

Presents an application of the EM-algorithm to two problems of estimation and testing in a multivariate normal distribution with missing data. The two models are tested applying the log-likelihood ratio test. Solves the problem of different and nonmonotone patterns of missing data by introducing suitable transformations and partitions of the data…

Describes the career and contributions of educational researcher Maurice M. Tatsuoka, best known professionally for his interest in multivariate statistics. (SLD)