Modeling Dependence Relationships of Anthropometric Variables Using Copula Approach

Funmilayo Westnand Oshogboye Saporu; Isaac Esbond Gongsin

doi:doi:10.11648/j.ajtas.20200905.18

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Modeling Dependence Relationships of Anthropometric Variables Using Copula Approach

Funmilayo Westnand Oshogboye Saporu, Isaac Esbond Gongsin

Published in American Journal of Theoretical and Applied Statistics (Volume 9, Issue 5)

Received: 3 September 2020 Accepted: 21 September 2020 Published: 22 October 2020

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Abstract

Copula model is introduced in modeling the co-dependence structures of anthropometric variables-Body mass index (BMI), Abdominal circumference, Adiposity and Percent body fat-because it can capture monotonic dependence. Four copula-based Kumaraswamy-epsilon distributions are derived and used to determine the best fit to the anthropometric data, these are new. These are the Gaussian, Clayton, Frank and Gumbel copulas. Clayton model provided the best fit in four bivariate pairs-BMI and Percent body fat, BMI and Abdominal circumference, Adiposity and Abdominal circumference and Abdominal circumference and Percent body fat-while Gaussian is best for BMI and Adiposity pair and Frank is best for Adiposity and Percent body fat pair. Copula-based Kendall’s tau and tail dependence are used as estimates for measuring the strength of the co-dependence. The results strongly recommend the use of BMI as an anthropometric index for estimating human body composition of adiposity. However for individuals with BMI values in the two extreme tails, their adiposity should be measured directly. The results do not find any suitable anthropometric indices for estimating percent body fat and therefore is recommended that for such epidemiological research, percent body fat should be measured directly. The results also clearly show that the Kendall’s tau and the corresponding Pearson correlation coefficient estimates are largely at variance whenever the co-dependence structure cannot be described as linear dependence. This can prompt contradictory conclusions. It is therefore suggested that for such research, whenever Pearson correlation coefficient method is in use, a coefficient of determination of a minimum of 75% should be obtained before any anthropometric index can be recommended for body composition substitution.

Published in	American Journal of Theoretical and Applied Statistics (Volume 9, Issue 5)
DOI	10.11648/j.ajtas.20200905.18
Page(s)	245-255
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), 2020. Published by Science Publishing Group

Keywords

Anthropometric Index, Body Composition, Correlation Matrix, Inference Function for Margin, Kendall’s Tau, Kumaraswamy-epsilon Distribution, Monotonic Dependence

References

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Funmilayo Westnand Oshogboye Saporu, Isaac Esbond Gongsin. (2020). Modeling Dependence Relationships of Anthropometric Variables Using Copula Approach. American Journal of Theoretical and Applied Statistics, 9(5), 245-255. https://doi.org/10.11648/j.ajtas.20200905.18

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Funmilayo Westnand Oshogboye Saporu; Isaac Esbond Gongsin. Modeling Dependence Relationships of Anthropometric Variables Using Copula Approach. Am. J. Theor. Appl. Stat. 2020, 9(5), 245-255. doi: 10.11648/j.ajtas.20200905.18

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AMA Style

Funmilayo Westnand Oshogboye Saporu, Isaac Esbond Gongsin. Modeling Dependence Relationships of Anthropometric Variables Using Copula Approach. Am J Theor Appl Stat. 2020;9(5):245-255. doi: 10.11648/j.ajtas.20200905.18

