Maximization of sums of quotients of quadratic forms and some generalizations

Monotonically convergent algorithms are described for maximizing six (constrained) functions of vectors x, or matricesX with columns x₁, ..., x _r . These functions are h₁(x)= _k (xA _kx)(xC _kx)^–1, H₁(X)= _k tr (XA _k X)(XC _k X)^–1, h₁(X)= _{k l} (x _l A _kx _l ) (x _l C _kx _l )^–1 withX constrained to be columnwise orthonormal, h₂(x)= _k (xA _kx)²(xC _kx)^–1 subject to xx=1, H₂(X)= _k tr(XA _kX)(XA_kX)(XC_kX)^–1 subject toXX=I, and h₂(X)= _{k l} (x _l A _kx _l )² (x _l C _kX _l )^–1 subject toXX=I. In these functions the matricesC _k are assumed to be positive definite. The matricesA _k can be arbitrary square matrices. The general formulation of the functions and the algorithms allows for application of the algorithms in various problems that arise in multivariate analysis. Several applications of the general algorithms are given. Specifically, algorithms are given for reciprocal principal components analysis, binormamin rotation, generalized discriminant analysis, variants of generalized principal components analysis, simple structure rotation for one of the latter variants, and set component analysis. For most of these methods the algorithms appear to be new, for the others the existing algorithms turn out to be special cases of the newly derived general algorithms.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the author. The author is obliged to Jos ten Berge for stimulating this research and for helpful comments on an earlier version of this paper.     

Perceptual unit formation in simple motion patterns

The present study investigated the proximal constraints that determine perceptual unit formation under minimal stimulus conditions. Projections of three moving dots, which could form two possible two-dot configurations, were presented to naive observers. In a forced-choice situation, their task was to report which two-dot configuration was perceived as a distinct perceptual unit. The results showed that common motions (arbitrary translations and rigid rotations in the frontoparallel plane) have stronger grouping power as compared to different relative motions (expansions/contractions, or simultaneous expansions/contractions and deformations in the frontoparallel plane). It was found that proximal changes of distances between elements in two-dot structures reduce grouping power. Changes of proximal directions, however, did not affect unit formation in two-dot structures at all. The effect of vector algebraic combinations on grouping power in three-dot strutures was also investigated. Evidently, visual vector analysis splits up motion combinations into their constituents, and in come cases this contributes to additive effects.     

教师解决结构不良问题策略的发展研究

以成人期个体解决结构不良问题的有关认知加工理论为框架,运用多因素设计的方法,对９０名不同年龄的教师在解决教育和教学实践中常见的三种冲突情景下使用策略的情况进行了探讨。结果发现,教师在解决结构不良问题时,从总体上说不存在年龄差异,但在处理教师与教师、教师与家长等较为复杂的冲突问题时,随着年龄的增长,更趋向于使用元认知和认识论认知策略。该研究对教师培训中如何根据不同年龄特点来进行教育机智训练有一定的理论意义和应用价值。     

Three-mode orthomax rotation

Factor analysis and principal components analysis (PCA) are often followed by an orthomax rotation to rotate a loading matrix to simple structure. The simple structure is usually defined in terms of the simplicity of the columns of the loading matrix. In Three-mode PCA, rotational freedom of the so called core (a three-way array relating components for the three different modes) can be used similarly to find a simple structure of the core. Simple structure of the core can be defined with respect to all three modes simultaneously, possibly with different emphases on the different modes. The present paper provides a fully flexible approach for orthomax rotation of the core to simple structure with respect to three modes simultaneously. Computationally, this approach relies on repeated (two-way) orthomax applied to supermatrices containing the frontal, lateral or horizontal slabs, respectively. The procedure is illustrated by means of a number of exemplary analyses. As a by-product, application of the Three-mode Orthomax procedures to two-way arrays is shown to reveal interesting relations with and interpretations of existing two-way simple structure rotation techniques.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the author. The author is obliged to Jos ten Berge and two anonymous reviewers for useful comments on an earlier version of this paper.     

Effect analysis and causation in linear structural equation models

This paper considers total and direct effects in linear structural equation models. Adopting a causal perspective that is implicit in much of the literature on the subject, the paper concludes that in many instances the effects do not admit the interpretations imparted in the literature. Drawing a distinction between concomitants and factors, the paper concludes that a concomitant has neither total nor direct effects on other variables. When a variable is a factor and one or more intervening variables are concomitants, the notion of a direct effect is not causally meaningful. Even when the notion of a direct effect is meaningful, the usual estimate of this quantity may be inappropriate. The total effect is usually interpreted as an equilibrium multiplier. In the case where there are simultaneity relations among the dependent variables in tghe model, the results in the literature for the total effects of dependent variables on other dependent variables are not equilibrium multipliers, and thus, the usual interpretation is incorrect. To remedy some of these deficiencies, a new effect, the total effect of a factorX on an outcomeY, holding a set of variablesF constant, is defined. When defined, the total and direct effects are a special case of this new effect, and the total effect of a dependent variable on a dependent variable is an equilibrium multiplier.For helpful comments, I am grateful to G. Arminger, K. Bollen, W. Faris, R. m. Hauser, T. Petersen, three anonymous Psychometrikas reviewers, and the Editor. For computational assistance, I am grateful to B. D. Kim.     

