Discriminant Analysis Procedures Under Non-optimal Conditions for Binary Variables

I. Egbo

doi:doi:10.11648/j.ajtas.20150406.32

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Discriminant Analysis Procedures Under Non-optimal Conditions for Binary Variables

I. Egbo

Published in American Journal of Theoretical and Applied Statistics (Volume 4, Issue 6)

Received: 12 October 2015 Accepted: 26 October 2015 Published: 10 December 2015

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Abstract

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.

Published in	American Journal of Theoretical and Applied Statistics (Volume 4, Issue 6)
DOI	10.11648/j.ajtas.20150406.32
Page(s)	602-609
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Apparent Error Rates, Fisher’s Linear Discriminant, Quadratic Discriminant Function, A-B Discriminant Function, Polynomial Discriminant Function

References

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[3]	Benerjee, K.S. & Marcus, L.F. (1965).In a Minimax Classification Procedure. Biometrics, 52, 654-654
[4]	Gilbert, S.E. (1968). “On Discrimination using Qualitative Variables” Journal of the American Statistical Association 1399-1418.
[5]	Gold Stein M. &Wolf (1977). On the problem of Bias multinomial classification. Biometrics 33, 325-331.
[6]	Hills, M. (1967). “Discriminantion and allocation with discrete data”, Applied Statistics. 16 237-250.
[7]	Lachenbruch, P.A. (1975) Discriminant Analysis. Hafner Press New York:
[8]	Marks, S. & Dunn, O.J. (1974). Discriminant functions when Covariance matrices are unequal. Journal of the American Statistical Association, 69, 555-559.
[9]	Martins, D.C., & Bradley, R.R. (1972). Probability Models, Estimation and Classification for Multivariate Dichotomous Populations, Biometrics,23, 203-221
[10]	Onyeagu S.I. (2003). Derivation of an optimal classification rule for discrete variables Journal of Nigerian Statistical Association, 73, 724-745.
[11]	Oluadare. S. (2011). Rubust Linear classifier for equal Cost Ratios of misclassification. CBN Journal of Applied Statistics.(2) (1)
[12]	Rao, C.R. (1965).Linear Statistical Inference and Its Applications: John Willey New York
[13]	Richard A.J. & Dean W.W. (1988).Applied Multivariate Statistical Analysis.4^th edition Prentice Hall. Inc. New Jessey.
[14]	Smith, H.F. (1936). A discriminant function for plant selection. Ann. Eugn. 7, 240 – 250.
[15]	Tou, J.T. & Gonzalez, R. C. (1974).Pattern Recognition Principles. Reading, Mass.; Addison –Wesley.
[16]	Slah, B.Y. & Abdelwaheb Rebai (2007). Comparison between Statistical Approaches and linear programming for resolving classification problem. International Mathematics Forum, 2,(63), 3125-3141.
[17]	Egbo, I., Onyeagu, S.I. & Ekezie, D.D. (2014). A comparison of multinomial classification rules for binary variables. International Journal of Mathematical Science and Engineering Applications (IJMSEA),8, 141-157.
[18]	Ekezie, D.D. (2012). Comparison of seven Asymptotic Error Rate Expansion for the sample linear Discriminant function. Unpublished Ph.D thesis submitted to Department of Statistics, Imo State University, Owerri, Nigeria.
[19]	Egbo, I., Onyeagu, S.I. & Ekezie, D.D. (2014).A Comparison of Multivariate Discrimination of Binary Data. International Journal of Mathematics and Statistics Studies, 2(4), 40-61.

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I. Egbo. (2015). Discriminant Analysis Procedures Under Non-optimal Conditions for Binary Variables. American Journal of Theoretical and Applied Statistics, 4(6), 602-609. https://doi.org/10.11648/j.ajtas.20150406.32

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I. Egbo. Discriminant Analysis Procedures Under Non-optimal Conditions for Binary Variables. Am. J. Theor. Appl. Stat. 2015, 4(6), 602-609. doi: 10.11648/j.ajtas.20150406.32

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I. Egbo. Discriminant Analysis Procedures Under Non-optimal Conditions for Binary Variables. Am J Theor Appl Stat. 2015;4(6):602-609. doi: 10.11648/j.ajtas.20150406.32

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@article{10.11648/j.ajtas.20150406.32,
  author = {I. Egbo},
  title = {Discriminant Analysis Procedures Under Non-optimal Conditions for Binary Variables},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {4},
  number = {6},
  pages = {602-609},
  doi = {10.11648/j.ajtas.20150406.32},
  url = {https://doi.org/10.11648/j.ajtas.20150406.32},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150406.32},
  abstract = {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.},
 year = {2015}
}

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TY  - JOUR
T1  - Discriminant Analysis Procedures Under Non-optimal Conditions for Binary Variables
AU  - I. Egbo
Y1  - 2015/12/10
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.20150406.32
DO  - 10.11648/j.ajtas.20150406.32
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 602
EP  - 609
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20150406.32
AB  - 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.
VL  - 4
IS  - 6
ER  -

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Author Information

I. Egbo

Department of Mathematics, Alvan Ikoku University of Education, Owerri, Nigeria

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APA Style

I. Egbo. (2015). Discriminant Analysis Procedures Under Non-optimal Conditions for Binary Variables. American Journal of Theoretical and Applied Statistics, 4(6), 602-609. https://doi.org/10.11648/j.ajtas.20150406.32

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ACS Style

I. Egbo. Discriminant Analysis Procedures Under Non-optimal Conditions for Binary Variables. Am. J. Theor. Appl. Stat. 2015, 4(6), 602-609. doi: 10.11648/j.ajtas.20150406.32

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AMA Style

I. Egbo. Discriminant Analysis Procedures Under Non-optimal Conditions for Binary Variables. Am J Theor Appl Stat. 2015;4(6):602-609. doi: 10.11648/j.ajtas.20150406.32

Copy | Download

@article{10.11648/j.ajtas.20150406.32,
  author = {I. Egbo},
  title = {Discriminant Analysis Procedures Under Non-optimal Conditions for Binary Variables},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {4},
  number = {6},
  pages = {602-609},
  doi = {10.11648/j.ajtas.20150406.32},
  url = {https://doi.org/10.11648/j.ajtas.20150406.32},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150406.32},
  abstract = {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.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Discriminant Analysis Procedures Under Non-optimal Conditions for Binary Variables
AU  - I. Egbo
Y1  - 2015/12/10
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.20150406.32
DO  - 10.11648/j.ajtas.20150406.32
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 602
EP  - 609
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20150406.32
AB  - 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.
VL  - 4
IS  - 6
ER  -

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