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@article{10.11648/j.ajtas.20200905.18,
  author = {Funmilayo Westnand Oshogboye Saporu and Isaac Esbond Gongsin},
  title = {Modeling Dependence Relationships of Anthropometric Variables Using Copula Approach},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {9},
  number = {5},
  pages = {245-255},
  doi = {10.11648/j.ajtas.20200905.18},
  url = {https://doi.org/10.11648/j.ajtas.20200905.18},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20200905.18},
  abstract = {Copula model is introduced in modeling the co-dependence structures of anthropometric variables-Body mass index (BMI), Abdominal circumference, Adiposity and Percent body fat-because it can capture monotonic dependence. Four copula-based Kumaraswamy-epsilon distributions are derived and used to determine the best fit to the anthropometric data, these are new. These are the Gaussian, Clayton, Frank and Gumbel copulas. Clayton model provided the best fit in four bivariate pairs-BMI and Percent body fat, BMI and Abdominal circumference, Adiposity and Abdominal circumference and Abdominal circumference and Percent body fat-while Gaussian is best for BMI and Adiposity pair and Frank is best for Adiposity and Percent body fat pair. Copula-based Kendall’s tau and tail dependence are used as estimates for measuring the strength of the co-dependence. The results strongly recommend the use of BMI as an anthropometric index for estimating human body composition of adiposity. However for individuals with BMI values in the two extreme tails, their adiposity should be measured directly. The results do not find any suitable anthropometric indices for estimating percent body fat and therefore is recommended that for such epidemiological research, percent body fat should be measured directly. The results also clearly show that the Kendall’s tau and the corresponding Pearson correlation coefficient estimates are largely at variance whenever the co-dependence structure cannot be described as linear dependence. This can prompt contradictory conclusions. It is therefore suggested that for such research, whenever Pearson correlation coefficient method is in use, a coefficient of determination of a minimum of 75% should be obtained before any anthropometric index can be recommended for body composition substitution.},
 year = {2020}
}

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TY  - JOUR
T1  - Modeling Dependence Relationships of Anthropometric Variables Using Copula Approach
AU  - Funmilayo Westnand Oshogboye Saporu
AU  - Isaac Esbond Gongsin
Y1  - 2020/10/22
PY  - 2020
N1  - https://doi.org/10.11648/j.ajtas.20200905.18
DO  - 10.11648/j.ajtas.20200905.18
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  - 245
EP  - 255
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20200905.18
AB  - Copula model is introduced in modeling the co-dependence structures of anthropometric variables-Body mass index (BMI), Abdominal circumference, Adiposity and Percent body fat-because it can capture monotonic dependence. Four copula-based Kumaraswamy-epsilon distributions are derived and used to determine the best fit to the anthropometric data, these are new. These are the Gaussian, Clayton, Frank and Gumbel copulas. Clayton model provided the best fit in four bivariate pairs-BMI and Percent body fat, BMI and Abdominal circumference, Adiposity and Abdominal circumference and Abdominal circumference and Percent body fat-while Gaussian is best for BMI and Adiposity pair and Frank is best for Adiposity and Percent body fat pair. Copula-based Kendall’s tau and tail dependence are used as estimates for measuring the strength of the co-dependence. The results strongly recommend the use of BMI as an anthropometric index for estimating human body composition of adiposity. However for individuals with BMI values in the two extreme tails, their adiposity should be measured directly. The results do not find any suitable anthropometric indices for estimating percent body fat and therefore is recommended that for such epidemiological research, percent body fat should be measured directly. The results also clearly show that the Kendall’s tau and the corresponding Pearson correlation coefficient estimates are largely at variance whenever the co-dependence structure cannot be described as linear dependence. This can prompt contradictory conclusions. It is therefore suggested that for such research, whenever Pearson correlation coefficient method is in use, a coefficient of determination of a minimum of 75% should be obtained before any anthropometric index can be recommended for body composition substitution.
VL  - 9
IS  - 5
ER  -

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Author Information

Funmilayo Westnand Oshogboye Saporu

National Mathematical Centre, Kwali, Abuja, Nigeria
Isaac Esbond Gongsin

Department of Mathematical Sciences, University of Maiduguri, Maiduguri, Nigeria

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Funmilayo Westnand Oshogboye Saporu, Isaac Esbond Gongsin. (2020). Modeling Dependence Relationships of Anthropometric Variables Using Copula Approach. American Journal of Theoretical and Applied Statistics, 9(5), 245-255. https://doi.org/10.11648/j.ajtas.20200905.18

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ACS Style

Funmilayo Westnand Oshogboye Saporu; Isaac Esbond Gongsin. Modeling Dependence Relationships of Anthropometric Variables Using Copula Approach. Am. J. Theor. Appl. Stat. 2020, 9(5), 245-255. doi: 10.11648/j.ajtas.20200905.18