Power of the likelihood ratio test in covariance structure analysis

A procedure for computing the power of the likelihood ratio test used in the context of covariance structure analysis is derived. The procedure uses statistics associated with the standard output of the computer programs commonly used and assumes that a specific alternative value of the parameter vector is specified. Using the noncentral Chi-square distribution, the power of the test is approximated by the asymptotic one for a sequence of local alternatives. The procedure is illustrated by an example. A Monte Carlo experiment also shows how good the approximation is for a specific case.This research was made possible by a grant from the Dutch Organization for Advancement of Pure Research (ZWO). The authors also like to acknowledge the helpful comments and suggestions from the editor and anonymous reviewers.     

突发公共事件中公众的补偿性控制

补偿性控制理论指出,当面临控制感的缺乏时,个体会表现出一种需求秩序的倾向,即努力寻求客观世界的秩序,对于具有秩序性、确定性、可预测性的物理或抽象事物表现出偏好与需求,这种表现被称为补偿性控制。基于突发公共事件常会引发人们控制感暂时的下降,补偿性控制理论的视角可以用来解释个体在突发公共事件中的一系列典型心理反应。如阴谋论信念、谣言传播、道德争论和非理性囤积,都可以从补偿性控制与秩序需求的角度来加以理解。未来研究可以更多考虑从补偿性控制的角度探讨突发公共事件中的公众心理反应,并基于此视角加强理论深化、研究细化和实践干预。     

ANZSJA's Songlines and Haerenga model of training

Part One and Part Two of this article present the Australian and New Zealand Society of Jungian Analysts' 2006 model of training. The authors describe the process and thinking behind ANZSJA's recent revision of training. The influences on the development of analytical psychology and analytic training in ANZSJA are traced in the first paper. The training review undertaken indicated the desire for ANZSJA to continue to train Jungian analysts by exploring new ways of conceptualizing training. The images, metaphors and thinking, which underlie this innovative training model, are explored. The challenge involved in providing and developing training across a large geographic region with widely distributed and slender resources was embraced. ANZSJA have acknowledged the traditional practices of Australian and New Zealand indigenous peoples. The motif of journey and movement is at the core of the ANZJSA model. The ANZJSA training is not held or contained in a building or buildings but rather held at 'meeting sites' across the landscape of these two countries. Accountability and transparency are central to this training model. In Part Two of the article the structure and documentation developed for this model are contextualized, outlined and linked to the ethos underpinning the current thrust of analytical training in Australia and New Zealand. The focus is the practical mechanisms and processes, which we have evolved to deliver our new training model. The process of engaging analysts in the new model is discussed.     

Pseudo maximum likelihood estimation and a test for misspecification in mean and covariance structure models

Using the theory of pseudo maximum likelihood estimation the asymptotic covariance matrix of maximum likelihood estimates for mean and covariance structure models is given for the case where the variables are not multivariate normal. This asymptotic covariance matrix is consistently estimated without the computation of the empirical fourth order moment matrix. Using quasi-maximum likelihood theory a Hausman misspecification test is developed. This test is sensitive to misspecification caused by errors that are correlated with the independent variables. This misspecification cannot be detected by the test statistics currently used in covariance structure analysis.For helpful comments on a previous draft of the paper we are indebted to Kenneth A. Bollen, Ulrich L. Küsters, Michael E. Sobel and the anonymous reviewers of Psychometrika. For partial research support, the first author wishes to thank the Department of Sociology at the University of Arizona, where he was a visiting professor during the fall semester 1987.     

价值观的神经机制:另一种研究视角

神经机制分析是价值观研究的一种新视角.内稳态机制和情绪反应的固有模式可能体现出价值观的神经生物原型.社会认知神经科学试图从子价值观、价值取向、价值观结构等方面寻找价值观的神经实体证据,也对价值评价、价值决策等相关过程进行了神经活动分析.初步发现了个体价值观与部分脑区活动的相关关系,涉及前额叶-顶叶-颞叶神经网络带的众多大脑结构.未来研究可沿循静态的价值观结构和动态的价值观加工过程两条线路,整合和完善现有分散的神经生理研究,将有助于更系统地理解价值观的神经机制.