The Creativity Matrix: Spotlights and Blind Spots in Our Understanding of the Phenomenon

In this paper, we organize past and present theories and models of creativity by using a new conceptual framework—the creativity matrix—with the aim of highlighting the dimensions of creativity we know a lot about and those we tend to either ignore or find difficult to study. This matrix is formed by bringing together a developmental model of creativity (the 4 C's) and a structural one (the 5 A's). We start by briefly describing these two conceptual frameworks, and then, we proceed to exploring the matrix itself by describing how the 5 A's are dynamically organized at each “level” of the 4 C's. Importantly, our overview of the matrix is informed by existing models and concepts that address one of more of the C's and the A's. This gives us a unique opportunity to take stock of what has been studied so far and, toward the end, consider new avenues for the development of theory and research agendas within creativity studies.     

Beyond principal component analysis: A trilinear decomposition model and least squares estimation

The paper derives sufficient conditions for the consistency and asymptotic normality of the least squares estimator of a trilinear decomposition model for multiway data analysis.     

Least-squares approximation of an improper correlation matrix by a proper one

An algorithm is presented for the best least-squares fitting correlation matrix approximating a given missing value or improper correlation matrix. The proposed algorithm is based upon a solution for Mosier's oblique Procrustes rotation problem offered by ten Berge and Nevels. A necessary and sufficient condition is given for a solution to yield the unique global minimum of the least-squares function. Empirical verification of the condition indicates that the occurrence of non-optimal solutions with the proposed algorithm is very unlikely. A possible drawback of the optimal solution is that it is a singular matrix of necessity. In cases where singularity is undesirable, one may impose the additional nonsingularity constraint that the smallest eigenvalue of the solution be , where is an arbitrary small positive constant. Finally, it may be desirable to weight the squared errors of estimation differentially. A generalized solution is derived which satisfies the additional nonsingularity constraint and also allows for weighting. The generalized solution can readily be obtained from the standard unweighted singular solution by transforming the observed improper correlation matrix in a suitable way.     

A nonparametric approach for assessing latent trait unidimensionality

Assuming a nonparametric family of item response theory models, a theory-based procedure for testing the hypothesis of unidimensionality of the latent space is proposed. The asymptotic distribution of the test statistic is derived assuming unidimensionality, thereby establishing an asymptotically valid statistical test of the unidimensionality of the latent trait. Based upon a new notion of dimensionality, the test is shown to have asymptotic power 1. A 6300 trial Monte Carlo study using published item parameter estimates of widely used standardized tests indicates conservative adherence to the nominal level of significance and statistical power averaging 81 out of 100 rejections for examinee sample sizes and psychological test lengths often incurred in practice.The referees' comments were remarkably detailed and greatly enhanced the writeup and sensitized the author to certain pertinent issues. Discussions with Fritz Drasgow, Lloyd Humphreys, Dennis Jennings, Brian Junker, Robert Linn, Ratna Nandakumar, and Robin Shealy were also very useful.This research was supported by the Office of Naval Research under grant N00014-84-K-0186; NR 150-533, and by the National Science Foundation under grant DMS 85-03321.     

A note on the computation of the second-order derivatives of the elementary symmetric functions in the rasch model

Jansen (1984) gave explicit formulas for the computation of the second-order derivatives of the elementary symmetric functions. But they are only applicable to those pairs of items which have unequal parameters. It is shown here that for equal parameters similar explicit formulas do exist, too, facilitating the application of the Newton-Raphson procedure to estimate the parameters in the Rasch model and related models according to the conditional maximum likelihood principle.The author wishes to thank the reviewers for their helpful comments on an earlier draft of this paper.     

Estimation for structural equation models with missing data

A direct method in handling incomplete data in general covariance structural models is investigated. Asymptotic statistical properties of the generalized least squares method are developed. It is shown that this approach has very close relationships with the maximum likelihood approach. Iterative procedures for obtaining the generalized least squares estimates, the maximum likelihood estimates, as well as their standard error estimates are derived. Computer programs for the confirmatory factor analysis model are implemented. A longitudinal type data set is used as an example to illustrate the results.This research was supported in part by Research Grant DAD1070 from the U.S. Public Health Service. The author is indebted to anonymous reviewers for some very valuable suggestions. Computer funding is provided by the Computer Services Centre, The Chinese University of Hong Kong.     

A general structural equation model with dichotomous,ordered categorical,and continuous latent variable indicators

A structural equation model is proposed with a generalized measurement part, allowing for dichotomous and ordered categorical variables (indicators) in addition to continuous ones. A computationally feasible three-stage estimator is proposed for any combination of observed variable types. This approach provides large-sample chi-square tests of fit and standard errors of estimates for situations not previously covered. Two multiple-indicator modeling examples are given. One is a simultaneous analysis of two groups with a structural equation model underlying skewed Likert variables. The second is a longitudinal model with a structural model for multivariate probit regressions.This research was supported by Grant No. 81-IJ-CX-0015 from the National Institute of Justice, by Grant No. DA 01070 from the U.S. Public Health Service, and by Grant No. SES-8312583 from the National Science Foundation. I thank Julie Honig for drawing the figures. Requests for reprints should be sent to Bengt Muthén, Graduate School of Education, University of California, Los Angeles, California 90024.     

An alternating least squares method for the weighted approximation of a symmetric matrix

Bailey and Gower examined the least squares approximationC to a symmetric matrixB, when the squared discrepancies for diagonal elements receive specific nonunit weights. They focussed on mathematical properties of the optimalC, in constrained and unconstrained cases, rather than on how to obtainC for any givenB. In the present paper a computational solution is given for the case whereC is constrained to be positive semidefinite and of a fixed rankr or less. The solution is based on weakly constrained linear regression analysis.The authors are obliged to John C. Gower for stimulating this research.     

Simultaneous auditory discrimination.

Stimuli in many visual stimulus control studies typically are presented simultaneously; in contrast the stimuli in auditory discrimination studies are presented successively. Many everyday auditory stimuli that control responding occur simultaneously. This suggests that simultaneous auditory discriminations should be readily acquired. The purpose of the present experiment was to train rats in a simultaneous auditory discrimination. The apparatus consisted of a cage with two response levers mounted on one wall and a speaker mounted adjacent to each lever. A feeder was mounted on the opposite wall. In a go-right/go-left procedure, two stimuli were presented on each trial, a wide-band noise burst through one speaker and a 2-kHz complex signal through the other. The stimuli alternated randomly from side to side across trials, and the stimulus correlated with reinforcement for presses varied across subjects. The rats acquired the discrimination in 400 to 700 trials, and no response position preference developed during acquisition. The ease with which the simultaneous discrimination was acquired suggests that procedures, such as matching to sample, that require simultaneous presentation of stimuli can be used with auditory stimuli in animals having poor vision.     

Some properties of estimated scale invariant covariance structures

Scale invariance is a property shared by many covariance structure models employed in practice. An example is provided by the well-known LISREL model subject only to classical normalizations and zero constraints on the parameters. It is shown that scale invariance implies that the estimated covariannce matrix must satisfy certain equations, and the nature of these equations depends on the fitting function used. In this context, the paper considers two classes of fitting functions: weighted least squares and the class of functions proposed by Swain.Constructive comments by the referees are greatly appreciated. The author gratefully acknowledges Michael Browne's interest in his work.