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.     

Design and implementation of a program for AIDS prevention in female prostitutes

The Companeros model of HIV infection prevention in Ciudad Juarez, Mexico, is presented as conceived by the National Institute of Drug Abuse (NIDA). 518 women who were IV drug users, sexual partners of drug addicts, or prostitutes were requested to participate, and 232 consented. Initial and follow-up AIDS assessments were utilized along with an assessment of sociodemographic variables, including knowledge, sexual behavior, use and abuse of drugs, and previous health history. Educative sessions about AIDs and sexually transmitted diseases (STDs) included group discussions and interaction, video watching, personal experiences, and sociodramas. 61% of prostitutes were 29, 12.6% were 13-19 years old, 31.1% were aged 30-39, and 8.9% were 40. 11% had no formal education, 58% had 6 years of primary and part of 3 years of secondary education, only 18.6% completed secondary education; and 13% had higher education. 19% lived in a hotel or shelter. Family disintegration reached 44%; these women did not live with their children. Only 5.2% thought they had excellent health, 51% said they had good health, 31% stated they had average health, and 12% admitted having had health problems. 14.6% had genital ulcers, 1.3% had herpes, 15% had gonorrhea, and 10% had syphilis. Since IV drug use among these women was almost nonexistent sexual relations constituted the principal risk factor. Responses to a questionnaire showed that the most frequent sexual behavior was vaginal penetration followed by fellatio; anal penetration was less common. 34.9% of the women practiced fellatio without protection, 16.3% had anal intercourse without protection. The proportion of AIDS cases in Mexico in women of reproductive age was growing at an exponential rate, possible because of misinformation about AIDS, a history of STDs, and a low rate of condom use.     

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.     

Control of responding during stimuli that precede transitions in reinforcement frequency

Pigeons' responses were reinforced on a variant of a mixed variable-interval extinction schedule of reinforcement in which the transition to the higher reinforcement rate was signaled by a trace stimulus projected on the response key prior to the onset of the component correlated with food delivery. In the first of two experiments, the duration of the trace stimulus preceding the component correlated with food delivery was varied from 1.5 to 50.0 s and in the second experiment, the reinforcement frequency in the same component was varied from 10 to 60 reinforcers per hour. Pigeons pecked at the trace stimulus preceding the onset of the component correlated with food delivery even though responding was not reinforced in its presence and only one of the changes in reinforcement rate (i.e., from extinction to reinforcement) was signaled. The rate of pecking during the trace stimulus was a function of its duration but not of the reinforcement frequency in the following component. Higher rates generally occurred at the shorter trace-stimulus durations. Component responding following the offset of the trace stimulus was under discriminative control of the trace stimulus whether or not responding occurred in the presence of the trace stimulus.     

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.