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.     

Insight without awareness: On the interaction of verbalization, instruction and practice in a simulated process control task

Four experiments in which subjects learned to control two versions of a complex simulated process control task show that verbalizable knowledge of procedures used to perform these tasks is very limited and is acquired late in learning. Individual learning curves associated with these tasks showed sudden improvements in performance, which were not accompanied by a similar increase in verbalizable knowledge. It was also found that verbal instructions consisting of exemplar memorization, strategies for rule induction, simple heuristics, and experts' instructions were all effective in enhancing novice subjects' performance. A theoretical framework is proposed in which subjects draw on two separate but interacting knowledge structures to perform these tasks. One knowledge structure is based on memory for past experiences (close analogies), and the other is based on one's current mental model of the task. Implicit sets of competing rules that control response selection are derived from both sources of knowledge. It is suggested that dissociations between task performance and verbalizing occur because memory-based processing tends to have more control over response selection because of its greater specificity, whereas a mental model tends to be the preferred mode for verbal reporting because of its greater accessibility.     

A componential model for mental addition

A componential model capable of representing simple and complex forms of mental addition was proposed and then tested by using chronometric techniques. A sample of 23 undergraduate students responded to 800 addition problems in a true-false reaction time paradigm. The 800 problems comprised 200 problems of each of four types: two single-digit addends, one single- and one double-digit addend, two double-digit addends, and three single-digit addends. The results revealed that the columnwise product of addends, a structural variable consistent with a memory network retrieval process, was the best predictor of mental addition for each of the four types of problem. Importantly, the componential model allowed estimation of effects of several other structural variables, e.g., carrying to the next column and speed of encoding of digits. High levels of explained variance verified the power of the model to represent the reaction time data, and the stability of estimates across types of problem implied consistent component use by subjects. Implications for research on mental addition are discussed.     

Twenty-four-hour sleep-wake patterns in a nursing home population

Sleep-activity patterns were objectively recorded over a 24-hr period in 19 elderly nursing home residents. On average, both sleep and wake times were observed during every hour of the 24 recorded hours; however, the sleep pattern of the residents was fragmented so that they rarely experienced even a single hour of consolidated time spent sleeping. It is hypothesized that several independent factors, including compensation for lost sleep, increased total time in bed, weakening of social constraints, and deterioration of the circadian sleep-wake rhythm, are interacting to produce this increase in sleep fragmentation.     

Comparative analysis of actual and mental movement times in two graphic tasks

This study compared the temporal organization of graphic movements executed either actually or mentally. Six subjects had to perform two tasks, writing a sentence and drawing a cube, either as a real performance or as an imagined one, with either the right or the left hand, and with either a small or a large tracing amplitude. In the same subject, for the same hand, mental and actual movement times were both very stable and very close from trial to trial regardless of the tracing amplitude. Thus, mental movements mimic closely real movements in their temporal organization and are likely to involve the same planning program.     

Forecasting the impact of the federal sentencing guidelines

The Sentencing Reform Act of 1984, which created the U.S. Sentencing Commission, required that the commisson consider prison capacity in drafting sentencing guidelines. As part of the commission's efforts to meet this requirement, we developed a computer simulation capable of projecting the impact of the commission's guidelines on future sentences and prison populations. According to our projections, “straight” probation sentences will be reduced significantly under the guidelines. However, reducing the use of probation will generate only modest demands on the prisons, and then mostly for community corrections phased in over the course of 5 years. We also project that, while average time served for violent offenses will increase substantially, average time served for most property crimes will remain largely the same. Finally, while we forecast that federal prison populations will grow markedly by the end of this century, this is more a result of the Anti-Drug Abuse Act of 1986 and the career offender provision of the Comprehensive Crime Control Act of 1984 than a result of the guidelines.     

How and when to correct for juror hindsight bias in mental health malpractice litigation: Some preliminary observations

This article examines the hindsight bias in the context of mental health malpractice litigation, analyzes various legal mechanisms for dealing with the bias, and discusses whether the law should strive for debiasing in all mental health malpractice cases.     

Sex role orientations,attributions for achievement,and personal goals of Chinese youth

The role of women in the People's Republic of China has changed dramatically in the last 40 years. This study assesses what impact these changes have had on the attitudes of Chinese youth. The sample consisted of 164 subjects (77 men and 87 women) who completed the Bem Sex Role Inventory, the Objective Fear of Success Measure, a locus of control scale, and a personal goals questionnaire. They also evaluated a painting attributed to artists of different gender and status. The results indicate that the sex role orientations of Chinese students were similar to those of American students. On the Bem inventory, the direction of the sex differences on the sex role scales was the same for U.S. and Chinese students, but the latter had a sex role orientation that, in our culture, is regarded as more “traditional.” Chinese women were significantly more likely to endorse statements expressing fear of success than were Chinese men. On the locus of control measures, Chinese women were more likely than men to attribute their achievement successes to luck and failures to a lack of ability. The women students also attributed affiliation outcomes more to luck than did the men. The most important personal goal cited by both men and women was that of career success. Chinese men placed greater importance than women on achieving wealth, and their expectancy of actually becoming wealthy was higher. Finally, in an evaluation of a painting, Chinese men, but not the women, devalued a painting when it was supposedly the work of a female student artist.     

The impact of ethnicity,nationality, counseling orientation,and mental health standards on stereotypic beliefs about women: A pilot study

People vary in the extent to which they hold stereotypic beliefs about women. The recently developed Beliefs About Women Scale (BAWS) was used in five investigations to examine the following aspects of people's stereotypic beliefs about women: (Study I) the impact of ethnicity (Hispanics and Anglos) on women's endorsement of traditional beliefs about women; (Study II) the impact of national culture (Mexico and the United States) on women's responses to the BAWS; (Study III) the extent to which U.S. women define women's and men's mental health in terms of stereotypic beliefs about women; (Study IV) the extent to which preferences for counseling orientation influence the beliefs about women attributed to mentally healthy women and men; and (Study V) the impact of national culture (Mexico and the United States) on the beliefs about women ascribed to mentally healthy women and men. The results indicated that (a) U.S. Anglo females disagreed more strongly with traditional beliefs about women than did U.S. Hispanic females; (b) U.S. women expressed greater agreement with traditional stereotypes about women's interpersonal abilities and greater disagreement with traditional stereotypes about women's personal competencies than did women from Mexico; (c) the beliefs about women held by U.S. psychology trainees, and the beliefs about women that they attributed to mentally healthy females, were more nontraditional than those that they attributed to mentally healthy males; (d) particular counseling preferences were associated with the stereotypic beliefs about women that female counseling trainees imputed to mentally healthy males and females; and (e) similarities and differences exist on the beliefs about women that female psychology trainees from the United States and Mexico ascribe to mentally healthy females and males. The discussion focuses on mentally healthy beliefs about women, and the implications of these findings for the delivery of mental health services to women and men from various cultures.