An algorithm, based on a solution for C. I. Mosier's oblique Procrustes rotation problem, is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. Results are of interest for missing value and tetrachoric correlation, indefinite matrix correlation, and constrained…

Presents and demonstrates three new concepts in innovation diffusion: the attribution matrix, the innovation profile, and the potential for adoption rating that determines which among similar innovations is most likely to be adopted. This predictive model represents a means of conducting formative evaluation research about the potential for…

The impact of general control processing and working memory capacity on a measure of abstract intelligence was examined with 577 military recruits. A new multicomponent latent trait model for covert response was applied to item response data for matrix problems. General control processing has a stronger impact. (SLD)

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)

A matrix is presented for evaluating outdoor development programs. The four quadrants (narrow skills, broad skills, fun/enjoyment, self/other awareness) are ranged along two dimensions: tight to loose task approach and low to high intensity process. (SK)

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…

Reanalysis with updated exploratory and confirmatory factor analytic methods of correlation matrices for 21 structure-of-intellect divergent production tests from the University of Southern California Aptitude Research Project suggests that the results cannot be replicated and support a higher order 2-factor oblique model of covariance among test…

Described are ways that errors of magnitude can be unwittingly caused when using various supercalculator algorithms to solve linear systems of equations that are represented by nearly singular matrices. Precautionary measures for the unwary student are included. (JJK)

Described is the hand-calculation method for the orthogonalization of a given set of vectors through the integration of Gaussian elimination with existing algorithms. Although not numerically preferable, this method adds increased precision as well as organization to the solution process. (JJK)

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)

Applications of the confirmatory factor analysis block-diagonal model to published data on 18 multitrait-multimethod matrices were reviewed to show widespread estimation problems. Possible causes of estimation difficulties were explored using computer simulations. These problems make the block-diagonal approach less useful than has generally been…

Considers models incorporating principal components from the perspectives of structural-equation modeling. These models include the following: (1) the principal-component analysis of patterned matrices; (2) multiple analysis of variance based on principal components; and (3) multigroup principal-components analysis. Discusses fitting these models…

Some uniqueness properties are presented for the PARAFAC2 model for covariance matrices, focusing on uniqueness in the rank two case of PARAFAC2. PARAFAC2 is shown to be usually unique with four matrices, but not unique with three unless a certain additional assumption is introduced. (SLD)

Discusses a real-world problem-solving lesson that emerged when a high school math teacher used a motion detector with a CBL and graphing calculator to obtain the bounce data of a ping-pong ball. Describes the lesson in which students collect bad data then fill in the missing parabolas that result using critical components of parabolas and…

Students find difficulty in learning linear algebra because of the abstraction and formalism associated with concepts such as vector space, linear independence, rank and invertible matrices. Learning the necessary procedures becomes insufficient, and imitating worked examples does not guarantee the maturity level necessary for understanding these…