Variable selection and interpretation of covariance principal components

被引:31
作者
Al-Kandari, NM
Jolliffe, IT
机构
[1] Kuwait Univ, Dept Stat & Operat Res, Kuwait 13060, Kuwait
[2] Univ Aberdeen, Dept Math Sci, Aberdeen AB24 3UE, Scotland
关键词
covariance structure; discarding variables; measures of efficiency; principal component analysis; principal variables; procrustes analysis;
D O I
10.1081/SAC-100002371
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
In practice, when a principal component analysis is applied on a large number of variables the resultant principal components may not be easy to interpret, as each principal component is a linear combination of all the original variables. Selection of a subset of variables that contains, in some sense, as much information as possible and enhances the interpretations of the first few covariance principal components is one possible approach to tackle this problem. This paper describes several variable selection criteria and investigates which criteria are best for this purpose. Although some criteria are shown to be better than others, the main message of this study is that it is unwise to rely on only one or two criteria. It is also clear that: the interdependence between variables and the choice of how to measure closeness between the original components and those using subsets of variables are both important in determining the best criteria to use.
引用
收藏
页码:339 / 354
页数:16
相关论文
共 13 条
[1]  
ALKANDARI NM, 1998, THESIS U ABERDEEN SC
[2]   POPULATION CORRELATION MATRICES FOR SAMPLING EXPERIMENTS [J].
BENDEL, RB ;
MICKEY, MR .
COMMUNICATIONS IN STATISTICS PART B-SIMULATION AND COMPUTATION, 1978, 7 (02) :163-182
[3]   LOADINGS AND CORRELATIONS IN THE INTERPRETATION OF PRINCIPAL COMPONENTS [J].
CADIMA, J ;
JOLLIFFE, IT .
JOURNAL OF APPLIED STATISTICS, 1995, 22 (02) :203-214
[4]  
Dunteman G. H., 1989, PRINCIPAL COMPONENTS
[5]  
Jackson JE, 1991, A user's guide to principal components
[6]  
Jollife IT., 1973, APPL STATIST, V22, P21, DOI [10.2307/2346300, DOI 10.2307/2346300]
[7]  
Jolliffe I., 2002, PRINCIPAL COMPONENT, DOI [DOI 10.1016/0169-7439(87)80084-9, 10.1007/0-387-22440-8_13, DOI 10.1007/0-387-22440-8_13]
[8]  
JOLLIFFE IT, 1972, J ROY STAT SOC C-APP, V21, P160
[9]  
KRZANOWSKI WJ, 1987, J R STAT SOC C-APPL, V36, P22
[10]  
Mardia K. V., 1979, MULTIVARIATE ANAL