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.     

Splitting visual space with attention

If a right-left spatial compatibility effect is observed, it can be maintained that the space has been segmented into right- and left-side parts. The present study aimed at showing a spatial compatibility effect (and, by implication, a right-left subdivision of space) solely attributable to the orienting of attention. Five groups of 8 normal subjects were required to give right-left discriminative responses to stimuli presented within one of six empty boxes arranged in a horizontal row. Reaction times and errors were recorded. The first two experiments showed that a right-left grouping of the boxes occurred regardless of whether subjects' fixation was kept at the intermediate position (Experiment 1) or at one extremity (Experiment 2) of the row. In Experiments 3 and 4, subjects' attention was not aligned with a fixed position but was moved, through peripheral cues, from trial to trial and positioned between different pairs of adjacent boxes. The results showed that the display was again subdivided into two regions and that the reference point for the right-left subdivision was the focus of attention. In Experiment 5, eye position was instrumentally monitored, and subjects' attention was directed by central cues. The results confirmed that the focusing of attention leads to a right-left partitioning of space, with the boundary at the locus of focal attention. In conclusion, we demonstrated, by employing a right-left spatial compatibility paradigm, that directing attention to a position in space brings about a right-left perceptual organization that predominates over that provided by the other egocentric reference axes.     

Comparative clinicogenetic study of schizophrenic psychoses

The author diagnoses 350 carefully selected schizophrenic subjects, their parents and their siblings during parallel studies using three different clinical classification systems and analyzes the results by multiple threshold analysis and the multifactorial inheritance model. The results suggest that, of the three classifications the author studied, Leonhard's and Sneshnewski's system yield relatively homogeneous subgroups; this indicates the future significance of these nosological systems for the planning of biopsychiatric research.