关于多指标综合评价中指标正向化和无量纲化方法的选择

在多指标综合评价中,有些是指标值越大评价越好的指标,称为正向指标(也称效益型指标或望大型指标);有些是指标值越小评价越好的指标,称为逆向指标(也称成本型指标或望小型指标),还有些是指标值越接近某个值越好的指标,称为适度指标。在综合评价时,首先必须将指标同趋势化,一般是将逆向指标和适度指标转化为正向指标,所以也称为指标的正向化。不同评价指标往往具有不同的量纲和量纲单位,为了消除由此带来的不可公度性,还应将各评价指标作无量纲化处理。指标的同趋势化和无量纲化都有多种方法,应用时,应根据实际情况选择合适的方法。否则将会…     

对多指标综合评价的主成分分析方法的改进

对多指标综合评价的主成分分析方法的改进陈述云,张崇甫国内关于应用主成分分析方法进行综合评价的案例很多。但在众多的案例研究中我们发现,主成分分析的应用还存在一些问题。问题之一：究竟应选取多少个主成分来对样本进行综合评优排序;问题之二：对主成分的经济含义...     

综合评价中如何正确运用主成分分析

主成分分析在综合评价中得到了广泛运用,但在运用的过程中,也存在一些技术上的问题,实证分析时如果不注意这些问题的研究会影响结论的准确性。本文主要从四个方面对这一问题阐述了看法:数据的处理、指标选取、主成分个数的选取以及使用范围和样本的一致性。     

循环经济评价指标体系的设计及评估方法

依据循环经济发展的基本内涵与原理及主成分方法,构建了包括经济发展指标、循环经济特征指标、生态环保指标及绿色管理指标在内的循环经济发展评价指标体系,并通过运用主成分模型,测算了指标权重,得到了主成分方法下的循环经济综合评价模型。     

基于核主成分分析和加权聚类分析的综合评价方法

针对传统主成分分析在处理非线性问题上的不足,文章阐述了应用核主成分分析进行数据处理的改进方法,并介绍了一种基于核主成分的加权聚类分析的综合评价方法.实验表明,该方法可以改进传统的综合评价方法.     

基于非线性主成分和聚类分析的综合评价方法

针对传统主成分在处理非线性问题上的不足，阐述了传统方法在数据无量纲化中“中心标准化”的缺点和处理“线性”数据时的缺陷，给出了数据无量纲化和处理“非线性”数据时的改进方法，并建立了一种基于“对数中心化”的非线性主成分分析和聚类分析的新的综合评价方法。实验表明，该方法能有效地处理非线性数据。     

线性综合评价模型中指标标准化方法的比较与选择

分析与比较各种指标一致化与无量纲化方法对综合评价结果的影响,并构建兼容度指标对无量纲化方法的相对有效性进行测度。结果表明：在线性综合评价模型中,减法一致化方法、Z-Score法和极差化法相比其他标准化方法更为有效。选择合适的指标标准化方法,能够有效提高综合评价结果的准确性。     

主成分综合评价方法存在的问题及改进

文章深入分析了用目前普遍采用的主成分分析法进行多指标综合评价时存在的指标权系数不合理问题,并对用主成分构建综合评价函数的方式作了改进,使综合评价函数的权系数变得较为合理。     

综合评价指标筛选及预处理的方法研究

本文对综合评价指标筛选及预处理的方法研究,得出多指标综合评价时,首先要对指标进行预处理,包括:必须在多个信息的重迭指标中筛选有效评价指标;必须将指标一致化;要将无量纲化处理。每一个步骤都有多种方法,应用时,应根据实际情况选择合适的方法。     

城市发展水平综合评价指标体系的设计及评估方法

文章根据城市发展的内涵及指标体系的构建原则,建立了包括经济发展指标、社会发展指标、人文发展指标、生态环境指标在内的城市发展水平综合评价指标体系,并通过运用主成分模型,测算了指标权重,得到了主成分方法下的城市发展水平评价模型.     

主成分分析与因子分析的异同比较及应用

主成分分析法和因子分析法都是从变量的方差-协方差结构入手,在尽可能多地保留原始信息的基础上,用少数新变量来解释原始变量的多元统计分析方法。教学实践中,发现学生运用主成分分析法和因子分析法处理降维问题的认识不够清楚,本文针对性地从主成分分析法、因子分析法的基本思想、使用方法及统计量的分析等多角度进行比较,并辅以实例。     

The evaluation of socio-economic development of development agency regions in Turkey using classical and robust principal component analyses

In this study, classical and robust principal component analyses are used to evaluate socioeconomic development of regions of development agencies that give service on the purpose of decreasing development difference among regions in Turkey. Due to the high differences between development levels of regions outlier problem occurs, hence robust statistical methods are used. Also, classical and robust statistical methods are used to investigate if there are any outliers in data set. In classic principal component analyse, the number of observations must be larger than the number of variables. Otherwise determinant of covariance matrix is zero. In Robust method for Principal Component Analysis (ROBPCA), a robust approach to principal component analyse in high-dimensional data, even if the number of variables is larger than the number of observations, principal components are obtained. In this paper, firstly 26 development agencies are evaluated with 19 variables by using principal component analysis based on classical and robust scatter matrices and then these 26 development agencies are evaluated with 46 variables by using the ROBPCA method.     

