On the Comparison of Some Link Functions of Binary Response Analysis Under Symmetric and Asymmetric Assumptions

Saddam Adams Damisa; Musa Tasi’u; Salamatu Yusuf Bello; Farouq Ndamadu Musa; Nurudeen Ayobami Ajadi; Samson Agboola

doi:doi:10.11648/j.bsi.20170204.13

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On the Comparison of Some Link Functions of Binary Response Analysis Under Symmetric and Asymmetric Assumptions

Saddam Adams Damisa, Musa Tasi’u, Salamatu Yusuf Bello, Farouq Ndamadu Musa, Nurudeen Ayobami Ajadi, Samson Agboola

Published in Biomedical Statistics and Informatics (Volume 2, Issue 4)

Received: 1 August 2017 Accepted: 29 August 2017 Published: 23 September 2017

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Abstract

Binary response analysis is modeled when the response variable is nominal and as such violates the use of the ordinary linear regression model. This paper utilizes the classical approach to fit a categorical response regression model using the logit, probit. loglog and the complementary loglog (Cloglog) link functions under symmetric and asymmetric assumptions. It is captured in past studies that we can only make comparisons between these link functions when n is large say (n > 1000), In this study we compared the link functions to investigate this claim with small values of n less than 1000. We fit the Cloglog and loglog models on 600 tuberculosis patients who may be co-infected with hypertension while the R package was initiated in simulating a binary data for fitting the logit and probit models using the Akaike Information Criterion (AIC) as a basis of comparison for the symmetric and asymmetric different model fitting techniques. The result of the simulated data of sample size 50 revealed that there is a difference between the two symmetric link functions with differing values of AIC with the Probit outperforming the logit link having least values of AIC which indicates that the probit link should be preferred under the symmetric assumption. While under the asymmetric link functions the loglog outperformed the cloglog with smaller values of AIC utilized on the life dataset which gives us the notion that the loglog link should be preferred under the asymmetric assumption. Furthermore table 6 also indicates that type of occupation is the only significant factor associated with hypertension in tuberculosis infected patients under study using both the cloglog and loglog link functions. On this note we recommend that patients with diabetes should be given less strenuous jobs and occupations to handle. Finally we were able to show that the link functions can be distinguished even with small values of (n < 1000) under the two assumptions.

Published in	Biomedical Statistics and Informatics (Volume 2, Issue 4)
DOI	10.11648/j.bsi.20170204.13
Page(s)	145-149
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), 2017. Published by Science Publishing Group

Keywords

Binary Responses Analysis, Loglog, Cloglog, Probit and Logit Links

References

[1]	Long, J. S. (1997). Regression Models for Categorical and Limited Dependent Variables. Thousand Oaks, CA: Sage.
[2]	Albert, J. H. and S. Chib (1993). Bayesian Analysis of Binary and Polychotomous Response Data. Journal of the American Statistical Association 88, 669–679.
[3]	Chambers, E. A. and D. R. Cox (1967). Discrimination between alternative Binary Response Models. Biometrika 54, 573–578.
[4]	Mc Cullagh, P., and Nelder, J. A. (1989), Generalized Linear Models, 2nd ed, London: Chapman and Hall.
[5]	Gill, J. (2001). Generalized Linear Models: A Unified Approach. Thousand Oaks, CA: Sage.
[6]	Maddala, G. S. (1983). Limited-Dependent and Qualitative Variables in Econometrics. Cambridge: Cambridge University Press.
[7]	Davidson, R. and J. G. MacKinnon (1993). Estimation and Inference in Econometrics. New York: Oxford.
[8]	Powers, D. A. and Y. Xie (2000). Statistical Methods for Categorical Data Analysis. San Diego: Academic Press.
[9]	Fahrmeir, L. and G. Tutz (2001). Multivariate Statistical Modelling Based on Generalized Linear Models (2nd ed.). New York: Springer.
[10]	Hardin, J. and J. Hilbe (2001). Generalized Linear Models and Extensions. College Station, TX: Stata Press.
[11]	Krejcie, R. V. and D. W. Morgan (1970) Determining Sample Sizes for Research Activities. Educational and Psychological Measurement 30, 607-610.
[12]	Kass, R. E. and A. E. Raftery (1995). Bayes Factors. Journal of the American Statistical Association 90, 773–794.
[13]	Spiegelhalter, D. J., N. G. Best, B. P. Carlin, and A. van der Linde (2002). Bayesian Measures of Model Complexity and Fit (with discussion). Journal of the Royal Statistical Society: Series B 64, 583–639.
[14]	Akaike, H. (1973). Information Theory and an Extension of the Maximum Likelihood Principle. In B. N. Petrov and F. Csaki (Eds.), Proceedings of the Second International Symposium on Information Theory, pp. 267–281. Budapest: Akademiai Kiado. Reprinted in breakthroughs in Statistics, vol. 1, pp. 610-624, eds. Kotz, S.
[15]	Man-suk, Oh, Eun, Sug Park and Boeng-Soo, So (2016) Bayesian Variable Selection in Binary Quantile Regression. Statistics and Probability Letters.

