Generalized approaches to the maxbet problem and the maxdiff problem,with applications to canonical correlations

Van de Geer has reviewed various criteria for transforming two or more matrices to maximal agreement, subject to orthogonality constraints. The criteria have applications in the context of matching factor or configuration matrices and in the context of canonical correlation analysis for two or more matrices. The present paper summarizes and gives a unified treatment of fully general computational solutions for two of these criteria, Maxbet and Maxdiff. These solutions will be shown to encompass various well-known methods as special cases. It will be argued that the Maxdiff solution should be preferred to the Maxbet solution whenever the two criteria coincide. Horst's Maxcor method will be shown to lack the property of monotone convergence. Finally, simultaneous and successive versions of the Maxbet and Maxdiff solutions will be treated as special cases of a fully flexible approach where the columns of the rotation matrices are obtained in successive blocks.The author is obliged to Henk Kiers for computational assistance and helpful comments.     

The effect of a non-informative cueing signal in a three-choice reaction-time task

Summary Many studies have shown that in a simple reaction-time (RT) task a non-informative leading cue decreases RT to a subsequent target presented in the same region as the cue. This facilitation lasts about 150 ms; it is then replaced by a sustained inhibition. Experiment 1 tests the hypothesis that the initial facilitation is due to motor, rather than perceptual, processes by using choice RT. Facilitation is greater and lasts longer in choice than in simple tasks, thus supporting the hypothesis. Experiment 2 shows that facilitation occurs even when the subject actively orients his or her attention away from the cue.     

Games teams play: A method for investigating team coordination and performance

Teams are playing an increasingly important role in the workplace. However, reviews of the team performance literature have suggested that there are serious deficiencies in our understanding of team processes and performance (e.g., Dyer, 1984). These difficulties may be attributable, in part, to the lack of laboratory methodologies to investigate team performance. This paper describes the use of low-fidelity simulations as a potentially useful paradigm for researching team coordination and performance. This paradigm is advantageous in that it offers relatively high levels of experimental control and task representation at a low cost.     

Alternating least squares algorithms for simultaneous components analysis with equal component weight matrices in two or more populations

Millsap and Meredith (1988) have developed a generalization of principal components analysis for the simultaneous analysis of a number of variables observed in several populations or on several occasions. The algorithm they provide has some disadvantages. The present paper offers two alternating least squares algorithms for their method, suitable for small and large data sets, respectively. Lower and upper bounds are given for the loss function to be minimized in the Millsap and Meredith method. These can serve to indicate whether or not a global optimum for the simultaneous components analysis problem has been attained.Financial support by the Netherlands organization for scientific research (NWO) is gratefully acknowledged.     

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.     

Concept learning,memory and transfer of dot pattern categories

In the first experiment, subjects rated the similarity of a sample of pairs of random dot patterns generated from 3 prototypes consisting of either 4, 6, or 9 dots. The results of the experiment tended to confirm the structure imposed on the patterns by the construction method. In the second experiment, subjects learned to classify random patterns generated from 2 prototypes with either short or long interprototype distance and consisting of either 4, 6, or 9 dots in a traditional concept identification task. After acquisition, memory for old and new distortions and the prototype, which was not presented during learning, was assessed. The tendency to call a pattern “new” increased with the distance between the pattern and its prototype. In a subsequent transfer test, all subjects saw patterns of either 4, 6, or 9 dots. Performance was above chance and the transfer from larger to smaller patterns tended to be greater than the transfer from smaller to larger patterns. This is consistent with a process of schema formation based on features common to most exemplars of the category. The results are discussed in relation to several theories of concept learning and schema abstraction.     

Bilingual frequency encoding

Two experiments are reported that examine the nature of the processing of frequency information in Spanish-English bilinguals. In the first study, subjects studied a list of English-only, Spanish-only, and mixed-language words varying in their frequency of occurrence, and under conditions of being either informed or uninformed about the later frequency test. Subjects were then shown pictures represeting the nominally presented items and had to give frequency judgments for the words depicting the objects. Frequency judgments were significantly faster when the words had been presented in a single language, suggesting a summation of access times for the mixed-language words. Instructional conditions had no effect on frequency judgments, but the latency to judge was significantly reduced for the informed subjects. In the second study, using similar acquisition procedures, subjects were shown test words in either the same or the different language from the one in which the words were originally experienced. Subjects demonstrated a clear ability to assign frequencies according to the relationship between acquisition and test language. The data were discussed in terms of supporting the hypothesis of separate bilingual language processing, and implications for the automatic nature of frequency acquisition were also addressed.This article is based on a paper originally presented at the meetings of the Southwestern Psychological Association, San Antonio, April 1983.