基于灰色动态聚类-粗糙集的绿色资源环境评价指标构建模型

以内蒙古自治区12个盟市的绿色资源环境发展为研究对象,采用灰色动态聚类与粗糙集相结合的方法,构建包含有全年供水量等11个指标的内蒙古自治区绿色资源环境指标体系,其要点在于:一是通过灰色关联分析建立样本间的灰色关联矩阵,进而进行样本间的灰色聚类,反映样本间的信息重复性;二是采用动态聚类方法,每次去除一个指标后继续通过灰色关联分析建立的灰色关联矩阵进行灰色样本聚类,为粗糙集约简提供信息数据;三是通过粗糙集约简理论判断海选指标对聚类结果的影响是否显著,将每一次的聚类结果与原始聚类结果比较,保留两次聚类结果不同且对评价样本分类有显著影响的海选指标;四是采用非参数Kruska-Wallis检验的P值检验法证明本文构建的指标体系是合理的。通过对比分析表明,本文的灰色动态聚类-粗糙集指标筛选模型优于现有研究的聚类-灰色关联指标筛选模型。     

灰色聚类法在课程评估中的应用

灰色聚类是以灰数的白化函数生成为基础的一种聚类方法。文章首先提出采用加权平均法则，对聚类结果可进行再分析，以充分利用信息，使评判结果更为合理。同时应用灰色聚类法对西安统计学院４门课程进行了综合评价分析，其结果符合实际。     

基于CSPC方法的房地产发展健康状况评价分析

传统的主成分分析进行综合评价存在许多不足,因此,提出基于聚类稀疏主成分分析的综合评价方法,使得评价结果更合理和符合实际,并使用该方法分析了上海、武汉、成都三个城市的房地产健康发展状况。     

非线性面板数据聚类方法研究

对于一类变量非线性相关的面板数据,现有的基于线性算法的面板数据聚类方法并不能准确地度量样本间的相似性,且聚类结果的可解释性低。综合考虑变量非线性相关问题及聚类结果可解释性问题,提出一种非线性面板数据的聚类方法,通过非线性核主成分算法实现对样本相似性的测度,并基于混合高斯模型进行样本概率聚类,实证表明该方法的有效性及其对聚类结果的可解释性有所提高。     

一种针对不完全观测数据的消费者聚类方法

现有聚类方法都是基于消费者全部的行为信息,对于观测不完全的信息,提出了三阶段聚类方法。首先,使用样本数据的全部信息对消费者聚类;接着仅使用人口统计变量建立分类模型;最后对上述结果进行修正。三阶段聚类方法最大优点是可以将没有入选样本的个体分配到由样本个体得到的行为集群中去,将这个方法应用于电视行业,得到了很有实际应有价值的结果。     

一种社会经济系统模糊C划分聚类数的确定方法

在社会经济系统建模和分析中,对目标系统进行分解时,适合采用模糊C均值聚类算法进行划分.由于聚类数未知,采用某个聚类有效性函数来确定时,往往聚类结果并不理想.将专家知识和科学聚类相结合,文章给出了一种针对现实社会经济系统的确定聚类数的方法,即由专家给出可供选择的聚类数集合,然后通过多个聚类有效性函数来对各个聚类数进行评价.以广东省作为目标系统,按照科技进步水平,对其21个地区进行了划分,结果表明了方法的可行性.     

Q型系统聚类分析中的统计检验问题

Q型系统聚类分析已经越来越成为人们广泛应用的多元统计分析方法。然而在应用中盲目套用系统聚类分析方法的情况很多，并对聚类分析方法的适用性、聚类过程的合理性、聚类结果的有效性等问题分析重视不够，更谈不上对聚类分析进行统计检验。因此，为了更好地应用Q型系统聚类分析，就应对Q型系统聚类分析结果进行统计检验并建立统计检验体系。Q型系统聚类分析统计检验体系主要包括：Q型系统聚类分析结果的有效性检验；聚类分析类（组）数选择合理性检验；聚类变量的显著性检验。     

农田土壤环境质量的最优模糊聚类及其分级

本文利用模糊聚类分析和多元统计分析,给出了求最优模糊聚类的方法和对基于重金属和有机氯的土壤环境质量进行聚类和分级的方法,并利用该聚类和分级的方法对太湖地区某市农田的土壤样进行聚类和分级。从聚类结果来看,本方法分类是将环境质量相近的土壤样分在同一类。从分类结果来看,绝大部分土壤样处于相对安全状态,适于一般农业经济产品的产生。本文所用方法有利于土壤环境质量研究的定量和数字化。     

基于动态时间规整的面板数据聚类方法研究及应用

以往的面板数据聚类方法存在一些缺陷,有必要基于动态时间规整的思路进一步改进与完善面板数据聚类方法。利用国家级经济技术开发区数据开展的实证分析结果表明：新的方法既能够很好地反映面板数据的动态变化、又避免了已有的面板数据聚类方法中各种距离如何赋权的问题,聚类结果较为稳定且有很好的可视化效果。     

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。     

ORDANOVA: Analysis of ordinal variation

In order to accelerate object evaluation, some measurement systems commonly use an ordinal scale (e.g., stick results, quality estimation). This paper presents a way to analyze ordinal data variation. As in classical ANOVA for continual data, ORDANOVA for ordinal data splits the total variation into within and between components. This decomposition has various practical applications such as classification, cluster analysis, distinguishing feature identification and so on.     