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APA Style

Saddam Adams Damisa, Musa Tasi’u, Salamatu Yusuf Bello, Farouq Ndamadu Musa, Nurudeen Ayobami Ajadi, et al. (2017). On the Comparison of Some Link Functions of Binary Response Analysis Under Symmetric and Asymmetric Assumptions. Biomedical Statistics and Informatics, 2(4), 145-149. https://doi.org/10.11648/j.bsi.20170204.13

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ACS Style

Saddam Adams Damisa; Musa Tasi’u; Salamatu Yusuf Bello; Farouq Ndamadu Musa; Nurudeen Ayobami Ajadi, et al. On the Comparison of Some Link Functions of Binary Response Analysis Under Symmetric and Asymmetric Assumptions. Biomed. Stat. Inform. 2017, 2(4), 145-149. doi: 10.11648/j.bsi.20170204.13

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AMA Style

Saddam Adams Damisa, Musa Tasi’u, Salamatu Yusuf Bello, Farouq Ndamadu Musa, Nurudeen Ayobami Ajadi, et al. On the Comparison of Some Link Functions of Binary Response Analysis Under Symmetric and Asymmetric Assumptions. Biomed Stat Inform. 2017;2(4):145-149. doi: 10.11648/j.bsi.20170204.13

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@article{10.11648/j.bsi.20170204.13,
  author = {Saddam Adams Damisa and Musa Tasi’u and Salamatu Yusuf Bello and Farouq Ndamadu Musa and Nurudeen Ayobami Ajadi and Samson Agboola},
  title = {On the Comparison of Some Link Functions of Binary Response Analysis Under Symmetric and Asymmetric Assumptions},
  journal = {Biomedical Statistics and Informatics},
  volume = {2},
  number = {4},
  pages = {145-149},
  doi = {10.11648/j.bsi.20170204.13},
  url = {https://doi.org/10.11648/j.bsi.20170204.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.bsi.20170204.13},
  abstract = {Binary response analysis is modeled when the response variable is nominal and as such violates the use of the ordinary linear regression model. This paper utilizes the classical approach to fit a categorical response regression model using the logit, probit. loglog and the complementary loglog (Cloglog) link functions under symmetric and asymmetric assumptions. It is captured in past studies that we can only make comparisons between these link functions when n is large say (n > 1000), In this study we compared the link functions to investigate this claim with small values of n less than 1000. We fit the Cloglog and loglog models on 600 tuberculosis patients who may be co-infected with hypertension while the R package was initiated in simulating a binary data for fitting the logit and probit models using the Akaike Information Criterion (AIC) as a basis of comparison for the symmetric and asymmetric different model fitting techniques. The result of the simulated data of sample size 50 revealed that there is a difference between the two symmetric link functions with differing values of AIC with the Probit outperforming the logit link having least values of AIC which indicates that the probit link should be preferred under the symmetric assumption. While under the asymmetric link functions the loglog outperformed the cloglog with smaller values of AIC utilized on the life dataset which gives us the notion that the loglog link should be preferred under the asymmetric assumption. Furthermore table 6 also indicates that type of occupation is the only significant factor associated with hypertension in tuberculosis infected patients under study using both the cloglog and loglog link functions. On this note we recommend that patients with diabetes should be given less strenuous jobs and occupations to handle. Finally we were able to show that the link functions can be distinguished even with small values of (n < 1000) under the two assumptions.},
 year = {2017}
}

