Population Proportion of Explained Variance in Principal Component Analysis: A Note on Its Evaluation Via a Large-Sample Approach

A large-sample procedure for examining explained population variance in principal component analysis is discussed. The method yields interval estimates for the proportions of variance accounted for by the considered for retention principal components. The obtained confidence intervals can be used to make decisions about the number of selected components, based on their performance in studied populations. The approach can also be employed for ascertaining group similarity or differences in percentage explained variance by the considered principal components. The procedure is illustrated with 2 examples.     

The Effect of Ignoring Classroom‐Level Variance in Estimating the Generalizability of School Mean Scores

Contemporary educational accountability systems, including state‐level systems prescribed under No Child Left Behind as well as those envisioned under the “Race to the Top” comprehensive assessment competition, rely on school‐level summaries of student test scores. The precision of these score summaries is almost always evaluated using models that ignore the classroom‐level clustering of students within schools. This paper reports balanced and unbalanced generalizability analyses investigating the consequences of ignoring variation at the level of classrooms within schools when analyzing the reliability of such school‐level accountability measures. Results show that the reliability of school means cannot be determined accurately when classroom‐level effects are ignored. Failure to take between‐classroom variance into account biases generalizability (G) coefficient estimates downward and standard errors (SEs) upward if classroom‐level effects are regarded as fixed, and biases G‐coefficient estimates upward and SEs downward if they are regarded as random. These biases become more severe as the difference between the school‐level intraclass correlation (ICC) and the class‐level ICC increases. School‐accountability systems should be designed so that classroom (or teacher) level variation can be taken into consideration when quantifying the precision of school rankings, and statistical models for school mean score reliability should incorporate this information.     

PC准则下方差分量模型参数的广义岭估计的优良性

方差分量模型中,随机效应向量为正态情形时,本文证明了PC准则下其参数的广义岭估计优于其广LSE。     

基于广义随机空间内的结构体系可靠度分析

在结构系统的可靠度计算过程中,当随机变量为相关的非正态分布时,利用正交变换或Rosenblatt变换计算其可靠指标,计算量较大。采用在广义随机空间内计算各机构可靠指标,然后利用PNET法计算结构体系可靠度,计算简便,精度也满足要求。     

NPID环上广义逆矩阵的刻划

对非交换主要理想整环(NPID)上广义逆矩阵的(1)-逆和(1，3)-逆,[5]已给出多种刻划，章利用维数、直和等关系，首先给出(1)-逆的11种刻划。然后在假定NPID环带有对合反自同构σ的条件下，又得到6种刻划。最后给出(1，3)-逆的一个新刻划．从而丰富和完善了广义逆矩阵的刻划理论．     

格值矩阵的逆及广义逆

探讨了基于格半群上的矩阵的逆和广义逆等问题,给出了格值矩阵的逆、{1}-广义逆和M—P广义逆的概念和它们存在的条件,以及格值矩阵A的任意一个{1}-广义逆的具体形式、M—P广义逆的存在性和唯一性．     

Variance of a Few Observations

This article demonstrates that the variance of three or four observations can be expressed in terms of the range and the first order differences of the observations. A more general result, which holds for any number of observations, is also stated.     

广义度量空间中几种映射的关系

主要讨论了序列覆盖的伪开映射与几乎开映射之间的关系,也讨论了在第一可数空间中与序列覆盖映射等价的几个条件,以及由定理得出的几个推论．     

试论诗歌语言的变异性

诗歌语言是一种变异性的艺术语言。从语言的组合和结构形式上来看,诗歌语言是对常规语言的超脱和违背,同时也是一种创造和发展。它与常规语言相比较,在语音、语义、语法等方面都存在着较大的变异性。正因为它的变异,使之更具诗性,成为诗歌区别于其它文体的重要特征之一,是诗之所以为诗的主要标志。     

分块广义幂等矩阵的广义Schur补的一些性质

给出了分块广义幂等矩阵的广义Schur补的一些性质,从而改进和推广了已有结果。     

基于统计学观点的成本差异计算分析

财务管理中的成本差异分析是个难点,通过统计学中的同度量因素分析方法就很清晰的对直接材料成本、直接人工成本、变动制造费用成本和固定制造费用成本进行分析。     

企业员工人格激励动机偏向的非参数方差分析

为了研究影响企业员工人格激励的因素,通过对来自某一企业的样本数据进行正态性检验并且采用非参数方差分析方法,从而探讨人格、年龄对人格激励的影响。结果表明,在这些因素中,人格、年龄对内在激励有极显著影响。     

广义量词的计算复杂性

广义量词的复杂性有两个层次：句法层面的复杂性和语义层面的复杂性,我们集中研究了广义量词的语义复杂性。在有穷的语境中可以找出自然语言量化语句真值的复杂性。这些复杂性与图灵机中的可计算性、作为算法的意义的等价性、计算复杂性、易处理性和不易处理性等内容相关。广义量词计算复杂性已有诸多相关研究成果。     

参数的广义矩法估计

对参数的矩法估计是一个基本方法,它首先要求随机变量的矩存在;但是对某些分布,它不存在矩,因此,对该分布参数的估计矩法将失效。本文提出广义矩概念,并给出了广义矩存在的条件,利用广义矩对参数作出估计,弥补了不存在短或矩的阶不够大时导致参数估计矩法失效的不足。     

线性混合效应模型中方差分量两种估计的比较

本文首先给出了由王松桂等提出的广义谱分解估计(GSDE)的定义,以及由Herderson方法得到的方差分量的方差分析估计(ANOVAE),在此基础上提出了谱和线性混合效应模型的概念,证明了在这类模型中,方差分析估计是广义谱分解估计的一种,并且考察了在一定条件下广义谱分解估计优于方差分析估计的充分条件.     

谈谈"材料成本差异"科目

抛弃了"材料成本差异"概念的束缚,从实际应用的角度出发,给该科目予以诠释.简单,明了,易于掌握.     

Evaluation of Dimensionality in the Assessment of Internal Consistency Reliability: Coefficient Alpha and Omega Coefficients

In the lead article, Davenport, Davison, Liou, & Love demonstrate the relationship among homogeneity, internal consistency, and coefficient alpha, and also distinguish among them. These distinctions are important because too often coefficient alpha—a reliability coefficient—is interpreted as an index of homogeneity or internal consistency. We argue that factor analysis should be conducted before calculating internal consistency estimates of reliability. If factor analysis indicates the assumptions underlying coefficient alpha are met, then it can be reported as a reliability coefficient. However, to the extent that items are multidimensional, alternative internal consistency reliability coefficients should be computed based on the parameter estimates of the factor model. Assuming a bifactor model evidenced good fit, and the measure was designed to assess a single construct, omega hierarchical—the proportion of variance of the total scores due to the general factor—should be presented. Omega—the proportion of variance of the total scores due to all factors—also should be reported in that it represents a more traditional view of reliability, although it is computed within a factor analytic framework. By presenting both these coefficients and potentially other omega coefficients, the reliability results are less likely to be misinterpreted.     

一类自相似分形的Hausdorff维数

构造了一类自相似分形 ,利用满足开集条件的压缩自相似映射的性质 ,给出它们的Hausdorff维数s =ln6k/ln( 1/ε) .     

广义转移的应用

进一步研究广义转移的性质,证明了几个较深刻的结果,推广了Grün第一定理.