Statistical inference of minimum rank factor analysis

For any given number of factors, Minimum Rank Factor Analysis yields optimal communalities for an observed covariance matrix in the sense that the unexplained common variance with that number of factors is minimized, subject to the constraint that both the diagonal matrix of unique variances and the observed covariance matrix minus that diagonal matrix are positive semidefinite. As a result, it becomes possible to distinguish the explained common variance from the total common variance. The percentage of explained common variance is similar in meaning to the percentage of explained observed variance in Principal Component Analysis, but typically the former is much closer to 100 than the latter. So far, no statistical theory of MRFA has been developed. The present paper is a first start. It yields closed-form expressions for the asymptotic bias of the explained common variance, or, more precisely, of the unexplained common variance, under the assumption of multivariate normality. Also, the asymptotic variance of this bias is derived, and also the asymptotic covariance matrix of the unique variances that define a MRFA solution. The presented asymptotic statistical inference is based on a recently developed perturbation theory of semidefinite programming. A numerical example is also offered to demonstrate the accuracy of the expressions.This work was supported, in part, by grant DMS-0073770 from the National Science Foundation.     

Reliability Beyond Theory and Into Practice

The critical reactions of Bentler (2009, doi:), Green and Yang (2009a, doi:; 2009b, doi:), and Revelle and Zinbarg (2009, doi:) to Sijtsma’s (2009, doi:) paper on Cronbach’s alpha are addressed. The dissemination of psychometric knowledge among substantive researchers is discussed.     

Doing Justice and Demonstrating Fairness in Small Claims Arbitration

This paper examines the intersection of technical law and common sense reasoning in small claims arbitration, a distinctive and increasingly prevalent kind of legal work. Following (Garfinkel, Ethnomethodology’s program: Working out Durkheim’s aphorism, 2002), the study explores the “reform of technical reason” and what a “just outcome” means by focusing on the arbitration of actual small claims cases and how technical-legal and non-technical/informal resources are brought into alignment to produce dispute resolution. The arbitrator elicits discussions that establish consensual and commonplace formulations of “the case,” formulations that foreshadow its disposition as technical matters of law. The research demonstrates how formal structures of equity, evenhandedness, and decisions without bias have their production in vivo, and how a just and fair course becomes a “just outcome.”

公共资源困境中领导对群体成员合作行为的影响

过去社会困境的领导研究大多都以被试作为领导, 发现贴上领导标签后, 被试倾向于拿取更多的公共资源, 从而有碍公共利益的实现。本研究指出, 如果领导的背叛行为能够使群体成员表现出自我节制行为的话, 那么设置领导则有可能促进公共利益的实现。研究通过三个实验, 考察领导与普通群体成员不同的行为方式以及领导的产生方式对群体成员行为的影响, 并检验公平理论和社会认同理论的解释力。研究结果表明, 领导表现出背叛行为时, 被试表现出更多的自我节制行为; 指派领导及外群体选举领导背叛时, 被试表现出更多的自我节制行为, 验证了社会认同理论的正确性。     

共同方法偏差的统计检验与控制方法

共同方法偏差是心理学研究中一个越来越被关注的课题,但国内心理学界对其的介绍、研究还比较少,导致研究中对共同方法偏差的控制还有所欠缺。共同方法偏差的控制方法分为程序控制和统计控制,该文介绍了共同方法偏差的多种统计控制法,如因素分析法、偏相关法、潜在的误差变量控制法、结构方程模型法等,分析了其各自的优缺点,并提出了如何选择采用这些方法的建议.     

Iterative and fixed point common belief

We define infinitary extensions to classical epistemic logic systems, and add also a common belief modality, axiomatized in a finitary, fixed-point manner. In the infinitary K system, common belief turns to be provably equivalent to the conjunction of all the finite levels of mutual belief. In contrast, in the infinitary monotonic system, common belief implies every transfinite level of mutual belief but is never implied by it. We conclude that the fixed- point notion of common belief is more powerful than the iterative notion of common belief.     

Are General Practitioners Willing and Able to Provide Genetic Services for Common Diseases?

Primary care in the United Kingdom has been advocated as an optimal location for the provision of genetic services for common diseases. Little, however, is known about general practitioners' own views toward this suggestion or the possible demand for such services from patients. To assess general practitioners' attitudes to providing genetic services for common diseases, and to estimate the demand from patients for these services, we used a single-page postal questionnaire survey of all 359 general practitioners registered with the Oxfordshire Health Authority; 339 (94%) responded. These physicians reported that a mean 4.1 patients (95% CI, 3.3–4.9) out of every 1,000 consulting them were concerned about their own risk of a common disease associated with a diagnosis in a family member. Half of the general practitioners (95% CI, 45–56%) counseled about genetics in the last year. A majority of general practitioners accept the need to provide genetic services, but far fewer are competent to do so. Although 60% (95% CI, 55–65%) believed they should be involved with genetic screening for common diseases, only 29% (95% CI, 24–34%) felt sufficiently prepared to take family histories and draw pedigrees, and only 15% (95% CI, 11–19%) felt sufficiently prepared to counsel patients about their genetic test results. Given the necessary training and information, 63% (95% CI, 58–68%) and 64% (95% CI, 59–69%) were willing to provide these services. Even with training and information, not all would be willing to provide these services, and lack of time may be a major deterrent. Practice-enabling strategies, such as computerized aids in genetics, may be useful.     

Determining the number of components from the matrix of partial correlations

A common problem for both principal component analysis and image component analysis is determining how many components to retain. A number of solutions have been proposed, none of which is totally satisfactory. An alternative solution which employs a matrix of partial correlations is considered. No components are extracted after the average squared partial correlation reaches a minimum. This approach gives an exact stopping point, has a direct operational interpretation, and can be applied to any type of component analysis. The method is most appropriate when component analysis is employed as an alternative to, or a first-stage solution for, factor analysis.     

On Bayesian estimation in unrestricted factor analysis

It is shown that the common and unique variance estimates produced by Martin & McDonald's Bayesian estimation procedure for the unrestricted common factor model have a predictable sum which is always greater than the maximum likelihood estimate of the total variance. This fact is used to justify a suggested simple alternative method of specifying the Bayesian parameters required by the procedure.     

Audiences,relevance, and cognitive environments

This paper discusses the fundamental sense in which the components of an argument should be relevant to the intended audience. In particular, the evidence advanced should be relevant to the facts and assumptions that are manifest in the cognitive environment of the audience. A version of Sperber and Wilson's concept of the cognitive environment is applied to argumentative concerns, and from this certain features of audience-relevance are explored: that the relevance of a premise can vary with the audience; that irrelevant premises can be made relevant; that evidence can be relevant by degrees; and that this notion of relevance will assist the argumentation analyst in the identification and assessment of hidden premises.