A Clustering Method for Categorical Ordinal Data

Often, categorical ordinal data are clustered using a well-defined similarity measure for this kind of data and then using a clustering algorithm not specifically developed for them. The aim of this article is to introduce a new clustering method suitably planned for ordinal data. Objects are grouped using a multinomial model, a cluster tree and a pruning strategy. Two types of pruning are analyzed through simulations. The proposed method allows to overcome two typical problems of cluster analysis: the choice of the number of groups and the scale invariance.     

MultiOrd: An R Package for Generating Correlated Ordinal Data

In this article, operational details of an R package MultiOrd that is designed for the generation of correlated ordinal data are described, and examples of some important functions are given. The package provides a valuable and needed tool that has been lacking for generating multivariate ordinal data.     

Reproducibility of clinical data II: categorical outcomes

In this second part of this paper, reproducibility of discrete ordinal and nominal outcomes is addressed. The first part deals with continuous outcomes, concentrating on intraclass correlation (ρ) in the context of one‐way analysis of variance. For categorical data, the focus has generally not been on a meaningful population parameter such as ρ. However, intraclass correlation has been defined for discrete ordinal data, ρ_c, and for nominal data, κ_I. Therefore, a unified approach to reproducibility is proposed. The relevance of these parameters is outlined. Estimation and inferential procedures for ρ_c and κ_I are reviewed, together with worked examples. Topics related to reproducibility that are not addressed in either this or the previous paper are highlighted. Considerations for designing reproducibility studies and for interpreting their results are provided. Copyright © 2004 John Wiley & Sons, Ltd.     

Linear Models Methods for Some Rank Function Analyses of Ordinal Categorical Data

This paper is concerned with the analysis of ordinal data through linear models for rank function measures.Primary attention is directed at pairwise Mann-Whitney statistics for which dimension reduction is managed by use of a Bradley-Terry log-linear structure.The nature of linear models for such quantities is contrasted with that for mean ranks (or ridits).Aspects of application are illustrated with an example for which results of other methods are also given.     

Clustering ranking data in market segmentation: a case study on the Italian McDonald's customers’ preferences†

Cluster analysis is often used for market segmentation. When the inputs in the clustering algorithm are ranking data, the intersubject (dis)similarities must be measured by matching-type measures, able to take account of the ordinal nature of the data. Among them, we used a Weighted Spearman's rho, suitably transformed into a (dis)similarity measure, in order to emphasize the concordance on the top ranks. This allows creating clusters grouping customers that place the same items (products, services, etc.) higher in their rankings. Also the statistical instruments used to interpret the clusters must be conceived to deal with ordinal data. The median and other location measures are appropriate but not always able to clearly differentiate groups. The so-called bipolar mean, with its related variability measure, may reveal some additional features. A case study on real data from a survey carried out in the Italian McDonald's restaurants is presented.     

Evaluation of an analysis approach used to account for extra-variation in clustered categorical responses

This article presents the results of a simulation study investigating the performance of an approach developed by Miller and Landis (1991) for the analysis of clustered categorical responses. Evaluation of this “two-step” approach, which utilizes the method of moments to estimate the extra-variation pardmeters and subsequently incorporates these parameters into estimating equations for modelling the marginal expectations, is carried out in an experimental setting involving a comparison between two groups of observations. We assume that data for both groups are collected from each cluster and responses are measured on a three-point ordinal scale. The performance of the estimators used in both “steps” of the analysisis investigated and comparisons are made to an alternative analysismethod that ignores the clustering. The results indicate that in the chosen setting the test for a difference between groups generally operatbs at the nominal α=0.05 for 10 or more clusters and hasincreasing power with both an increasing number of clusters and an inrreasing treatment effect. These results provide a striking contrasc to those obtained from an improper analysis that ignores clustering.     

A proposal for handling ordinal categorical variables in co-inertia analysis

This paper is about the problem of the treatment of ordinal qualitative variables in co-inertia analysis. In the literature, there are different proposals based on the application of known statistical techniques to quantify ordinal variables. Here we propose to use a new procedure for the coding considering the empirical distributions of the variables involved in the analysis. We present an application to a real dataset, comparing the results obtained with the different kinds of quantification.     

General mixed‐data model: Extension of general location and grouped continuous models

The authors propose a general model for the joint distribution of nominal, ordinal and continuous variables. Their work is motivated by the treatment of various types of data. They show how to construct parameter estimates for their model, based on the maximization of the full likelihood. They provide algorithms to implement it, and present an alternative estimation method based on the pairwise likelihood approach. They also touch upon the issue of statistical inference. They illustrate their methodology using data from a foreign language achievement study.     

Joint modeling of mixed skewed continuous and ordinal longitudinal responses: a Bayesian approach

In this paper, a joint model for analyzing multivariate mixed ordinal and continuous responses, where continuous outcomes may be skew, is presented. For modeling the discrete ordinal responses, a continuous latent variable approach is considered and for describing continuous responses, a skew-normal mixed effects model is used. A Bayesian approach using Markov Chain Monte Carlo (MCMC) is adopted for parameter estimation. Some simulation studies are performed for illustration of the proposed approach. The results of the simulation studies show that the use of the separate models or the normal distributional assumption for shared random effects and within-subject errors of continuous and ordinal variables, instead of the joint modeling under a skew-normal distribution, leads to biased parameter estimates. The approach is used for analyzing a part of the British Household Panel Survey (BHPS) data set. Annual income and life satisfaction are considered as the continuous and the ordinal longitudinal responses, respectively. The annual income variable is severely skewed, therefore, the use of the normality assumption for the continuous response does not yield acceptable results. The results of data analysis show that gender, marital status, educational levels and the amount of money spent on leisure have a significant effect on annual income, while marital status has the highest impact on life satisfaction.