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)

The study of confusion data is a well established practice in psychology. Although many types of analytical approaches for confusion data are available, among the most common methods are the extraction of 1 or more subsets of stimuli, the partitioning of the complete stimulus set into distinct groups, and the ordering of the stimulus set. Although…

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…

We use the sum property for determinants of matrices to give a three-stage proof of an identity involving Fibonacci numbers. Cassini's and d'Ocagne's Fibonacci identities are obtained at the ends of stages one and two, respectively. Catalan's Fibonacci identity is also a special case.

Meta-analytic structural equation modeling (MA-SEM) is increasingly being used to assess model-fit for variables' interrelations synthesized across studies. MA-SEM researchers have analyzed synthesized correlation matrices using structural equation modeling (SEM) estimation that is designed for covariance matrices. This can produce incorrect…

A novel and simple formula for computing the matrix exponential function is presented. Specifically, it can be used to derive explicit formulas for the matrix exponential of a general matrix A satisfying p(A) = 0 for a polynomial p(s). It is ready for use in a classroom and suitable for both hand as well as symbolic computation.

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…