The Suszko Operator. Part I.

The paper is conceived as a first study on the Suszko operator. The purpose of this paper is to indicate the existence of close relations holding between the properties of the Suszko operator and the structural properties of the model class for various sentential logics. The emphasis is put on generality both of the results and methods of tackling the problems that arise in the theory of this operator. The attempt is made here to develop the theory for non-protoalgebraic logics.     

Exploratory second-order analyses for components and factors

Abstract: Exploratory methods using second‐order components and second‐order common factors were proposed. The second‐order components were obtained from the resolution of the correlation matrix of obliquely rotated first‐order principal components. The standard errors of the estimates of the second‐order component loadings were derived from an augmented information matrix with restrictions for the loadings and associated parameters. The second‐order factor analysis proposed was similar to the classical method in that the factor correlations among the first‐order factors were further resolved by the exploratory method of factor analysis. However, in this paper the second‐order factor loadings were estimated by the generalized least squares using the asymptotic variance‐covariance matrix for the first‐order factor correlations. The asymptotic standard errors for the estimates of the second‐order factor loadings were also derived. A numerical example was presented with simulated results.     

Identifying a Reordering of Rows and Columns for Multiple Proximity Matrices Using Multiobjective Programming

This paper is concerned with a problem where K (n×n) proximity matrices are available for a set of n objects. The goal is to identify a single permutation of the n objects that provides an adequate structural fit, as measured by an appropriate index, for each of the K matrices. A multiobjective programming approach for this problem, which seeks to optimize a weighted function of the K indices, is proposed, and illustrative examples are provided using a set of proximity matrices from the psychological literature. These examples show that, by solving the multiobjective programming model under different weighting schemes, the quantitative analyst can uncover information about the relationships among the matrices and often identify one or more permutations that provide good to excellent index values for all matrices.     

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.     

采用理想点方法检验生活取向测验及其修订版的单维性

该文从项目反应过程出发,认为可能是由于原有的维度分析方法将生活取向测验（LOT）及其修订版（LOT-R）这两个测验的项目反应理想点过程错误地限定为优势过程,导致两个测验违背单维性的结论;进而采用主成分分析的未旋转成分负荷散点图和对应分析的维度分数散点图,并结合项目相关矩阵法验证LOT和LOT-R的维度。结果显示LOT-R的单维性得到了验证,LOT由于包含两个测量应对的项目而导致违背单维性。最后作者提出应该与理想点过程相一致的心理计量学模型对LOT-R的数据进行分析。     

Tatsuoka 矩阵理论的修正

K .K.Tatsuoka和她同事开发的规则空间模型（RSM）是一种在国内外有较大影响的认知诊断模型,但是Tatsuoka的RSM中 矩阵理论存在缺陷和错误,这些失误使得RSM中用布尔描述函数（BDF）计算被试理想项目反应模式（IRP）的方法缺乏理论依据。这里揭示了Tatsuoka的 矩阵理论的缺陷和错误并引进既不使用BDF又便于应用的计算IRP的方法;接着还介绍一种由可达阵计算简化 阵的方法,该方法显示了可达阵在构造认知诊断测验的重要性。这些结果对丰富 矩阵理论及正确使用RSM进行认知诊断有一定的意义     

THE RHYTHM OF GOD'S ETERNAL MUSIC: ON ANTJE JACKELÉN'S TIME AND ETERNITY

Antje Jackelén's book Time and Eternity is a thorough and carefully presented theology of time and, by its very essence, an incomplete and open thought model because time will always be dynamic and relational. This approach is an excellent example for the dialogue between science and religion because it uses resources not tapped in the dialogue so far: hymn‐books stemming from Germany, Sweden, and the English‐speaking world published between 1975 and 1995. They are taken as resources for a critical investigation on the meaning and importance of the notion of eternity for the interdisciplinary dialogue, which is characterized not as a synthesis but as holding a beneficial tension, or “eutonia.” I suggest that this approach can be taken even further by merging it with a model of time developed by the German mathematician A. M. Klaus Müller: The crossing over of time modes in a relational matrix of time also gives clear insights into the time of God not only as futurum—time as extrapolation of the past and present—but also as adventus—time which is to come.     

An inequality between the weighted average and the rowwise correlation coefficient for proximity matrices

De Vries (1993) discusses Pearson's product-moment correlation, Spearman's rank correlation, and Kendall's rank-correlation coefficient for assessing the association between the rows of two proximity matrices. For each of these he introduces a weighted average variant and a rowwise variant. In this note it is shown that for all three types, the absolute value of the first variant is greater than or equal to the absolute value of the second.The author is obliged to Frits E. Zegers for useful comments on an earlier version of this paper.     

模拟互变问题解决认知策略的实验研究

本实验通过对模拟互变问题解决认知策略的定性和定量分析,研究认知策略的类型及其信息加工程序。结果表明,存在尝试性策略、分析性策略和直觉性策略三类策略。最佳策略属于分析性策略。