Although many textbooks on multivariate statistics discuss the common factor analysis model, few of these books mention the problem of factor score indeterminacy (FSI). Thus, many students and contemporary researchers are unaware of an important fact. Namely, for any common factor model with known (or estimated) model parameters, infinite sets of…

The methodology and mathematical treatment of several classic multivariate methods for the analysis of spectroscopic data is demonstrated in a straightforward way that can be used as a basis for teaching an undergraduate introductory course on chemometric analysis. The multivariate techniques of classical least-squares (CLS), principal component…

The Reduced Reparameterized Unified Model (Reduced RUM) is a diagnostic classification model for educational assessment that has received considerable attention among psychometricians. However, the computational options for researchers and practitioners who wish to use the Reduced RUM in their work, but do not feel comfortable writing their own…

Computing the mean and covariance matrix of some multivariate distributions, in particular, multivariate normal distribution and Wishart distribution are considered in this article. It involves a matrix transformation of the normal random vector into a random vector whose components are independent normal random variables, and then integrating…

Proposes a comprehensive approach, generalized constrained multiple correspondence analysis, for imposing both row and column constraints on multivariate discrete data. Each set of discrete data is decomposed into several submatrices and then multiple correspondence analysis is applied to explore relationships among the decomposed submatrices.…

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)

Provides power comparisons for three permutation tests and the Bartlett-Nanda-Pillai trace test (BNP) (M. Bartlett, 1939; D. Nanda, 1950; K. Pillai, 1955) in completely randomized experimental designs with correlated multivariate-dependent variables. The power of the BNP was generally found to be less than that of at least one of the permutation…

Proposes a procedure for generating multivariate nonnormal distributions. The procedure, an extension of the Fleishman power method (A. Fleishman, 1978), generates the average value of intercorrelations much closer to population parameters than competing procedures for skewed and heavy tailed distributions and small sample sizes. Reports Monte…