Detection of Multicollinearity Using Min-Max and Point-Coordinates Approach

Umeh Edith Uzoma; Awopeju Kabir Abidemi; Ajibade F. Bright

doi:doi:10.11648/j.ajtas.20150406.36

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Detection of Multicollinearity Using Min-Max and Point-Coordinates Approach

Umeh Edith Uzoma, Awopeju Kabir Abidemi, Ajibade F. Bright

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

Received: 14 December 2015 Accepted: 23 December 2015 Published: 23 January 2016

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Abstract

Multicollinearity is one of the problems or challenges of modeling or multiple regression usually encountered by Economists and Statisticians. It is a situation where by some of the independent variables in the formulated model are significantly or highly related/correlated. In the past, methods such as Variance Inflation Factor, Eigenvalue and Product moment correlation have been used by researchers to detect multicollinearity in models such as financial models, fluctuation of market price model, determination of factors responsible for survival of man and market model, etc. The shortfalls of these methods include rigorous computation which discourages researchers from testing for multicollinearity, even when necessary. This paper presents moderate and easy algorithm of the detection of multicollinearity among variables no matter their numbers. Using Min-Max approach with the principle of parallelism of coordinates, we are able to present an algorithm for the detection of multicollinearity with appropriate illustrative examples.

Published in	American Journal of Theoretical and Applied Statistics (Volume 4, Issue 6)
DOI	10.11648/j.ajtas.20150406.36
Page(s)	640-643
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), 2016. Published by Science Publishing Group

Keywords

Variance Inflation Factor, Matrix, Eigen Values, Characteristics Root, Range, Gradient

References

[1]	Brien, R. M. (2007). "A Caution Regarding Rules of Thumb for Variance Inflation Factors". Quality & Quantity 41(5): 673. doi: 10.1007/s11135-006-9018-6.
[2]	Belsley, D. (1991). Conditioning Diagnostics: Collinearity and Weak Data in Regression. New York: Wiley. ISBN0-471-52889-7.
[3]	Draper, N. R., Smith, H. (2003). Applied regression analysis, 3^rd edition, Wiley, New York.
[4]	Gujrati, D. N. (2004). Basic econometrics 4^th edition, Tata McGraw-Hill, New Delhi.
[5]	Hawking, R. R. and Pendleton, O. J. (1983). “The regression dilemma”, Commun. Stat.-Theo. Meth, 12,497-527.
[6]	Jim F. (2013). “What Are the Effects of Multicollinearity and When Can Ignore Them?” http://blog.minitab.com/blog/adventures-in-statistics/what-are-the-effects-of-multicollinearity-and-when-can-i-ignore-them.Assessed:17^th, Dec., 2015.
[7]	Johnston, J. and Dinardo, J. (1997) Econometric methods, 4^th edition, McGraw-Hill, Singapore.
[8]	Kennedy, P. E. (2002), “More on Venn Diagrams for Regression,” Journal of Statistics Education [Online], 10(1). (www.amstat.org/publications/jse/v10n1/kennedy.html).
[9]	Kumar, T. K. (1975). "Multicollinearity in Regression Analysis". Review of Economics and Statistics 57(3): 365–366. JSTOR 1923925.
[10]	Kock, N.; Lynn, G. S. (2012). "Lateral collinearity and misleading results invariance-based SEM: An illustration and recommendations". Journal of the Association for Information Systems 13(7): 546–580.
[11]	Math Centre (2009); Equations of Straight Lines. www.mathcentre.ac.uk/resources/uploaded/mc-ty-strtlines-2009-1.pdf. Assessed: 10/12/2015.
[12]	Montgomery, D. C., Peck, E. A., Vining, G. G. (2001). Introduction to linear regression analysis, 3^rd edition, Wiley, New York.
[13]	Vaughan, T. S., and Berry, K. E. (2005): “Using Monte Carlo Techniques to Demonstrate the Meaning and Implications of Multicollinearity”. Journal of Statistics Education. Vol.13, Number 1.
[14]	Wetherill, G. B., Duncombe, P., Kenward, M., Kollerstrom, J. (1986). Regression analysis with application, 1^st edition, Chapman and Hall, New York.

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Umeh Edith Uzoma, Awopeju Kabir Abidemi, Ajibade F. Bright. (2016). Detection of Multicollinearity Using Min-Max and Point-Coordinates Approach. American Journal of Theoretical and Applied Statistics, 4(6), 640-643. https://doi.org/10.11648/j.ajtas.20150406.36

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ACS Style

Umeh Edith Uzoma; Awopeju Kabir Abidemi; Ajibade F. Bright. Detection of Multicollinearity Using Min-Max and Point-Coordinates Approach. Am. J. Theor. Appl. Stat. 2016, 4(6), 640-643. doi: 10.11648/j.ajtas.20150406.36

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AMA Style

Umeh Edith Uzoma, Awopeju Kabir Abidemi, Ajibade F. Bright. Detection of Multicollinearity Using Min-Max and Point-Coordinates Approach. Am J Theor Appl Stat. 2016;4(6):640-643. doi: 10.11648/j.ajtas.20150406.36

