Generating Spatial Correlated Binary Data Through a Copulas Method

Renhao Jin; Sha Wang; Fang Yan; Jie Zhu

doi:doi:10.11648/j.sr.20150304.18

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Generating Spatial Correlated Binary Data Through a Copulas Method

Renhao Jin, Sha Wang, Fang Yan, Jie Zhu

Published in Science Research (Volume 3, Issue 4)

Received: 5 July 2015 Accepted: 16 July 2015 Published: 25 July 2015

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Abstract

Simulating spatial correlated binary data is very important on many cases, but it is not easily to accomplish, as there are restrictions on the parameters of Bernoulli variables. This paper develops a copulas method to generate spatial correlated binary data. The spatial binary data generated by this method has an inverse spatial pattern comparing with the latent Gaussian random field data, however they have similar empirical variograms, although the closed form for the spatial correlation is not available specifically.

Published in	Science Research (Volume 3, Issue 4)
DOI	10.11648/j.sr.20150304.18
Page(s)	206-212
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

Spatial Binary Data, Copulas, Simulation, Variogram

References

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[6]	Gotway, C. A., & Stroup, W. W. (1997). A generalized linear model approach to spatial data analysis and prediction. Journal of Agricultural, Biological, and Environmental Statistics, 2(2), 157-178.
[7]	Jin, R. & Kelly G.E. (2015): Comparison of Sampling Grids, Cut Off Distance and Type of Residuals in Parametric Variogram Estimation. Communications in Statistics - Simulation and Computation, DOI: 10.1080/03610918.2015.1011785
[8]	Lunn, A. D., & Davies, S. J. (1998). A note on generating correlated binary variables. Biometrika, 85(2), 487-490.
[9]	Liang, K. Y., & Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73(1), 13-22.
[10]	Nelsen, Roger B. (1999), An Introduction to Copulas, New York: Springer, ISBN 0-387-98623-5
[11]	Park, C. G., Park, T., & Shin, D. W. (1996). A simple method for generating correlated binary variates. The American Statistician, 50(4), 306-310.
[12]	Qaqish, B. F. (2003). A family of multivariate binary distributions for simulating correlated binary variables with specified marginal means and correlations.Biometrika, 90(2), 455-463.
[13]	SAS Institute Inc, (2008). SAS/STAT® 9.2 User’s Guide: The GLIMMIX Procedure (Book Excerpt). NC: SAS Institute Inc, Cary.
[14]	SAS Institute Inc, (2008). SAS/STAT® 9.2 User’s Guide: The SIM2D Procedure (Book Excerpt). NC: SAS Institute Inc, Cary.
[15]	Schabenberger, O. and Gotway, C. A. (2005). Statistical methods for spatial data analysis, Chapman & Hall/CRC, Boca Raton.
[16]	Stiratelli, R., Laird, N., & Ware, J. H. (1984). Random-effects models for serial observations with binary response. Biometrics, 961-971.
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[18]	Wolfinger, R., & O'connell, M. (1993). Generalized linear mixed models a pseudo-likelihood approach. Journal of statistical Computation and Simulation,48(3-4), 233-243.
[19]	Zeger, S. L., & Liang, K. Y. (1986). Longitudinal data analysis for discrete and continuous outcomes. Biometrics, 42(1), 121-130.
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Renhao Jin, Sha Wang, Fang Yan, Jie Zhu. (2015). Generating Spatial Correlated Binary Data Through a Copulas Method. Science Research, 3(4), 206-212. https://doi.org/10.11648/j.sr.20150304.18

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ACS Style

Renhao Jin; Sha Wang; Fang Yan; Jie Zhu. Generating Spatial Correlated Binary Data Through a Copulas Method. Sci. Res. 2015, 3(4), 206-212. doi: 10.11648/j.sr.20150304.18

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AMA Style

Renhao Jin, Sha Wang, Fang Yan, Jie Zhu. Generating Spatial Correlated Binary Data Through a Copulas Method. Sci Res. 2015;3(4):206-212. doi: 10.11648/j.sr.20150304.18

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@article{10.11648/j.sr.20150304.18,
  author = {Renhao Jin and Sha Wang and Fang Yan and Jie Zhu},
  title = {Generating Spatial Correlated Binary Data Through a Copulas Method},
  journal = {Science Research},
  volume = {3},
  number = {4},
  pages = {206-212},
  doi = {10.11648/j.sr.20150304.18},
  url = {https://doi.org/10.11648/j.sr.20150304.18},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sr.20150304.18},
  abstract = {Simulating spatial correlated binary data is very important on many cases, but it is not easily to accomplish, as there are restrictions on the parameters of Bernoulli variables. This paper develops a copulas method to generate spatial correlated binary data. The spatial binary data generated by this method has an inverse spatial pattern comparing with the latent Gaussian random field data, however they have similar empirical variograms, although the closed form for the spatial correlation is not available specifically.},
 year = {2015}
}

