Correspondence Analysis in Statistical Package Programs

BMDP, Version 7.0: Available from BMDP, Statistical Software, Inc., 12121 Wilshire Blvd., Suite 300, Los Angeles, CA 90025; phone: 310-207-8800; fax: 310-207-8844. $695.

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Correspondence analysis of square asymmetric matrices

The application of correspondence analysis to square asymmetric tables is often unsuccessful because of the strong role played by the diagonal entries of the matrix, obscuring the data off the diagonal. A simple modification of the centring of the matrix, coupled with the corresponding change in row and column masses and row and column metrics, allows the table to be decomposed into symmetric and skew symmetric components, which can then be analysed separately. The symmetric and skew symmetric analyses can be performed by using a simple correspondence analysis program if the data are set up in a special block format. The methodology is demonstrated on a social mobility table from the first democratically elected Parliament in Germany, the Frankfurter Nationalversammlung . The table cross-tabulates the jobs of parliamentarians when first entering the labour market and their jobs in May 1848 when the Parliament started its first session.     

Correspondence Analysis and Its Application in Oncology

To explore the application value of correspondence analysis in oncology, we adopted correspondence analysis method to analyze the relationship between the amount of food eaten in some cities in China and the male gastric carcinoma mortality. According to scatter plots of row and column points, there are regional differences among the male gastric carcinoma mortality in different cities of China. Southern male citizens ate more rice and salt, less wheaten food, and fewer light vegetables than northern ones. There may be some carcinogenic factors in some food.     

Cumulative Correspondence Analysis of Two-Way Ordinal Contingency Tables

A suitable measure of association for two ordered variables is the doubly cumulative chi-squared statistic (Hirotsu, 1994 Hirotsu , C. ( 1994 ). Modelling and analysing the generalized interaction . Proc. Third IEEE Conf. Control Applic. 2 : 1283 – 1288 .[Crossref] , [Google Scholar]). This statistic is obtained by considering the cumulative sum of cell frequencies across the variables. In this article, we explore the development of correspondence analysis which takes into account the presence of two ordered variables by partitioning the doubly cumulative chi-squared statistic.     

属性数据的多变量对应分析模型及应用

属性数据的建模和分析是市场研究活动中最重要的一类应用问题,学术界和市场研究行业一般使用列联表及统计检验的方法进行分析。故将法国统计学家J.P.Beozecri提出的对应分析法导入市场研究实证过程,使问卷调查中常见的多变量属性数据分析建模过程呈现出稳健的统计结论和直观的二维图示,并推广到广义多变量对应分析场合,其结论可靠,有应用创新。     

对应分析统计检验体系探讨

对应分析因其结果的易读性,近些年得到了越来越广泛的应用。为了更好地应用对应分析,提出建立对应分析统计检验体系,包括对应分析适用性的统计检验以及对应分析效果的检验,同时还提出应用对应分析时应注意的其它问题。     

The Confidence Ellipses in Decomposition Multiple Non Symmetric Correspondence Analysis

Non Symmetric Correspondence Analysis (NSCA) (D'Ambra and Lauro, 1989 D'Ambra , L. , Lauro , N. ( 1989 ). Non symmetrical analysis of three way contingency tables . In: Multiway Data Analysis , Coppi , R. , Bolasco , S. , Eds., North Holland , Amsterdam : pp. 301 – 315 . [Google Scholar]) is a useful technique for analyzing a two-way contingency table.

The key difference between the symmetrical and non symmetrical versions of correspondence analysis rests on the measure of the association used to quantify the relationship between the variables. For a two-way, or multi-way, contingency table, the Pearson chi-squared statistic is commonly used when it can be assumed that the categorical variables are symmetrically related. However, for a two-way table, it may be that one variable can be treated as a predictor variable and the second variable can be considered as a response variable.

Yet, for such a variable structure, the Pearson chi-squared statistic is not an appropriate measure of the association. Instead, one may consider the Goodman-Kruskal tau index. In the case that there are more than two cross-classified variables, multivariate versions of the Goodman-Kruskal tau index can be considered. These include Marcotorchino's index (Marcotorchino, 1985) and Gray-Williams’ index (Gray and Williams, 1975 Gray , L. N. , Williams , J. S. ( 1975 ). Goodman and Kruskals Tau B: Multiple and partial analogy. Amer. Statist. Assoc. Proc. Soc. Statist. Sec. pp. 444 – 448 . [Google Scholar]).

In this article, the Multiple non Symmetric Correspondence Analysis (MNSCA), along with the decomposition of the TAU by Gray-Williams in main effects and interaction (D'Ambra et al., 2011 D'Ambra , L. , D'Ambra , A. , Sarnacchiaro , P. ( 2011 ). Visualising main effects and interaction term in multiple non symmetric correspondence analysis. Submitted.  [Google Scholar]), is used for the evaluation of the innovative performance of the manufacturing enterprises in Campania.

Finally, to identify a category which is statistically significant, the confidence ellipses have been proposed for the Multiple Non Symmetric Correspondence Analysis starting from the ellipses suggested by Beh (2010 Beh , E. J. ( 2010 ). Elliptical confidence regions for simple correspondence analysis . J. Statisti. Plann. Infer. [Web of Science ®] , [Google Scholar]) for the symmetrical analysis.     

Correspondence Analysis of Cumulative Frequencies Using a Decomposition of Taguchi's Statistic

Taguchi's statistic has long been known to be a more appropriate measure of association for ordinal variables than the Pearson chi-squared statistic. Therefore, there is some advantage in using Taguchi's statistic for performing correspondence analysis when a two-way contingency table consists of one ordinal categorical variable. This article will explore the development of correspondence analysis using a decomposition of Taguchi's statistic.     

Correspondence analysis of repair data: a case study for electric cable shovels

In mining operation, effective maintenance scheduling is very important because of its effect on the performance of equipment and production costs. Classifying equipment on the basis of repair durations is considered one of the essential works to schedule maintenance activities effectively. In this study, repair data of electric cable shovels used in the Western Coal Company, Turkey, has been analyzed using correspondence analysis to classify shovels in terms of repair durations. Correspondence analysis, particularly helpful in analysing cross-tabular data in the form of numerical frequencies, has provided a graphical display that permitted more rapid interpretation and understanding of the repair data. The results indicated that there are five groups of shovels according to their repair duration. Especially, shovels numbered 2, 3, 7, 10 and 11 required a repair duration of<1 h and maintained relatively good service condition when compared with others. Thus, priority might be given to repair them in maintenance job scheduling even if there is another failed shovel waiting to be serviced. This type of information will help mine managers to increase the number of available shovels in operation.     

加快推进统计制度改革

加快推进统计制度改革林贤郁党的十五大为进一步深化经济体制改革,加快建立社会主义市场经济体制指明了方向。十五大在理论上的一系列重大突破,在经济体制改革和经济建设方面的重大决策,既对统计工作提出了新的更高要求,也为统计工作更快、更好地发展提供了机遇。因此...