The analysis of multitrait-multimethod matrices via constrained components analysis

Multitrait-Multimethod (MTMM) matrices are often analyzed by means of confirmatory factor analysis (CFA). However, fitting MTMM models often leads to improper solutions, or non-convergence. In an attempt to overcome these problems, various alternative CFA models have been proposed, but with none of these the problem of finding improper solutions was solved completely. In the present paper, an approach is proposed where improper solutions are ruled out altogether and convergence is guaranteed. The approach is based on constrained variants of components analysis (CA). Besides the fact that these methods do not give improper solutions, they have the advantage that they provide component scores which can later on be used to relate the components to external variables. The new methods are illustrated by means of simulated data, as well as empirical data sets.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the first author. The authors are obliged to three anonymous reviewers and an associate editor for constructive suggestions on the first version of this paper.     

Component analysis with different sets of constraints on different dimensions

Many of the classical multivariate data analysis and multidimensional scaling techniques call for approximations by lower dimensional configurations. A model is proposed, in which different sets of linear constraints are imposed on different dimensions in component analysis and classical multidimensional scaling frameworks. A simple, efficient, and monotonically convergent algorithm is presented for fitting the model to the data by least squares. The basic algorithm is extended to cover across-dimension constraints imposed in addition to the dimensionwise constraints, and to the case of a symmetric data matrix. Examples are given to demonstrate the use of the method.The work reported in this paper has been supported by the Natural Sciences and Engineering Research Council of Canada, grant number A6394, and by the McGill-IBM Cooperative Grant, both granted to the first author. The research of H. A. L. Kiers has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. We thank Michael Hunter for his helpful comments on earlier drafts of this paper.     

On the relations among regular, equal unique variances, and image factor analysis models

We investigate under what conditions the matrix of factor loadings from the factor analysis model with equal unique variances will give a good approximation to the matrix of factor loadings from the regular factor analysis model. We show that the two models will give similar matrices of factor loadings if Schneeweiss' condition, that the difference between the largest and the smallest value of unique variances is small relative to the sizes of the column sums of squared factor loadings, holds. Furthermore, we generalize our results and discus the conditions under which the matrix of factor loadings from the regular factor analysis model will be well approximated by the matrix of factor loadings from Jöreskog's image factor analysis model. Especially, we discuss Guttman's condition (i.e., the number of variables increases without limit) for the two models to agree, in relation with the condition we have shown, and conclude that Schneeweiss' condition is a generalization of Guttman's condition. Some implications for practice are discussed.Kentaro Hayashi is a visiting Assistant Professor, Department of Mathematics, Bucknell University, Lewisburg PA 17837, and Peter M. Bentler is Professor, Departments of Psychology and Statistics, University of California, Los Angeles CA 90095-1563. (Emails: Khayashi@bucknell.edu, bentler@ucla.edu) Parts of this paper were discussed in a session on Factor Analysis (J. ten Berge, Chair) at the IFCS-98 International Conference, Rome, July, 1998. This work was supported by National Institute on Drug Abuse grant DA 01070. The authors thank Professors Hans Schneeweiss and Ke-Hai Yuan, and four anonymous referees, for their invaluable comments which led to an improved version of this paper.     

Quasivarieties with Definable Relative Principal Subcongruences

For quasivarieties of algebras, we consider the property of having definable relative principal subcongruences, a generalization of the concepts of definable relative principal congruences and definable principal subcongruences. We prove that a quasivariety of algebras with definable relative principal subcongruences has a finite quasiequational basis if and only if the class of its relative (finitely) subdirectly irreducible algebras is strictly elementary. Since a finitely generated relatively congruence-distributive quasivariety has definable relative principal subcongruences, we get a new proof of the result due to D. Pigozzi: a finitely generated relatively congruence-distributive quasivariety has a finite quasi-equational basis. Presented by W. Dziobiak     

临床肺减容术发展历程中的矛盾思辨

晚期肺气肿是进行性恶化的常见呼吸系统疾病。由于内科药物治疗不能彻底遏制疾病的自然进程,外科肺减容术应时而生。但手术治疗有着与生俱来的缺点,因此内科介入肺减容术基于相似的机理出现了,并可与外科手术序贯应用。这种矛盾双方的对立与统一促进了该领域的发展,也是一种解决临床问题的重要辩证思维。     

基督教普世主义及其矛盾

本文主要从教会论而非救赎论的层面来讨论基督教普世主义,目的是探讨普世主义教会观产生的源头、发展线索以及在实践中的矛盾表现。本文认为从教会教义的形成与发展以及圣经教训内容本身两方面来看,普世主义教会观直接秉承罗马普世主义思想文化资源;论述了古代和中世纪教会普世主义的矛盾发展及其引发教会分裂的历史过程,认为难以解决的矛盾主要表现在制定教会教义与确立教会权威这两个问题上;探讨了普世主义在20世纪取得突飞猛进的原因,并简略讨论了普世主义在中国新教教会中的情况。     

Ist die linguistische Theorie des logischen Apriori obsolet?

The linguistic theory of the logical A Priori: is it obsolete In holistic interpretations, the logical truths are considered as continuous with empirical science: they are revisable, a posteriori, though very near to the centre of our web of belief. In this paper, we consider the merits and demerits of this approach, and we propose that it is necessary to revaluate holistic philosophies of logic. Some arguments are put forward which point in favour of the logical empiricists’ theory of logical truth. We argue (following Hartry Field) that the concept of “correlation between logical facts and logical beliefs” (which is at the heart of the holistic theory) is inconsistent. Finally, we concentrate on the principle of contradiction and argue (following Manley Thompson) that this principle is fundamental for meaning, truth, and thinking. This thesis is derived from considerations on the nature of intentionality. This revised version was published online in August 2006 with corrections to the Cover Date.     

医学生临床实习与考研矛盾的思考及对策

近几年来由于各种原因造成的医学生临床实习与考研的矛盾在全国各地已经非常普遍,也引起了医学院校和教学医院相关人士的诸多讨论,但目前仍没有一个两全其美的解决方案。就这个问题进行了总结和思考,并提出了一个有可能解决这一矛盾的方案。     

Simultaneous optimization of factor assessibility and representativeness

P. M. Bentler has shown that Rao's canonical factor analysis is in effect a psychometric analysis, leading to factors that are maximally assessible from the data. He contrasts this with Kaiser and Caffrey's alpha factor analysis that leads to factors that maximally represent the true factors in the content domain. Noting the problems associated with factors that may be highly assessible, but not very representative, or vice versa, Bentler suggests the need for a technique that would, insofar as possible, be optimal with respect to both criteria. Such a technique is presented here, and is shown to resolve into a traditional scaling method, which in turn acquires a richer psychometric interpretation.The author would like to gratefully acknowledge support for this research from the Workshop in Political Theory and Policy Analysis (Indiana University) and Esco Research Associates. The paper benefitted substantially from the criticisms and suggestions of an anonymous referee.