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Generating Spatial Correlated Binary Data Through a Copulas Method

Received: 05 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.

DOI 10.11648/j.sr.20150304.18
Published in Science Research (Volume 3, Issue 4, August 2015)
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), 2024. Published by Science Publishing Group

Keywords

Spatial Binary Data, Copulas, Simulation, Variogram

References
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[3] Crainiceanu, C. M., Diggle, P. J., & Rowlingson, B. (2008). Bivariate binomial spatial modeling of Loa loa prevalence in tropical Africa. Journal of the American Statistical Association, 103(481), 21-37.
[4] Cox, D. R., & Wermuth, N. (1991). A simple approximation for bivariate and trivariate normal integrals. International Statistical Review/Revue Internationale de Statistique, 59(2), 263-269.
[5] Engel, B. and Keen, A. (1992). A simple approach for the analysis of generalized linear mixed models. LWA-92-6, Agricultural Mathematics Group (GLW-DLO), Wageningen, The Netherlands.
[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.
[17] Waclawiw, M. A. and Liang, K. Y. (1993). Prediction of random effects in the generalized linear model. Journal of American Statistical Association 88, 171-8.
[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.
[20] Zeger, S. L., Liang, K. Y., & Albert, P. S. (1988). Models for longitudinal data: a generalized estimating equation approach. Biometrics, 1049-1060.
Author Information
  • School of Information, Beijing Wuzi University, Beijing, China

  • School of Information, Beijing Wuzi University, Beijing, China

  • School of Information, Beijing Wuzi University, Beijing, China

  • School of Information, Beijing Wuzi University, Beijing, China

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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://download.sciencepg.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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    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
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    DO  - 10.11648/j.sr.20150304.18
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    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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