A modified technique of separable programming was used to maximize the squared correlation ratio of weighted responses to partially ordered categories. The technique employs a polygonal approximation to each single-variable function by choosing mesh points around the initial approximation supplied by Nishisato's method. Numerical examples were…

Two Statistical Analysis System (SAS) macros are presented that perform the modified principal components approach of L. R. Tucker (1966) to modeling generalized learning curves analysis up to a rotation of the components. Three SAS macros are described that rotate the factor patterns to have characteristics Tucker considered desirable. (SLD)

A globally optimal solution is presented for a class of functions composed of a linear regression function and a penalty function for the sums of squared regression weights. A completing-the-squares approach is used, rather than calculus, because it yields global minimality easily in two of three cases examined. (SLD)

An algorithm based on the majorization theory of J. de Leeuw and W. J. Heiser is presented for fitting the slide-vector model. It views the model as a constrained version of the unfolding model. A three-way variant is proposed, and two examples from market structure analysis are presented. (SLD)

An algorithm for obtaining initial values for the minimization process in covariance structure analysis is developed that is more generally applicable for computing parameters connected to latent variables than the currently existing ones. The algorithm is formulated in terms of the RAM model but can be extended. (SLD)

The DEcomposition into DIrectional COMponents (DEDICOM) method for analysis of asymmetric data gives representations that are identified only up to a non-singular transformation. To identify solutions, it is proposed that subspace constraints be imposed on the stimulus coefficients. Procedures are discussed for several cases. (SLD)

The Galois-lattice is a graphic method for representing all possible developmental phases to reach a given total knowledge via different partial knowledge structures. Algorithms are proposed for incorporating statistical analysis into the Galois-lattice method. A comparison to the Rasch model and application for educational research are given. (BS)

A general approach for fitting a model to a data matrix by weighted least squares (WLS) is studied. The approach consists of iteratively performing steps of existing algorithms for ordinary least squares fitting of the same model and is based on maximizing a function that majorizes WLS loss function. (Author/SLD)

R. A. Bailey and J. C. Gower explored approximating a symmetric matrix "B" by another, "C," in the least squares sense when the squared discrepancies for diagonal elements receive specific nonunit weights. A solution is proposed where "C" is constrained to be positive semidefinite and of a fixed rank. (SLD)

An asymptotic theory is developed for a new time series model introduced in TM 502 289. An algorithm for computing estimates of the parameters of this time series model is given, and it is shown that these estimators are asymptotically efficient in that they have the same asymptotic distribution as the maximum likelihood estimators. (Author/RC)

The first part of this four-part dissertation reviews conceptual and operational approaches to human communication systems. A new conceptual model for studying communication, General Algorithm for Studying Structuring in Complex Systems (GASSICS), is developed in the second part, and an operational method for applying GASSICS is presented in part…

Several computer programs were developed to solve various versions of the quadratic capacitated facilities location problem. Matrices, which represent various business costs, are defined for the factors of sites, facilities, customers, commodities, and production units. The objective of the program is to find an optimization matrix for the lowest…

This yearbook provides the mathematics education community with specific perceptions about discrete mathematics concerning its importance, its composition at various grade levels, and ideas about how to teach it. Many practical suggestions with respect to the implementation of a discrete mathematics school program are included. A unifying thread…