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.     

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.     

School administrators, parents, and sex education: a resolvable paradox?

The emergence of AIDS as an untreatable, lethal disease, responding to educational prevention strategies in high-risk populations, has brought the issues of sex education in the public schools to the forefront. However, administrators, teachers, and parents perceive different barriers to sex education implementation. This study, undertaken in a northeastern, multigenerational, ethnic city, characterized by adolescent pregnancy rates a third higher than the state overall, polled 42 junior and senior high school administrators regarding educational priorities, perceived barriers to expansion of sex education, and preferred methods of introducing sex education. Administrators perceive parents as a major barrier to the introduction of more formalized sex education in their schools. Paradoxically, these same administrators felt that parents were generally uncomfortable in talking to their children about human sexuality. Recommendations are offered from existing models of health education for resolution of administrators' conflicting views on parental roles.     

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.     

The effects of verbal reinforcement of intrinsic motivation for sex-linked tasks

Recent studies have demonstrated that positive verbal feedback enhances males' intrinsic motivation for a task, while decreasing that of females. This result has been attributed to differential socialization forces which make the controlling aspects of rewards more salient for females as opposed to males, for whom the informational aspects are prepotent. A weakness in this conclusion stems from the use of a masculine sex-linked task in prior experiments, producing a result which may be due to gender congruence/incongruence rather than to socialization differences. Two laboratory experiments were performed to examine the effects of verbal praise on intrinsic motivation, controlling for sex-typing of the experimental activity. Experiment I found that verbal praise increased females' and males' intrinsic motivation on both a feminine and masculine task, and intrinsic motivation was higher for sex-appropriate than sex-inappropriate tasks. The sexes did not show a differential pattern of response to praise. In Experiment 2, verbal praise also enhanced sex-role traditional females' intrinsic motivation on the same activity used in prior research. These results suggest that socialization content has changed sufficiently to make concerns about competence and self-determination equally salient for females and males.