A least-squares strategy is proposed for representing a two-mode proximity matrix as an approximate sum of a small number of matrices that satisfy certain simple order constraints on their entries. The primary class of constraints considered defines Q-forms for particular conditions in a two-mode matrix. (SLD)

Influence curves of some parameters under various methods of factor analysis depend on the influence curves for either the covariance or the correlation matrix used in the analysis. The differences between the two types of curves are derived, and simple formulas for the differences are presented. (SLD)

Introduces a method for fitting order-constrained matrices that satisfy the strongly anti-Robinson restrictions (SAR). The method permits a representation of the fitted values in a (least-squares) SAR approximating matrix as lengths of paths in a graph. The approach is illustrated with a published proximity matrix. (SLD)

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,…

The hippocampal CA3 subregion is critical for rapidly encoding new memories, which suggests that neuronal computations are implemented in its circuitry that cannot be performed elsewhere in the hippocampus or in the neocortex. Recording studies show that CA3 cells are bound to a large degree to a spatial coordinate system, while CA1 cells can…

The interpretation of a Thurstonian model for paired comparisons where the utilities' covariance matrix is unrestricted proved to be difficult due to the comparative nature of the data. We show that under a suitable constraint the utilities' correlation matrix can be estimated, yielding a readily interpretable solution. This set of identification…

To teach the rigorous skills and knowledge students need to succeed in future college-entry courses and workforce training programs, education stakeholders have increasingly called for more rigorous curricula, instruction, and assessments. Identifying the critical attributes of rigor and measuring its appearance in curricular materials is…

An illustration of a test for independence was provided with a mixed set of variables. The matrix consisted of 10 tests of interest and four random deviates in which the relationship between sets was demonstrated to be minimal. The result was discussed for a situation in which factoring methods might be considered. (Author)

A Fortran V program is described derived for the Univac 1100 Series Computer for clustering into hierarchical structures large matrices, up to 1000 x 1000 and larger, of interassociations between objects. (RC)

Methods for rotating factor analysis matrices to a least squares fit with a specified structure are discussed. Existing solutions are shown to be not valid in some cases or to not work when matrices are not of full rank. A general solution is derived, addressing both issues. (Author/JKS)

Some effects of using inappropriate criteria for sufficiency of factors are discussed, and examples from the literature are used to show how procedures leading to the rotation of large numbers of factors may result in fragmentation and difficulty in interpretation. (Author/JKS)

Two models for scaling of paired comparison data are compared to the Thurstone case III model. Two goodness of fit indices are presented for each model for five data sets. The results illustrate the inability of the Thurstone model to adequately account for data when the scale includes extreme stimuli. (Author)