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
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Authors
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
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Abstract
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.
Keywords
Scaling Indicators, Coefficient of Variation, Multivariate Techniques, Dimensional Reduction, Computation of PCAs and Factors
To cite this article
Priyadarshana Dharmawardena, Raphel Ouseph Thattil, Sembakutti Samita, 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. doi: 10.11648/j.ajtas.20170602.13
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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.
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