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TY  - JOUR
T1  - Generating Spatial Correlated Binary Data Through a Copulas Method
AU  - Renhao Jin
AU  - Sha Wang
AU  - Fang Yan
AU  - Jie Zhu
Y1  - 2015/07/25
PY  - 2015
N1  - https://doi.org/10.11648/j.sr.20150304.18
DO  - 10.11648/j.sr.20150304.18
T2  - Science Research
JF  - Science Research
JO  - Science Research
SP  - 206
EP  - 212
PB  - Science Publishing Group
SN  - 2329-0927
UR  - https://doi.org/10.11648/j.sr.20150304.18
AB  - Simulating spatial correlated binary data is very important on many cases, but it is not easily to accomplish, as there are restrictions on the parameters of Bernoulli variables. This paper develops a copulas method to generate spatial correlated binary data. The spatial binary data generated by this method has an inverse spatial pattern comparing with the latent Gaussian random field data, however they have similar empirical variograms, although the closed form for the spatial correlation is not available specifically.
VL  - 3
IS  - 4
ER  -

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Author Information

Renhao Jin

School of Information, Beijing Wuzi University, Beijing, China
Sha Wang

School of Information, Beijing Wuzi University, Beijing, China
Fang Yan

School of Information, Beijing Wuzi University, Beijing, China
Jie Zhu

School of Information, Beijing Wuzi University, Beijing, China

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APA Style

Renhao Jin, Sha Wang, Fang Yan, Jie Zhu. (2015). Generating Spatial Correlated Binary Data Through a Copulas Method. Science Research, 3(4), 206-212. https://doi.org/10.11648/j.sr.20150304.18

Copy | Download

ACS Style

Renhao Jin; Sha Wang; Fang Yan; Jie Zhu. Generating Spatial Correlated Binary Data Through a Copulas Method. Sci. Res. 2015, 3(4), 206-212. doi: 10.11648/j.sr.20150304.18

Copy | Download

AMA Style

Renhao Jin, Sha Wang, Fang Yan, Jie Zhu. Generating Spatial Correlated Binary Data Through a Copulas Method. Sci Res. 2015;3(4):206-212. doi: 10.11648/j.sr.20150304.18

Copy | Download

@article{10.11648/j.sr.20150304.18,
  author = {Renhao Jin and Sha Wang and Fang Yan and Jie Zhu},
  title = {Generating Spatial Correlated Binary Data Through a Copulas Method},
  journal = {Science Research},
  volume = {3},
  number = {4},
  pages = {206-212},
  doi = {10.11648/j.sr.20150304.18},
  url = {https://doi.org/10.11648/j.sr.20150304.18},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sr.20150304.18},
  abstract = {Simulating spatial correlated binary data is very important on many cases, but it is not easily to accomplish, as there are restrictions on the parameters of Bernoulli variables. This paper develops a copulas method to generate spatial correlated binary data. The spatial binary data generated by this method has an inverse spatial pattern comparing with the latent Gaussian random field data, however they have similar empirical variograms, although the closed form for the spatial correlation is not available specifically.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Generating Spatial Correlated Binary Data Through a Copulas Method
AU  - Renhao Jin
AU  - Sha Wang
AU  - Fang Yan
AU  - Jie Zhu
Y1  - 2015/07/25
PY  - 2015
N1  - https://doi.org/10.11648/j.sr.20150304.18
DO  - 10.11648/j.sr.20150304.18
T2  - Science Research
JF  - Science Research
JO  - Science Research
SP  - 206
EP  - 212
PB  - Science Publishing Group
SN  - 2329-0927
UR  - https://doi.org/10.11648/j.sr.20150304.18
AB  - Simulating spatial correlated binary data is very important on many cases, but it is not easily to accomplish, as there are restrictions on the parameters of Bernoulli variables. This paper develops a copulas method to generate spatial correlated binary data. The spatial binary data generated by this method has an inverse spatial pattern comparing with the latent Gaussian random field data, however they have similar empirical variograms, although the closed form for the spatial correlation is not available specifically.
VL  - 3
IS  - 4
ER  -

Copy | Download