Study of variable selection in multivariate methods without external variables and development of variable selection software

我们研究了无外部变量的多变量方法中的变量选择，如主成分分析（PCA），因子分析（FA）和对应分析（CA）。本文主要讨论以下几个问题：1.从文献中收集了无外变量多元方法中变量选择的现有方法。本文综述了这三种方法，并将其作为变量选择的综述发表在我们的论文和网络上（见4）。在PCA修改后的主成分作为一个选择标准进行评估，信息应该使用多少变量进行了讨论，使用计算机密集型的方法，并提出了一个选择标准的意义上的回归和评估的AIC。在FA中，考虑使用RV系数来评估基于所有变量的因子得分配置与基于选定变量的因子得分配置之间的接近程度的标准。在元胞自动机中，讨论了用RV系数表示两个样本得分的贴近度的选择准则和用普通拟合优度表示元胞自动机的选择准则。结果表明，每一个准则都适用于真实的情况，而且诸如前向-后向逐步选择等选择过程提供了与所有可能的选择相似的结果。4.可变选择环境“VASMM”（Variable Selection in Multivariate Methods）建立在网络（http：//mo161.soci.ous.ae.jp/vasmm/）上，以提供关于在没有外部变量的情况下多变量方法中的变量选择的信息和在线选择功能。开发了用于R和XploRe等通用统计软件包的宏。使用这些工具可以随时随地进行变量选择。

We study variable selection in multivariate methods without external variables such as principal component analysis (PCA), factor analysis (FA) and correspondence analysis (CA). In this study we discuss the followings.1.Existing methods of variable selection in multivariate methods without external variables are collected from literatures. They are reviewed and then published as overviews of variable selection in our papers and on the web (see 4)2.New selection criteria in PCA, FA and CA are proposed. In PCA modified principal component as a selection criterion is evaluated, information on how many variables should be used is discussed using computer-intensive methods, and a selection criterion in the sense of regression is proposed and evaluated by AIC. In FA, criteria using RV-coefficient to evaluate the closeness between a configuration of factor scores based on all variables and one on selected variables is considered. In CA, a selection criterion using RV-coefficient for the closeness on two case scores and criteria using ordinary goodness of fit in CA are discussed.3.Applying the proposed criteria to real data sets, they are found that every criterion can be used in the real situations and that selection procedures such as forward-backward stepwise selection provide similar results to all possible selection.4.Variable selection environment"VASMM"(VAriable Selection in Multivariate Methods) is established on the web (http://mo161.soci.ous.ae.jp/vasmm/) to provide information on variable selection in multivariate methods without external variables and on-line selection function. Macros for general statistical packages such as R and XploRe are developed. Using these tools variable selection can be performed anytime and anywhere.