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.     

The psychophysics of spending

Several theories of decision making are based, in part, upon the principles of psychophysics (Kahneman and Tversky, 1979; Thaler, 1985). For example, due to the psychophysics of quantity, the difference between $10 and $20 seems greater than the difference between $110 and $120. To determine whether psychophysics influences consumers' decisions, subjects in four studies made real or hypothetical purchases. It was predicted that as the size of the purchase increased, subjects would be more willing to buy additional smaller items. Small extra purchases should seem like minor expenditures when they follow larger purchases. Results of the four studies supported our hypothesis. In addition, it was found that subjects responded not only to actual changes in purchase size but also to changes in the presentation or framing of a purchase.     

Time reallocation in a multiresponse environment: Effects of restricting response classes

Four adult male rats were each placed for three hours daily into an apparatus that provided individual compartments for six separate location-defined responses. The available responses consisted of: (1) the opportunity to turn off room lighting, producing darkness; (2) the opportunity to view a female rat; (3) the opportunity to turn off white noise; (4) the opportunity to drink; (5) the opportunity to eat; and (6) "other," representing time in the hallway between compartments. Each subject underwent a series of conditions characterized as an A-B-A-C-A design. Manipulations consisted of the removal of a low-probability response (darkness) and of a high-probability response (escape from noise) in a counter-balanced manner across subjects. The dependent measure for all subjects was the percentage of total session time spent in each compartment. Four predictive rules concerning the redistribution of behavior after response restriction were tested, including the constant-ratio rule, equal time redistribution, the most probable alternative, and the sequential-dependency rule. The results indicate no support for any of the four predictive rules and suggest that empirical assessment of restriction effects is necessary in reinforcement studies involving temporally extended responses.     

Political Extremism and a Generalized Propensity to Discriminate Among Values

Research exploring the psychological differences between people supporting extreme versus moderate ideologies is growing. However, this research has rarely examined the domain of values. Here, we explore this domain by assessing the possibility that political extremists discriminate more among values compared to moderates, namely, that extremists exhibit strong commitment toward some values at the expense of other values, whereas moderates would acknowledge a multiplicity of values as equally important. First, we propose a model positing that a value discriminability parameter captures a general tendency to discriminate among values. Second, we test empirically the prediction that, compared to moderates, political extremists exhibit a higher discriminability parameter. This prediction is supported by four studies (including one based on the European Social Survey where representative samples from 29 European countries are examined) where participants reported their ideological orientation and rated the importance of basic human values (we focused on basic values because these transcend the political domain, thus highlighting general effects). Specifically, in all studies we observed a positive correlation between political extremism and residual variability in ratings, a hallmark of a higher discriminability parameter. These findings highlight the value domain as critical to understanding differences between political extremists and moderates.     

从情绪描述看青少年期到成人期认知结构的发展

该研究依据研究者制定的认知发展水平评价系统,对年龄范围在13—55岁之间的90名被试关于生气、害怕、伤心、高兴四种情绪的自我描述进行了评价分析。结果表明,青少年期的思维具有形式化、外在、抽象等特点,成人期的思维具有内在、具体、形象等特点,前者具有刻板性、封闭性,后者具有灵活性、开放性。     

大学生镜像书写及其机制探讨

本研究选择60名右利大学生(男女各半)为被试,在笔划水平上对十四种不同书写方式下快速书写时所出现的自发性镜像书写进行了研究。所有被试随机分为人数相等的实验、对照两组,组内男女各半。对实验组加以注意干扰。书写内容是十个阿拉伯数字(0—9)及十三个汉字组成的一句话。本研究结果表明:注意干扰、感觉的反馈调节,书写内容的特点是影响镜像书写出现的重要因素。作者在分析国内外有关镜像书写工作的基础上,进一步提出了“稳态系统”理论。     

BELIEF VS. COMMITMENT, VALIDITY VS. VALUE: A RESPONSE TO WARD GOODENOUGH

Abstract. This paper is on Ward Goodenough's recent article (27: 3), suggesting that his points can be clarified by reiterating the distinction between the realms of meaning and relevance. Religion's "truth" is in the form of its ualue; the "proof" which it requires is uindication; and the resulting "faith" must be understood as commitment.     