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@article{10.11648/j.ajtas.20150406.36,
  author = {Umeh Edith Uzoma and Awopeju Kabir Abidemi and Ajibade F. Bright},
  title = {Detection of Multicollinearity Using Min-Max and Point-Coordinates Approach},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {4},
  number = {6},
  pages = {640-643},
  doi = {10.11648/j.ajtas.20150406.36},
  url = {https://doi.org/10.11648/j.ajtas.20150406.36},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150406.36},
  abstract = {Multicollinearity is one of the problems or challenges of modeling or multiple regression usually encountered by Economists and Statisticians. It is a situation where by some of the independent variables in the formulated model are significantly or highly related/correlated. In the past, methods such as Variance Inflation Factor, Eigenvalue and Product moment correlation have been used by researchers to detect multicollinearity in models such as financial models, fluctuation of market price model, determination of factors responsible for survival of man and market model, etc. The shortfalls of these methods include rigorous computation which discourages researchers from testing for multicollinearity, even when necessary. This paper presents moderate and easy algorithm of the detection of multicollinearity among variables no matter their numbers. Using Min-Max approach with the principle of parallelism of coordinates, we are able to present an algorithm for the detection of multicollinearity with appropriate illustrative examples.},
 year = {2016}
}

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TY  - JOUR
T1  - Detection of Multicollinearity Using Min-Max and Point-Coordinates Approach
AU  - Umeh Edith Uzoma
AU  - Awopeju Kabir Abidemi
AU  - Ajibade F. Bright
Y1  - 2016/01/23
PY  - 2016
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DO  - 10.11648/j.ajtas.20150406.36
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
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PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20150406.36
AB  - Multicollinearity is one of the problems or challenges of modeling or multiple regression usually encountered by Economists and Statisticians. It is a situation where by some of the independent variables in the formulated model are significantly or highly related/correlated. In the past, methods such as Variance Inflation Factor, Eigenvalue and Product moment correlation have been used by researchers to detect multicollinearity in models such as financial models, fluctuation of market price model, determination of factors responsible for survival of man and market model, etc. The shortfalls of these methods include rigorous computation which discourages researchers from testing for multicollinearity, even when necessary. This paper presents moderate and easy algorithm of the detection of multicollinearity among variables no matter their numbers. Using Min-Max approach with the principle of parallelism of coordinates, we are able to present an algorithm for the detection of multicollinearity with appropriate illustrative examples.
VL  - 4
IS  - 6
ER  -

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Author Information

Umeh Edith Uzoma

Department of Statistics, Nnamdi Azikiwe University, Awka, Anambra State, Nigeria
Awopeju Kabir Abidemi

Department of Statistics, Nnamdi Azikiwe University, Awka, Anambra State, Nigeria
Ajibade F. Bright

Department of General Studies, Petroleum Training Institute, Effurun, Delta State, Nigeria

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APA Style

Umeh Edith Uzoma, Awopeju Kabir Abidemi, Ajibade F. Bright. (2016). Detection of Multicollinearity Using Min-Max and Point-Coordinates Approach. American Journal of Theoretical and Applied Statistics, 4(6), 640-643. https://doi.org/10.11648/j.ajtas.20150406.36

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ACS Style

Umeh Edith Uzoma; Awopeju Kabir Abidemi; Ajibade F. Bright. Detection of Multicollinearity Using Min-Max and Point-Coordinates Approach. Am. J. Theor. Appl. Stat. 2016, 4(6), 640-643. doi: 10.11648/j.ajtas.20150406.36

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AMA Style

Umeh Edith Uzoma, Awopeju Kabir Abidemi, Ajibade F. Bright. Detection of Multicollinearity Using Min-Max and Point-Coordinates Approach. Am J Theor Appl Stat. 2016;4(6):640-643. doi: 10.11648/j.ajtas.20150406.36

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@article{10.11648/j.ajtas.20150406.36,
  author = {Umeh Edith Uzoma and Awopeju Kabir Abidemi and Ajibade F. Bright},
  title = {Detection of Multicollinearity Using Min-Max and Point-Coordinates Approach},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {4},
  number = {6},
  pages = {640-643},
  doi = {10.11648/j.ajtas.20150406.36},
  url = {https://doi.org/10.11648/j.ajtas.20150406.36},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150406.36},
  abstract = {Multicollinearity is one of the problems or challenges of modeling or multiple regression usually encountered by Economists and Statisticians. It is a situation where by some of the independent variables in the formulated model are significantly or highly related/correlated. In the past, methods such as Variance Inflation Factor, Eigenvalue and Product moment correlation have been used by researchers to detect multicollinearity in models such as financial models, fluctuation of market price model, determination of factors responsible for survival of man and market model, etc. The shortfalls of these methods include rigorous computation which discourages researchers from testing for multicollinearity, even when necessary. This paper presents moderate and easy algorithm of the detection of multicollinearity among variables no matter their numbers. Using Min-Max approach with the principle of parallelism of coordinates, we are able to present an algorithm for the detection of multicollinearity with appropriate illustrative examples.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Detection of Multicollinearity Using Min-Max and Point-Coordinates Approach
AU  - Umeh Edith Uzoma
AU  - Awopeju Kabir Abidemi
AU  - Ajibade F. Bright
Y1  - 2016/01/23
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20150406.36
DO  - 10.11648/j.ajtas.20150406.36
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  - 640
EP  - 643
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20150406.36
AB  - Multicollinearity is one of the problems or challenges of modeling or multiple regression usually encountered by Economists and Statisticians. It is a situation where by some of the independent variables in the formulated model are significantly or highly related/correlated. In the past, methods such as Variance Inflation Factor, Eigenvalue and Product moment correlation have been used by researchers to detect multicollinearity in models such as financial models, fluctuation of market price model, determination of factors responsible for survival of man and market model, etc. The shortfalls of these methods include rigorous computation which discourages researchers from testing for multicollinearity, even when necessary. This paper presents moderate and easy algorithm of the detection of multicollinearity among variables no matter their numbers. Using Min-Max approach with the principle of parallelism of coordinates, we are able to present an algorithm for the detection of multicollinearity with appropriate illustrative examples.
VL  - 4
IS  - 6
ER  -

Copy | Download