ADE-4: a multivariate analysis and graphical display software

We present ADE-4, a multivariate analysis and graphical display software. Multivariate analysis methods available in ADE-4 include usual one-table methods like principal component analysis and correspondence analysis, spatial data analysis methods (using a total variance decomposition into local and global components, analogous to Moran and Geary indices), discriminant analysis and within/between groups analyses, many linear regression methods including lowess and polynomial regression, multiple and PLS (partial least squares) regression and orthogonal regression (principal component regression), projection methods like principal component analysis on instrumental variables, canonical correspondence analysis and many other variants, coinertia analysis and the RLQ method, and several three-way table (k-table) analysis methods. Graphical display techniques include an automatic collection of elementary graphics corresponding to groups of rows or to columns in the data table, thus providing a very efficient way for automatic k-table graphics and geographical mapping options. A dynamic graphic module allows interactive operations like searching, zooming, selection of points, and display of data values on factor maps. The user interface is simple and homogeneous among all the programs; this contributes to making the use of ADE-4 very easy for non- specialists in statistics, data analysis or computer science.     

因子分析精确模型的基本思想与方法

文章从统计思想、等价性的方法入手,给出了初始因子分析精确模型及解、因子分析精确模型及解、主成分分析与因子分析的关系式等结论。从基本思想、方法上完善了因子分析精确模型和理论。     

稳健主成分分析方法研究及其在经济管理中的应用

传统的多元统计分析方法,如主成分分析方法和因子分析方法等的共同点是计算样本的均值向量和协方差矩阵,并在这两者的基础上计算其他统计量。当样本数据中没有离群值时,这些方法都能得到优良的结果。但是当样本数据中包括离群值时,计算结果就会很容易受到这些离群值的影响,这是因为传统的均值向量和协方差矩阵都不是稳健的统计量。本文对目前较流行的FAST-MCD方法的算法进行研究,构造了稳健的均值向量和稳健的协方差矩阵,应用到主成分分析中,并针对其不足之处提出改进方法。从模拟和实证的结果来看,改进后的的方法和新的稳健估计量确实能够对离群值起到很好的抵抗作用,大幅度地降低它们对计算结果的影响。     

Functional Analysis of Variance,Discriminant Analysis,and Clustering in a Manifold of Elastic Curves

We develop functional data analysis techniques using the differential geometry of a manifold of smooth elastic functions on an interval in which the functions are represented by a log-speed function and an angle function. The manifold's geometry provides a method for computing a sample mean function and principal components on tangent spaces. Using tangent principal component analysis, we estimate probability models for functional data and apply them to functional analysis of variance, discriminant analysis, and clustering. We demonstrate these tasks using a collection of growth curves from children from ages 1–18.     

一类基于模型的聚类方法

在聚类问题中,若变量之间存在相关性,传统的应对方法主要是考虑采用马氏距离、主成分聚类等方法,但其可操作性或可解释性较差,因此提出一类基于模型的聚类方法,先对变量间的相关性结构建模(作为辅助信息)再做聚类分析。这种方法的优点主要在于:适用范围更宽泛,不仅能处理(线性)相关问题,而且还可以处理变量间存在的其他复杂结构生成的数据聚类问题;各个变量的重要性也可以通过模型的回归系数来体现;比马氏距离更稳健、更具操作性,比主成分聚类更容易得到解释,算法上也更为简洁有效。     

析主成分分析和因子分析——以Frobenius范数下矩阵近似的新视角

本文通过引入数据阵在Frobenius范数下的最优近似等概念来重新探讨主成分和因子分析。我发现，主成分分析中主成分和因子分析中因子得分（通过主成分解因子载荷，然后用最小二乘解因子得分）的估计为数据阵的最优近似（在Frobenius范数下）在不同正交坐标方向矩阵下的坐标。两种方法分别采用了不同的约束条件分解的最优近似（在Frobenius范数下），因为该分解并不唯一。     

Common Factor Analysis versus Principal Component Analysis: A Comparison of Loadings by Means of Simulations

Common factor analysis (CFA) and principal component analysis (PCA) are widely used multivariate techniques. Using simulations, we compared CFA with PCA loadings for distortions of a perfect cluster configuration. Results showed that nonzero PCA loadings were higher and more stable than nonzero CFA loadings. Compared to CFA loadings, PCA loadings correlated weakly with the true factor loadings for underextraction, overextraction, and heterogeneous loadings within factors. The pattern of differences between CFA and PCA was consistent across sample sizes, levels of loadings, principal axis factoring versus maximum likelihood factor analysis, and blind versus target rotation.     

Hierarchical clustering of variables: a comparison among strategies of analysis

In this paper some hierarchical methods for identifying groups of variables are illustrated and compared. It is shown that the use of multivariate association measures between two sets of variables can overcome the drawbacks of the usually employed bivariate correlation coefficient, but the resulting methods are generally not monotonic. Thus a new multivariate association measure is proposed, based on the links existing between canonical correlation analysis and principal component analysis, which can be more suitably used for the purpose at hand. The hierarchical method based on the suggested measure is illustrated and compared with other possible solutions by analysing simulated and real data sets. Finally an extension of the suggested method to the more general situation of mixed (qualitative and quantitative) variables is proposed and theoretically discussed.