Scale Independent Principal Component Analysis and Factor Analysis with Preserved Inherent Variability of the Indicators
American Journal of Theoretical and Applied Statistics
Volume 6, Issue 2, March 2017, Pages: 90-94
Received: Feb. 2, 2017;
Accepted: Feb. 17, 2017;
Published: Mar. 2, 2017
Views 1988 Downloads 97
Priyadarshana Dharmawardena, Department of Census and Statistics, Battaramulla, Sri Lanka
Raphel Ouseph Thattil, Postgraduate Institute of Agriculture, University of Peradeniya, Peradeniya, Sri Lanka
Sembakutti Samita, Postgraduate Institute of Agriculture, University of Peradeniya, Peradeniya, Sri Lanka
Follow on us
Principal Component Analysis (PCA) and Factor Analysis (FA) are common multivariate techniques used for dimensionality reduction. With these techniques it is expected to identify actual number of dimensions while accounting almost all observed variability. Standard PCA is based either on correlation matrix (CORM) or covariance matrix (COVM). When it is based on CORM, scale dependency can be removed but inherent variability cannot be preserved. On the other hand, when PCA is based on COVM, inherent variability can be preserved but scale dependency cannot be removed. As a solution to this issue, this paper suggests scaling each indicator by its mean, resulting in new mean equal to 1 and standard deviation equal to the coefficient of variance (CV). This leads to PCs, which are scale independent while retaining the observed variability. The computation of PCs and factors under the suggested method is derived in the study. The procedure is illustrated using the lowest level administrative division census data of Western province of Sri Lanka.
Scaling Indicators, Coefficient of Variation, Multivariate Techniques, Dimensional Reduction, Computation of PCAs and Factors
To cite this article
Raphel Ouseph Thattil,
Scale Independent Principal Component Analysis and Factor Analysis with Preserved Inherent Variability of the Indicators, American Journal of Theoretical and Applied Statistics.
Vol. 6, No. 2,
2017, pp. 90-94.
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Silva, G. (2000) Construction of Human Development Indices using Multivariate Techniques, PGIA, University of Peradeniya.
The Organization for Economic Co-operation and Development, (2004) The OECD-JRC Handbook on Practices for Developing Composite Indicators. https://stats.oecd.org/glossary/detail.asp?ID=6278.
Jolliffe, T. (2002) Principal Component Analysis, Springer Verlag, New York.
Josseph, F. et al. (2010) Multivariate Data Analysis. A Global Perspective, Pearson Education Inc, New Jersey.
Fernando, S., Samita, S and Abenayake R (2011). Modified factor analysis to construct composite indices: Illustration on Urbanization index. Tropical Agricultural Research, 24, 271–281.
Tuan, A. and Magi, S. (2009) Principal Component Analysis: Final Paper in Financial Pricing. National Cheng Kung University, 3-26.
Farrugia. N, (2007) conceptual issues in constructing composite indices. Occasional papers on islands and small states, 2/2007.
Yutaka, K., Yusuke, M. and Shohei, S. (2003) factor rotation and ica. 4th International Symposium on Independent Component Analysis and Blind Signal Separation (ICA2003), Japan.
Delchambre, L. (2014) Weighted principal component analysis: a weighted covariance eigen decomposition approach, University of Liege, Belgium.
Abdi, H., and Williams, J., Principal component analysis John Wiley & Sons; WIREs Comp Stat 2010 2 433–459 2010.
The Organization for Economic Co-operation and Development, (2008) Handbook on constructing composite indicators: methodology and user guide.