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TY  - JOUR
T1  - On the Comparison of Some Link Functions of Binary Response Analysis Under Symmetric and Asymmetric Assumptions
AU  - Saddam Adams Damisa
AU  - Musa Tasi’u
AU  - Salamatu Yusuf Bello
AU  - Farouq Ndamadu Musa
AU  - Nurudeen Ayobami Ajadi
AU  - Samson Agboola
Y1  - 2017/09/23
PY  - 2017
N1  - https://doi.org/10.11648/j.bsi.20170204.13
DO  - 10.11648/j.bsi.20170204.13
T2  - Biomedical Statistics and Informatics
JF  - Biomedical Statistics and Informatics
JO  - Biomedical Statistics and Informatics
SP  - 145
EP  - 149
PB  - Science Publishing Group
SN  - 2578-8728
UR  - https://doi.org/10.11648/j.bsi.20170204.13
AB  - Binary response analysis is modeled when the response variable is nominal and as such violates the use of the ordinary linear regression model. This paper utilizes the classical approach to fit a categorical response regression model using the logit, probit. loglog and the complementary loglog (Cloglog) link functions under symmetric and asymmetric assumptions. It is captured in past studies that we can only make comparisons between these link functions when n is large say (n > 1000), In this study we compared the link functions to investigate this claim with small values of n less than 1000. We fit the Cloglog and loglog models on 600 tuberculosis patients who may be co-infected with hypertension while the R package was initiated in simulating a binary data for fitting the logit and probit models using the Akaike Information Criterion (AIC) as a basis of comparison for the symmetric and asymmetric different model fitting techniques. The result of the simulated data of sample size 50 revealed that there is a difference between the two symmetric link functions with differing values of AIC with the Probit outperforming the logit link having least values of AIC which indicates that the probit link should be preferred under the symmetric assumption. While under the asymmetric link functions the loglog outperformed the cloglog with smaller values of AIC utilized on the life dataset which gives us the notion that the loglog link should be preferred under the asymmetric assumption. Furthermore table 6 also indicates that type of occupation is the only significant factor associated with hypertension in tuberculosis infected patients under study using both the cloglog and loglog link functions. On this note we recommend that patients with diabetes should be given less strenuous jobs and occupations to handle. Finally we were able to show that the link functions can be distinguished even with small values of (n < 1000) under the two assumptions.
VL  - 2
IS  - 4
ER  -

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Author Information

Saddam Adams Damisa

Department of Statistics, Ahmadu Bello University, Zaria, Nigeria
Musa Tasi’u

Department of Statistics, Ahmadu Bello University, Zaria, Nigeria
Salamatu Yusuf Bello

Department of Statistics, Ahmadu Bello University, Zaria, Nigeria
Farouq Ndamadu Musa

Department of Mathematics and Statistics, Kaduna Polytechnic, Kaduna, Nigeria
Nurudeen Ayobami Ajadi

Department of Statistics, College of Physical Sciences, Federal University of Agriculture, Abeokuta, Nigeria
Samson Agboola

Department of Statistics, Ahmadu Bello University, Zaria, Nigeria

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APA Style

Saddam Adams Damisa, Musa Tasi’u, Salamatu Yusuf Bello, Farouq Ndamadu Musa, Nurudeen Ayobami Ajadi, et al. (2017). On the Comparison of Some Link Functions of Binary Response Analysis Under Symmetric and Asymmetric Assumptions. Biomedical Statistics and Informatics, 2(4), 145-149. https://doi.org/10.11648/j.bsi.20170204.13

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ACS Style

Saddam Adams Damisa; Musa Tasi’u; Salamatu Yusuf Bello; Farouq Ndamadu Musa; Nurudeen Ayobami Ajadi, et al. On the Comparison of Some Link Functions of Binary Response Analysis Under Symmetric and Asymmetric Assumptions. Biomed. Stat. Inform. 2017, 2(4), 145-149. doi: 10.11648/j.bsi.20170204.13

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AMA Style

Saddam Adams Damisa, Musa Tasi’u, Salamatu Yusuf Bello, Farouq Ndamadu Musa, Nurudeen Ayobami Ajadi, et al. On the Comparison of Some Link Functions of Binary Response Analysis Under Symmetric and Asymmetric Assumptions. Biomed Stat Inform. 2017;2(4):145-149. doi: 10.11648/j.bsi.20170204.13

