This seventh in a series of articles discussing expert system construction focuses on two ways to create a structure that determines a decision: (1) rule-based, or deductive, implementation; and (2) example-based, or inductive, implementation. Probability factors and confidence levels are discussed, and an example is given for selecting an…

A summary and a unified treatment of fully general computational solutions for two criteria for transforming two or more matrices to maximal agreement are provided. The two criteria--Maxdiff and Maxbet--have applications in the rotation of factor loading or configuration matrices to maximal agreement and the canonical correlation problem. (SLD)

The identification of two factors when one factor is expected is an artifact caused by using factor analysis on data that would be more appropriately analyzed with a unidimensional unfolding model. A numerical illustration is given, and ways to determine whether data conform to the unidimensional unfolding model are reviewed. (SLD)

A class of oblique rotation procedures is proposed to rotate a pattern matrix so that it optimally resembles a matrix that has an exact simple pattern. It is demonstrated that the method can recover relatively complex simple structures where other simple structure rotation techniques fail. (SLD)

The phenomenon of 2 x 2 x 2 arrays having nonmaximal rank with positive probability, pointed out by J. Kruskal (1989), is generalized to 2 x "n" x "n" arrays. It is concluded that a pair of asymmetric square matrices can be diagonalized simultaneously with positive probability. (SLD)

Rowwise matrix correlation, based on the weighted sum of correlations between all pairs of corresponding rows of two proximity matrices, is discussed. Rowwise and columnwise indices are particularly suited for evaluating different types of conjectures of a similar pattern of entries across the two matrices. (SLD)

Describes the development of a functional indexing system that is tailored to the thinking involved in the process of invention. Classification by function is discussed; matrix representation is explained; a controlled vocabulary of verbs, objects, and modifiers is described; and the relation to other indexing systems is examined. (13 references)…

Discusses the benefits of and strategies for integrating various disciplines within physical education, suggesting that by communicating with classroom teachers, planning for integration, and organizing using a matrix, the integration process can be easier, less time-consuming, and more consistent. The paper explains how to begin (start small,…

Assessed two models for confirmatory factor analysis of multitrait-multimethod data through Monte Carlo simulation. The correlated traits-correlated methods (CTCM) and the correlated traits-correlated uniqueness (CTCU) models were compared. Results suggest that CTCU is a good alternative to CTCM in the typical multitrait-multimethod matrix, but…

Compares approaches to occupational analysis and develops a framework that identifies the role, skill, and function of each of the following dimensions: focus, conception of rationality, view of knowledge, concept of intelligence, learning process, individual/expertise relationship, enabling factors, psychological theory, model of social…

H. F. Kaiser, S. Hunka, and J. Bianchini have presented a method (1971) to compare two matrices of factor loadings based on the same variables, but different groups of individuals. The optimal rotation involved is examined from a mathematical point of view, and the method is shown to be invalid. (SLD)

The way in which computer algebra systems, such as Maple, have made the study of complex problems accessible to undergraduate mathematicians with modest computational skills is illustrated by some large matrix calculations, which arise from representing the Earth's surface by digital elevation models. Such problems are often considered to lie in…

A multivariate reduced-rank growth curve model is proposed that extends the univariate reduced rank growth curve model to the multivariate case, in which several response variables are measured over multiple time points. The proposed model allows us to investigate the relationships among a number of response variables in a more parsimonious way…

In this note, we give a method for finding the inverse of a three by three magic square matrix without using the usual methods for finding the inverse of a matrix. Also we give a method for finding the inverse of a three by three magic square matrix whose entries are also matrices. By using these ideas, we can construct large matrices whose…

Characteristic polynomials are used to determine when magic squares have magic inverses. A resulting method constructs arbitrary examples of such squares.