Some properties of estimated scale invariant covariance structures

Scale invariance is a property shared by many covariance structure models employed in practice. An example is provided by the well-known LISREL model subject only to classical normalizations and zero constraints on the parameters. It is shown that scale invariance implies that the estimated covariannce matrix must satisfy certain equations, and the nature of these equations depends on the fitting function used. In this context, the paper considers two classes of fitting functions: weighted least squares and the class of functions proposed by Swain.Constructive comments by the referees are greatly appreciated. The author gratefully acknowledges Michael Browne's interest in his work.     

Some contributions to efficient statistics in structural models: Specification and estimation of moment structures

Current practice in structural modeling of observed continuous random variables is limited to representation systems for first and second moments (e.g., means and covariances), and to distribution theory based on multivariate normality. In psychometrics the multinormality assumption is often incorrect, so that statistical tests on parameters, or model goodness of fit, will frequently be incorrect as well. It is shown that higher order product moments yield important structural information when the distribution of variables is arbitrary. Structural representations are developed for generalizations of the Bentler-Weeks, Jöreskog-Keesling-Wiley, and factor analytic models. Some asymptotically distribution-free efficient estimators for such arbitrary structural models are developed. Limited information estimators are obtained as well. The special case of elliptical distributions that allow nonzero but equal kurtoses for variables is discussed in some detail. The argument is made that multivariate normal theory for covariance structure models should be abandoned in favor of elliptical theory, which is only slightly more difficult to apply in practice but specializes to the traditional case when normality holds. Many open research areas are described.     

A note on the consistency of estimators in the analysis of moment structures

This paper is concerned with the consistency of estimators in the analysis of moment structures. An example is given where in spite of identifiability of the parameters the associated estimator is inconsistent. Consistency is shown to hold under the additional condition of compactness of the parameter space.     

Action of structures,structure of actions

This paper was throught of as a form of silent dialogue with my friend Michael Wright. As such, it has the merits, if any, and the defects of a flowing course of thoughts that entersin medias res with less feignings than in standard philosophical literature.     

A re-examination of the algebraic properties of the AHP as a ratio-scaling technique

The Analytic Hierarchy Process (AHP) ratio-scaling approach is re-examined in view of the recent developments in mathematical psychology based on the so-called separable representations. The study highlights the distortions in the estimates based on the maximum eigenvalue method used in the AHP distinguishing the contributions due to random noises from the effects due to the nonlinearity of the subjective weighting function of separable representations. The analysis is based on the second order expansion of the Perron eigenvector and Perron eigenvalue in reciprocally symmetric matrices with perturbations. The asymptotic distributions of the Perron eigenvector and Perron eigenvalue are derived and related to the eigenvalue-based index of cardinal consistency used in the AHP. The results show the limits of using the latter index as a rule to assess the quality of the estimates of a ratio scale. The AHP method to estimate the ratio scales is compared with the classical ratio magnitude approach used in psychophysics.     

An algebraic solution for the communalities

Factorial analysis begins with ann ×n correlation matrixR, whose principal diagonal entries are unknown. If the common test space of the battery is under investigation, the communality of each test is entered in the appropriate diagonal cell. This value is the portion of the test's variance shared with others in the battery. The communalities must be so estimated thatR will maintain the rank determined by its side entries, after the former have been inserted. Previous methods of estimating the communalities have involved a certain arbitrariness, since they depended on selecting test subgroups or parts of the data inR. A theory is presented showing that this difficulty can be avoided in principle. In its present form, the theory is not offered as a practical computing procedure. The basis of the new method lies in the Cayley-Hamilton theorem: Any square matrix satisfies its own characteristic equation.     

Diagnostic Model for Assessing the Effect of Developmental Issues on Career Action

The authors describe a Diagnostic Model for Assessing the Effect of Developmental Issues on Career Action that is designed to help career counselors diagnose problems that are interfering with clients' career development and to determine appropriate interventions.     

