Discriminant Analysis Procedures Under Non-optimal Conditions for Binary Variables
American Journal of Theoretical and Applied Statistics
Volume 4, Issue 6, November 2015, Pages: 602-609
Received: Oct. 12, 2015; Accepted: Oct. 26, 2015; Published: Dec. 10, 2015
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I. Egbo, Department of Mathematics, Alvan Ikoku University of Education, Owerri, Nigeria
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The performance of four discriminant analysis procedures for the classification of observations from unknown populations was examined by Monte Carlo methods. The procedures examined were the Fisher Linear discriminant function, the quadratic discriminant function, a polynomial discriminant function and A-B linear procedure designed for use in situations where covariance matrices are equal. Each procedure was observed under conditions of equal sample sizes, equal covariance matrices, and in conditions where the sample was drawn from populations that have a multivariate normal distribution. When the population covariance matrices were equal, or not greatly different, the quadratic discriminant function performed similarly or marginally the same like Linear procedures. In all cases the polynomial discriminate function demonstrated the poorest, linear discriminant function performed much better than the other procedures. All of the procedures were greatly affected by non-normality and tended to make many more errors in the classification of one group than the other, suggesting that data be standardized when non-normality is suspected.
Apparent Error Rates, Fisher’s Linear Discriminant, Quadratic Discriminant Function, A-B Discriminant Function, Polynomial Discriminant Function
To cite this article
I. Egbo, Discriminant Analysis Procedures Under Non-optimal Conditions for Binary Variables, American Journal of Theoretical and Applied Statistics. Vol. 4, No. 6, 2015, pp. 602-609. doi: 10.11648/j.ajtas.20150406.32
Copyright © 2015 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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