Skip to main content

Variable selection in multivariate methods using global score estimation

  • Original Paper
  • Published:
Computational Statistics Aims and scope Submit manuscript

Abstract

A variable selection method using global score estimation is proposed, which is applicable as a selection criterion in any multivariate method without external variables such as principal component analysis, factor analysis and correspondence analysis. This method selects a subset of variables by which we approximate the original global scores as much as possible in the context of least squares, where the global scores, e.g. principal component scores, factor scores and individual scores, are computed based on the selected variables. Global scores are usually orthogonal. Therefore, the estimated global scores should be restricted to being mutually orthogonal. According to how to satisfy that restriction, we propose three computational steps to estimate the scores. Example data is analyzed to demonstrate the performance and usefulness of the proposed method, in which the proposed algorithm is evaluated and the results obtained using four cost-saving selection procedures are compared. This example shows that combining these steps and procedures yields more accurate results quickly.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bonifas I, Escoufier Y, Gonzalez PL, Sabatier R (1984) Choix de variables en analyse en composantes principales. Rev Stat Appl 23: 5–15

    MathSciNet  Google Scholar 

  • Falguerolles A, Jmel S (1993) Un critere de choix de variables en analyse en composantes principales fonde sur des modeles graphiques gaussiens particuliers. Rev Can Stat 21(3): 239–256

    Article  MATH  Google Scholar 

  • Fueda K, Iizuka M, Mori Y (2003) Orthogonal score estimation with variable selection in multivariate methods (in Japanese). In: Proceedings of the 17th symposium of Japanese society of computational statistics, pp 129–132

  • Iizuka M, Mori Y, Tarumi T, Tanaka Y (2002) Statistical software VASMM for variable selection in multivariate methods. In: Härdle W, Rönz B(eds) COMPSTAT2002 proceedings in computational statistics. Springer, Heidelberg, pp 563–568

    Google Scholar 

  • Iizuka M, Mori Y, Tanaka Y, Tarumi T (2002b) Some new modules in variable selection software VASMM. In: Proceedings of the 4th ARS conference of the IASC, pp 166–169

  • Jolliffe IT (1972) Discarding variables in a principal component analysis I—Artificial data. Appl Stat 21: 160–173

    Article  MathSciNet  Google Scholar 

  • Jolliffe IT (1973) Discarding variables in a principal component analysis II—Real data. Appl Stat 22: 21–31

    Article  Google Scholar 

  • Kano Y, Harada A (2000) Stepwise variable selection in factor analysis. Psychometrika 65(1): 7–22

    Article  MathSciNet  Google Scholar 

  • Krzanowski WJ (1987a) Selection of variables to preserve multivariate data structure, using principal components. Appl Stat 36: 22–33

    Article  Google Scholar 

  • Krzanowski WJ (1987b) Cross-validation in principal component analysis. Biometrics 43: 575–584

    Article  MathSciNet  Google Scholar 

  • McCabe GP (1984) Principal variables. Technometrics 26: 137–144

    Article  MATH  MathSciNet  Google Scholar 

  • Mori Y (1997) Statistical software VASPCA—variable selection in PCA. Bull Okayama Univ Sci 33(A): 329–340

    Google Scholar 

  • Mori M, Du X, Iizuka M (2004) Considering variable selection criteria in correspondence analysis (in Japanese). Bull Faculty Environ Sci Technol Okayama Univ 10(2): 49–56

    Google Scholar 

  • Mori Y, Fueda K, Iizuka M (2004) Orthogonal score estimation with variable selection in multivariate methods. In: Antoch J(eds) COMPSTAT2004 proceedings in computational statistics. Springer, Heidelberg, pp 1527–1534

    Google Scholar 

  • Mori Y, Fueda K, Iizuka M (2007) Variable selection based on global score estimation and its numerical investigation (in Japanese). J Faculty Environ Sci Technol Okayama Univ 12(1): 29–40

    Google Scholar 

  • Mori Y, Tarumi T, Tanaka Y (1998) Principal Component analysis based on a subset of variables—numerical investigation on variable selection procedures (in Japanese). Bull Comput Stat Jpn 11(1): 1–12

    Google Scholar 

  • Nikkei Research Inc (1997–2006). In: Environmental management survey (1st in 1997 to 9th in 2006), Nihon Keizai Shimbun

  • Robert P, Escoufier Y (1976) A unifying tool for linear multivariate statistical methods: the RV-coefficient. Appl Stat 25: 257–265

    Article  MathSciNet  Google Scholar 

  • Tanaka Y (1983) Some criteria for variable selection in factor analysis. Behaviormetrika 13: 31–45

    Article  Google Scholar 

  • Tanaka Y, Kodake K (1981) A method of variable selection in factor analysis and its numerical investigation. Behaviormetrika 10: 49–61

    Article  Google Scholar 

  • Tanaka Y, Mori Y (1997) Principal component analysis based on a subset of variables: variable selection and sensitivity analysis. Am J Math Manage Sci 17: 61–89

    MATH  MathSciNet  Google Scholar 

  • Xia L, Yang Y (1988) A method of variable selection in Hayashi’s third method of quantification. J Jpn Soc Comp Stat 1: 27–43

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kaoru Fueda.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fueda, K., Iizuka, M. & Mori, Y. Variable selection in multivariate methods using global score estimation. Comput Stat 24, 127–144 (2009). https://doi.org/10.1007/s00180-008-0109-9

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00180-008-0109-9

Keywords