Some properties of binormamin

Three properties of the binormamin criterion for analytic transformation in factor analysis are discussed. Particular reference is made to Carroll's oblimin class of criteria.The research reported in this note was supported in part by the Program in Applied Mathematics and Statistics. National Science Foundation, and by the National Institute of Education, Department of Health, Education, and Welfare.     

Schrödinger's Cat and Divine Action: Some Comments on the Use of Quantum Uncertainty to Allow for God's Action in the World

I present results of recent work in the field of quantum optics and relate this work to discussions about the theory of quantum mechanics and God's divine action in the world. Experiments involving atomic decay, relevant to event uncertainty in quantum mechanics, as well as experiments aimed at elucidating the so–called Schrödinger's–cat paradox, help clarify apparent ambiguities or paradoxes that I believe are at the heart of renewed attempts to locate God within our constructed physical theories and tend to narrow the gaps proposed as an opening for divine action. Some problems arise because of imprecise use of nonmathematical language to force quantum mechanics into an intuitive "classical" framework.     

Some properties of auditory memory for rapid formant transitions

In the three experiments reported here, subjects indicate whether two sequentially presented syllables, differing in the place of articulation of an initial stop consonant, are phonernically the same or not. The first experiment finds faster |ldsame” responses to acoustically identical pairs than to pairs that are phonemically identical but acoustically distinct. provided that the second syllable is presented within 400 msec of the first. This is interpreted as indicating the persistence of a memory which preserves auditory information about within-category distinctions. The third experiment shows that this advantage remains when a tone is interposed between the two syllables, but is removed when a brief vowel is similarly interposed. The second experiment presents the second syllable of each pair dichotically with a noise burst, and shows that the size of the right-ear advantage for this reaction time task is reduced when the result of comparisons based on this auditory memory is compatible with the required phonemic decision, but that the right-ear advantage is increased when auditory comparisons would contradict the phonemic relationship.     

Some properties of the olfactory system of man

Preliminary investigations into the effects of a 12-h diurnal variation suggested there was a 10-fold decrease in odor sensitivity from morning to evening. For a selected group of odorants (methyl, t-butyl, and phenyl isonitrile), the difference between detection and recognition thresholds in general was found to be 10-fold; however, for some Ss the difference was less. When Ss were blindfolded, no changes in odor sensitivity were noted. Similarly, imposing an auditory stress on the test situation did not significantly alter odor sensitivity in either experienced or naive Ss,     

理性行动-社会认同整合性集体行动模型

为探究理性行动理论和社会认同理论两大社会心理学宏论对于个体集体行动参与倾向的共同解释力,以“中日撞船事件”为考察蓝本向天津市431名大学生被试进行调查研究,结果发现：效能和社会规范作为态度和行动倾向的中介变量,在不同情境下对行动倾向的作用不同,符合理性行动原则;内部动机作为态度和效能、社会规范之间的中介变量,并受到学校认同和国家认同的直接或间接影响,支持了社会认同理论对遵从规范行为的解释;回归分析验证了不同水平认同对行动倾向作用程度的差异,整合模型则揭示了其具体的作用路径和影响机制.结论：理性行动理论与社会认同理论可彼此互补成为集体行动参与的整合性解释框架.     

Helping the Less Fortunate: A Predictive Model of Collective Action

A model of factors that lead members of an advantaged group to perform collective action intended to help a disadvantaged out-group is tested. A distinction is made between easy and demanding collective activities. Two different routes are expected to lead to collective action. First, an indirect link is proposed between a common in-group identity and collective action. This link is believed to be mediated by perceived mobilization resources. Second, the link between relative deprivation on behalf of others (RDBO) and collective action will vary according to the type of behavior considered. While, RDBO is expected to be directly associated with easy collective behavior, the link between RDBO and demanding collective activities is mediated through perceived mobilization resources. In turn, perceived resources are linked to both forms of collective behaviors. The predicted model is tested among 273 undergraduate respondents. Findings point to the relevance of all factors considered and the pivotal role of perceived mobilization resources on collective action.