At United States Military Academy, a unit on biological modeling applications forms the culminating component of the first semester core mathematics course for freshmen. The course emphasizes the use of problem-solving strategies and modeling to solve complex and ill-defined problems. Topic areas include functions and their shapes, data fitting,…

A revised theorem is presented concerning uniqueness of minimum rank solutions in common factor analysis. (Author)

Centering a matrix row-wise and rescaling it column-wise to a unit sum of squares requires an iterative procedure. It is shown that this procedure converges to a stable solution that need not be centered row-wise. The results bear directly on several types of preprocessing methods in Parafac/Candecomp. (Author/TJH)

Procrustean analysis is a form of factor analysis where a target matrix of results is specified and then approximated. Procrustean analysis is extended here to the case where matrices have different row order. (Author/JKS)

The first eigenvalue of a correlation matrix indicates the maximum amount of the variance of the variables which can be accounted for with a linear model by a single underlying factor. The first eigenvalue measures the primary cluster in the matrix, its number of variables and average correlation. (Author/RL)

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)

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)

Presents a LISREL model for the estimation of the repeated measures analysis of variance (ANOVA) with a patterned covariance matrix. The model is demonstrated for a 5 x 2 (Time x Group) ANOVA in which the data are assumed to be serially correlated. Similarities with the Statistical Analysis System PROC MIXED model are discussed. (SLD)

Most researchers using factor analysis extract factors from a matrix of Pearson product-moment correlation coefficients. A method is presented for extracting factors in a non-parametric way, by extracting factors from a matrix of Spearman rho (rank correlation) coefficients. It is possible to factor analyze a matrix of association such that…

The logic and procedures underlying a disturbance term regression test of logical consistency for structural models are reviewed for recursive and nonrecursive designs. It is shown that in a simple three-variable, complete mediational case the test procedure is mathematically equivalent to a part correlation. (Author/LMO)

The problem of combining information to estimate standardized partial regression coefficients in a linear model is considered. A combined estimate obtained from the pooled correlation matrix is proposed, and its large sample distribution is obtained. This estimate can be generalized to address situations in which not every study measures every…

Principal components analysis is generalized to the case where any of the variables under consideration can be nominal, ordinal or interval. Hotelling's original formulation is seen to be a special case of this generalization. (JKS)

Structural models that yield circumplex inequality patterns are reviewed, focusing on a model developed by T. W. Anderson (1960). A modification is proposed to this model to allow for negative correlations. This model may be reparameterized as a factor analysis model with nonlinear constraints on the factor loadings. (SLD)

An equal-level approach is proposed for investigating multitrait-multimethod (MTMM) matrices with respect to other organizational units that contain additional information concerning a MTMM matrix's validity. The approach requires equality in "data level" before coefficients are submitted for evaluation. Disaggregation is central to…

This paper discusses the issue of multiple testing and overall Type I error rates in contexts other than multiple comparisons of means. It demonstrates, using a 5 x 5 correlation matrix, the application of 5 recently developed modified Bonferroni procedures developed by the following authors: (1) Y. Hochberg (1988); (2) B. S. Holland and M. D.…