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@article{10.11648/j.bsi.20170204.13,
  author = {Saddam Adams Damisa and Musa Tasi’u and Salamatu Yusuf Bello and Farouq Ndamadu Musa and Nurudeen Ayobami Ajadi and Samson Agboola},
  title = {On the Comparison of Some Link Functions of Binary Response Analysis Under Symmetric and Asymmetric Assumptions},
  journal = {Biomedical Statistics and Informatics},
  volume = {2},
  number = {4},
  pages = {145-149},
  doi = {10.11648/j.bsi.20170204.13},
  url = {https://doi.org/10.11648/j.bsi.20170204.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.bsi.20170204.13},
  abstract = {Binary response analysis is modeled when the response variable is nominal and as such violates the use of the ordinary linear regression model. This paper utilizes the classical approach to fit a categorical response regression model using the logit, probit. loglog and the complementary loglog (Cloglog) link functions under symmetric and asymmetric assumptions. It is captured in past studies that we can only make comparisons between these link functions when n is large say (n > 1000), In this study we compared the link functions to investigate this claim with small values of n less than 1000. We fit the Cloglog and loglog models on 600 tuberculosis patients who may be co-infected with hypertension while the R package was initiated in simulating a binary data for fitting the logit and probit models using the Akaike Information Criterion (AIC) as a basis of comparison for the symmetric and asymmetric different model fitting techniques. The result of the simulated data of sample size 50 revealed that there is a difference between the two symmetric link functions with differing values of AIC with the Probit outperforming the logit link having least values of AIC which indicates that the probit link should be preferred under the symmetric assumption. While under the asymmetric link functions the loglog outperformed the cloglog with smaller values of AIC utilized on the life dataset which gives us the notion that the loglog link should be preferred under the asymmetric assumption. Furthermore table 6 also indicates that type of occupation is the only significant factor associated with hypertension in tuberculosis infected patients under study using both the cloglog and loglog link functions. On this note we recommend that patients with diabetes should be given less strenuous jobs and occupations to handle. Finally we were able to show that the link functions can be distinguished even with small values of (n < 1000) under the two assumptions.},
 year = {2017}
}

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TY  - JOUR
T1  - On the Comparison of Some Link Functions of Binary Response Analysis Under Symmetric and Asymmetric Assumptions
AU  - Saddam Adams Damisa
AU  - Musa Tasi’u
AU  - Salamatu Yusuf Bello
AU  - Farouq Ndamadu Musa
AU  - Nurudeen Ayobami Ajadi
AU  - Samson Agboola
Y1  - 2017/09/23
PY  - 2017
N1  - https://doi.org/10.11648/j.bsi.20170204.13
DO  - 10.11648/j.bsi.20170204.13
T2  - Biomedical Statistics and Informatics
JF  - Biomedical Statistics and Informatics
JO  - Biomedical Statistics and Informatics
SP  - 145
EP  - 149
PB  - Science Publishing Group
SN  - 2578-8728
UR  - https://doi.org/10.11648/j.bsi.20170204.13
AB  - Binary response analysis is modeled when the response variable is nominal and as such violates the use of the ordinary linear regression model. This paper utilizes the classical approach to fit a categorical response regression model using the logit, probit. loglog and the complementary loglog (Cloglog) link functions under symmetric and asymmetric assumptions. It is captured in past studies that we can only make comparisons between these link functions when n is large say (n > 1000), In this study we compared the link functions to investigate this claim with small values of n less than 1000. We fit the Cloglog and loglog models on 600 tuberculosis patients who may be co-infected with hypertension while the R package was initiated in simulating a binary data for fitting the logit and probit models using the Akaike Information Criterion (AIC) as a basis of comparison for the symmetric and asymmetric different model fitting techniques. The result of the simulated data of sample size 50 revealed that there is a difference between the two symmetric link functions with differing values of AIC with the Probit outperforming the logit link having least values of AIC which indicates that the probit link should be preferred under the symmetric assumption. While under the asymmetric link functions the loglog outperformed the cloglog with smaller values of AIC utilized on the life dataset which gives us the notion that the loglog link should be preferred under the asymmetric assumption. Furthermore table 6 also indicates that type of occupation is the only significant factor associated with hypertension in tuberculosis infected patients under study using both the cloglog and loglog link functions. On this note we recommend that patients with diabetes should be given less strenuous jobs and occupations to handle. Finally we were able to show that the link functions can be distinguished even with small values of (n < 1000) under the two assumptions.
VL  - 2
IS  - 4
ER  -

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