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

研究了主成分分析(PCA)、因子分析(FA)和对应分析(CA)等不含外部变量的多元方法中的变量选择问题。在本研究中，我们讨论了以下几点：1.从文献中收集了现有的不含外部变量的多元方法中的变量选择方法。在我们的论文和网站(见4)中，它们被作为变量选择的综述发表。2.在主成分分析、FA和CA中提出了新的选择标准。在主成分分析中，评价了修正的主成分作为选择标准，利用计算机密集的方法讨论了应使用多少变量的信息，并提出了回归意义上的选择标准，并由AIC进行了评估。在FA中，考虑了使用RV系数来评估基于所有变量的因素分数配置与基于选定变量的因素分数配置之间的贴近程度的标准。在CA中，讨论了用RV系数表示两个案例得分的贴近度的选择准则和CA中使用普通拟合度的准则。3.将所提出的准则应用于实际数据集，发现每种准则都可以在实际情况下使用，并且选择过程如前向后向逐步选择提供了与所有可能的选择相似的结果。4.在网上建立了变量选择环境(http://mo161.soci.ous.ae.jp/vasmm/))，以提供无外部变量和在线选择函数的多变量方法中变量选择的信息。开发了R和Xplore等通用统计软件包的宏。使用这些工具，可以随时随地执行变量选择。

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.