Exploring the set-theoretical structure of objects by additive trees

Arrangements of feature sets that have been proposed to represent qualitative and quantitative variation among objects are shown to generate identical sets of set-symmetric distances. The set-symmetric distances for these feature arrangements can be represented by path lengths in an additive linear tree. Imperfect versions of these feature arrangements are proposed, which also are indistinguishable by the set-symmetric distance model. The distances for the imperfect versions can be represented by path lengths in an additive imperfectly linear tree. When dissimilarities are defined by the more general contrast model and a constant may be added to proximity data, then for both the perfect and imperfect arrangements an additive tree analysis obtains a perfect fit with an imperfectly linear tree. However, in the case of the contrast model also the distinction between the perfect and imperfect arrangements disappears in that also for the perfect arrangements the resulting tree need no longer be linear.The author is grateful to Mathieu Koppen for detailed comments on an earlier version of this article.     

Contrast and reallocation of extraneous reinforcers as a function of component duration and baseline rate of reinforcement

Four pigeons responded on multiple schedules arranged on a “main” key in a two-key experimental chamber. A constant schedule component was alternated with another component that was varied over conditions. On an extra response key, conjoint schedules of reinforcement that operated in both components were arranged concurrently with the multiple schedule on the main key. On the main key, changes in reinforcement rate in the varied component were inversely related to changes in response rates in the constant component (behavioral contrast). On the extra key, some reinforcers were reallocated between components, depending on the schedules in effect on the main key in the varied component. In the varied component, the obtained rates of reinforcement on the extra key were inversely related to main-key reinforcement rate. In the constant component, extra-key reinforcer rates were positively related to main-key reinforcer rates obtained in the varied component, and were not a function of response rates on the extra key. In two comparisons, the rate at which components alternated and the value of the main-key schedule in the constant component were varied. Consistent with earlier work, long components reduced the extent of contrast. Reductions in contrast as a function of component duration were accompanied by similar reductions in the extent of reinforcer reallocation on the extra key. In the second comparison, lowering the rate of reinforcement in the constant component increased the rate at which extra-key reinforcers were obtained, reduced the extent of reinforcer reallocation, and reduced contrast. Overall, the results are consistent with the suggestion that some contrast effects are due to the changes in extraneous reinforcement during the constant component, and that manipulations of component duration, and manipulations of the rate of reinforcement in the constant component, affect contrast because they influence the extent of extraneous reinforcer real-location.     

教师评分用语词义赋值特征的分析

本研究运用模糊统计试验方法对教师的六组定性的评分用语词 (符号 )进行了经验赋值。参加赋值的是 2 66名小学教师。结果表明 ,六组评分用语词 (符号 )都是模糊概念 ,其中每种评分方式中处于最高等级的词 (符号 )的模糊度最小 ,处于中间等级的词 (符号 )的模糊度居中 ,处于最低等级的词 (符号 )的模糊度最大。词 (符号 )义的模糊度与评价的把握度呈现负相关 ,即词 (符号 )义越具体 ,模糊度越小 ,赋值的把握度就越大 ;反之 ,词义越含混 ,模糊度越大 ,赋值的把握度就越小。教师对各种评分用语词 (符号 )的赋值受百分制的“及格—不及格”的划分的影响 ,受评分方式中等级数目的影响 ,即增加评分等级会减少评分用语词 (符号 )的模糊度 ,增加赋值的把握度 ,还受评分用语词 (符号 )本身数量特征的影响。在各种评分方式中 ,评语词 (符号 )在心理量表上的距离是不等的。本研究的结果对教育评价的实践具有一定的参考价值。