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AMA Style

Funmilayo Westnand Oshogboye Saporu, Isaac Esbond Gongsin. Modeling Dependence Relationships of Anthropometric Variables Using Copula Approach. Am J Theor Appl Stat. 2020;9(5):245-255. doi: 10.11648/j.ajtas.20200905.18

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@article{10.11648/j.ajtas.20200905.18,
  author = {Funmilayo Westnand Oshogboye Saporu and Isaac Esbond Gongsin},
  title = {Modeling Dependence Relationships of Anthropometric Variables Using Copula Approach},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {9},
  number = {5},
  pages = {245-255},
  doi = {10.11648/j.ajtas.20200905.18},
  url = {https://doi.org/10.11648/j.ajtas.20200905.18},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20200905.18},
  abstract = {Copula model is introduced in modeling the co-dependence structures of anthropometric variables-Body mass index (BMI), Abdominal circumference, Adiposity and Percent body fat-because it can capture monotonic dependence. Four copula-based Kumaraswamy-epsilon distributions are derived and used to determine the best fit to the anthropometric data, these are new. These are the Gaussian, Clayton, Frank and Gumbel copulas. Clayton model provided the best fit in four bivariate pairs-BMI and Percent body fat, BMI and Abdominal circumference, Adiposity and Abdominal circumference and Abdominal circumference and Percent body fat-while Gaussian is best for BMI and Adiposity pair and Frank is best for Adiposity and Percent body fat pair. Copula-based Kendall’s tau and tail dependence are used as estimates for measuring the strength of the co-dependence. The results strongly recommend the use of BMI as an anthropometric index for estimating human body composition of adiposity. However for individuals with BMI values in the two extreme tails, their adiposity should be measured directly. The results do not find any suitable anthropometric indices for estimating percent body fat and therefore is recommended that for such epidemiological research, percent body fat should be measured directly. The results also clearly show that the Kendall’s tau and the corresponding Pearson correlation coefficient estimates are largely at variance whenever the co-dependence structure cannot be described as linear dependence. This can prompt contradictory conclusions. It is therefore suggested that for such research, whenever Pearson correlation coefficient method is in use, a coefficient of determination of a minimum of 75% should be obtained before any anthropometric index can be recommended for body composition substitution.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Modeling Dependence Relationships of Anthropometric Variables Using Copula Approach
AU  - Funmilayo Westnand Oshogboye Saporu
AU  - Isaac Esbond Gongsin
Y1  - 2020/10/22
PY  - 2020
N1  - https://doi.org/10.11648/j.ajtas.20200905.18
DO  - 10.11648/j.ajtas.20200905.18
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  - 245
EP  - 255
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20200905.18
AB  - Copula model is introduced in modeling the co-dependence structures of anthropometric variables-Body mass index (BMI), Abdominal circumference, Adiposity and Percent body fat-because it can capture monotonic dependence. Four copula-based Kumaraswamy-epsilon distributions are derived and used to determine the best fit to the anthropometric data, these are new. These are the Gaussian, Clayton, Frank and Gumbel copulas. Clayton model provided the best fit in four bivariate pairs-BMI and Percent body fat, BMI and Abdominal circumference, Adiposity and Abdominal circumference and Abdominal circumference and Percent body fat-while Gaussian is best for BMI and Adiposity pair and Frank is best for Adiposity and Percent body fat pair. Copula-based Kendall’s tau and tail dependence are used as estimates for measuring the strength of the co-dependence. The results strongly recommend the use of BMI as an anthropometric index for estimating human body composition of adiposity. However for individuals with BMI values in the two extreme tails, their adiposity should be measured directly. The results do not find any suitable anthropometric indices for estimating percent body fat and therefore is recommended that for such epidemiological research, percent body fat should be measured directly. The results also clearly show that the Kendall’s tau and the corresponding Pearson correlation coefficient estimates are largely at variance whenever the co-dependence structure cannot be described as linear dependence. This can prompt contradictory conclusions. It is therefore suggested that for such research, whenever Pearson correlation coefficient method is in use, a coefficient of determination of a minimum of 75% should be obtained before any anthropometric index can be recommended for body composition substitution.
VL  - 9
IS  - 5
ER  -

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