Two forms of stationarity prior to criterion in absorbing Markov chains are examined. Both forms require that the probability of a particular response on a particular trial before absorption be independent of trial number. Simple, necessary and sufficient conditions for both forms are developed and applied to several examples. (Author)

Relations between Tucker's three-mode multidimensional scaling and Carroll and Chang's INDSCAL are discussed. A technique to transform a three-mode solution to the general form of an INDSCAL solution along with applications to two sets of data from the literature are presented. (Author/JKS)

The residual variance is often used as an approximation to the uniqueness in factor analysis. An upper bound approximation to the residual variance is presented for the case when the correlation matrix is singular. (Author/JKS)

A full-fledged matrix derivation of Sherin's matrix formulation of Kaiser's varimax criterion is provided. Matrix differential calculus is used in conjunction with the Hadamard (or Schur) matrix product. Two results on Hadamard products are presented. (Author/JKS)

Developed a procedure for overcoming the computational and technological limitations of analyzing data with missing observations by extracting data from a sparsely filled data matrix into analyzable smaller subsets of data. Demonstrated the validity of this subdividing method using a Monte Carlo simulation. (SLD)

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.…

Procedures for oblique rotation of factors or principal components typically focus on rotating the pattern matrix so that it becomes optimally simple. How the Harris and Kaiser independent cluster (1964) rotation can be modified to obtain a simple weights matrix rather than a simple pattern is described and illustrated. (SLD)

Gives sufficient and necessary conditions for the observability of factors in terms of the parameter matrices and a finite number of variables. Outlines five conditions that rigorously define indeterminacy and shows that (un)observable factors are (in)determinate, and extends L. Guttman's (1955) proof of indeterminacy to Heywood (H. Heywood, 1931)…

Derives the asymptotic standard errors and intercorrelations for several matrix correlations assuming multivariate normality for manifest variables and derives the asymptotic standard errors of the matrix correlations for two factor-loading matrices. (SLD)

Provides a fully flexible approach for orthomax rotation of the core to simple structure with respect to three modes simultaneously. Computationally the approach relies on repeated orthomax rotation applied to supermatrices containing the frontal, lateral, or horizontal slabs, respectively. Exemplary analyses illustrate the procedure. (Author/SLD)

In three-mode principal components analysis, the P x Q x R core matrix "G" can be transformed to simple structure before it is interpreted. This paper shows that, when P=QR-1, G can be transformed to have nearly all the elements equal to values specified a priori. A closed-form solution for this transformation is offered. (SLD)

A sufficient condition in terms of the unique variances of a common factor model is given for the results of factor analysis to come closer to those of principal components analysis. In general, vectors corresponding to loading matrices can be related to each other by a specific measure of closeness, which is illustrated. (SLD)

This study uses a Cook's distance type diagnostic statistic to identify unusual observations in a data set that unduly influence the estimation of a covariance matrix. Similar to many other deletion-type diagnostic statistics, this proposed measure is susceptible to masking or swamping effect in the presence of several unusual observations. In…

This article shows how to use six parameters describing the International Space Station's orbit to predict when and in what part of the sky observers can look for the station as it passes over their location. The method requires only a good background in trigonometry and some familiarity with elementary vector and matrix operations. An included…

This article details the application of an economic theory to the fiscal operation of a small engineering consulting firm. Nobel Prize-winning economist Wassily Leontief developed his general input-output economic theory in the mid-twentieth century to describe the flow of goods and services in the U.S. economy. We use one mathematical model that…