On equivariance and invariance of standard errors in three exploratory factor models

Current practice in factor analysis typically involves analysis of correlation rather than covariance matrices. We study whether the standardz-statistic that evaluates whether a factor loading is statistically necessary is correctly applied in such situations and more generally when the variables being analyzed are arbitrarily rescaled. Effects of rescaling on estimated standard errors of factor loading estimates, and the consequent effect onz-statistics, are studied in three variants of the classical exploratory factor model under canonical, raw varimax, and normal varimax solutions. For models with analytical solutions we find that some of the standard errors as well as their estimates are scale equivariant, while others are invariant. For a model in which an analytical solution does not exist, we use an example to illustrate that neither the factor loading estimates nor the standard error estimates possess scale equivariance or invariance, implying that different conclusions could be obtained with different scalings. Together with the prior findings on parameter estimates, these results provide new guidance for a key statistical aspect of factor analysis.We gratefully acknowledge the help of the Associate Editor and three referees whose constructive comments lead to an improved version of the paper. This work was supported by National Institute on Drug Abuse Grants DA01070 and DA00017 and by the University of North Texas Faculty Research Grant Program.     

Duality and Canonical Extensions of Bounded Distributive Lattices with Operators,and Applications to the Semantics of Non-Classical Logics I

The main goal of this paper is to explain the link between the algebraic and the Kripke-style models for certain classes of propositional logics. We start by presenting a Priestley-type duality for distributive lattices endowed with a general class of well-behaved operators. We then show that finitely-generated varieties of distributive lattices with operators are closed under canonical embedding algebras. The results are used in the second part of the paper to construct topological and non-topological Kripke-style models for logics that are sound and complete with respect to varieties of distributive lattices with operators in the above-mentioned classes. This revised version was published online in June 2006 with corrections to the Cover Date.     

Note on the squared multiple correlation as a lower bound to communality

It is demonstrated that the squared multiple correlation of a variable with the remaining variables in a set of variables is a function of the communalities and the squared canonical correlations between the observed variables and common factors. This equation is shown to imply a strict inequality between the squared multiple correlation and communality.     

中小学教师工作满意度与教学动机的关系

以1197名中小学教师为被试,通过问卷调查考察工作满意度与教学动机的关系。典型相关分析发现两组变量之间存在三对典型相关关系:环境满意度、升迁进修满意度、收入满意度和管理满意度作为抑制变量强化了活动满意度与内部动机的正相关;活动满意度和收入满意度对环境满意度与外部动机的正相关关系有调节作用,管理满意度作为抑制变量影响着升迁进修满意度、环境满意度与外部内化动机之间的负相关关系。鉴于工作满意度对教学动机的影响更为明显,采用分层回归分析进一步明确了可能存在显著回归效应。     

The Development of Symbolic Uses of Objects in Infants in a Triadic Context: A Pragmatic and Semiotic Perspective

In this study, we address the construction of the first symbolic uses of objects in contexts of triadic interaction (adult–child–object). We assume that symbolic productions are based on public rules of the use of objects previously agreed by the community. The first symbols are not rooted in any literal, evident reality, but in shared rules of uses about the material world. We observed six dyads communicating and interacting together with 10 objects in a semi‐structured situation longitudinally from 9 to 15 months of age. We found that the infants gradually constructed symbolic meanings, and we identified five symbolic levels and sublevels. At 9 months, the infants attended and engaged in the symbolic uses produced by an adult even though they themselves were not yet able to produce them. At 12 months, infants began to use objects symbolically to communicate with adults. The highest percentage of these first symbolic uses was of level 1, that is, with a close relation to the conventional use of the object used to perform the symbol. At 15 months, children increased their symbolic uses and performed symbolic uses at all levels, whereas adults reduced such practices. Adult semiotic mediation and the social meanings of objects can be considered important factors in children's symbolic productions. Copyright © 2014 John Wiley & Sons, Ltd.