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A Simple Conditional Approach for Generating Spatial Correlated Binary Data

Received: 29 June 2015     Accepted: 8 July 2015     Published: 17 July 2015
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Abstract

Generating a spatial random field in which the observations are binary random variables with a particular covariance function may be impossible, because there are restrictions on the parameters of Bernoulli variables. This paper develops a conditional method based from spatial GLMM for generating spatial correlated binary data, which can generate spatial correlated binary data, with the variograms of the simulated data are similar to the variograms of the corresponding latent Gaussian random field. However, the closed form for their spatial correlation is not available specifically.

Published in American Journal of Theoretical and Applied Statistics (Volume 4, Issue 4)
DOI 10.11648/j.ajtas.20150404.21
Page(s) 305-311
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, Generalized Linear Mixed Model, Variogram

References
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[2] Breslow, N. E., & Clayton, D. G. (1993). Approximate inference in generalized linear mixed models. Journal of the American Statistical Association, 88(421), 9-25.
[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] Lunn, A. D., & Davies, S. J. (1998). A note on generating correlated binary variables. Biometrika, 85(2), 487-490.
[8] Liang, K. Y., & Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73(1), 13-22.
[9] Park, C. G., Park, T., & Shin, D. W. (1996). A simple method for generating correlated binary variates. The American Statistician, 50(4), 306-310.
[10] 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.
[11] SAS Institute Inc, (2008). SAS/STAT® 9.2 User’s Guide: The GLIMMIX Procedure (Book Excerpt). NC: SAS Institute Inc, Cary.
[12] SAS Institute Inc, (2008). SAS/STAT® 9.2 User’s Guide: The SIM2D Procedure (Book Excerpt). NC: SAS Institute Inc, Cary.
[13] Schabenberger, O. and Gotway, C. A. (2005). Statistical methods for spatial data analysis, Chapman & Hall/CRC, Boca Raton.
[14] Stiratelli, R., Laird, N., & Ware, J. H. (1984). Random-effects models for serial observations with binary response. Biometrics, 961-971.
[15] 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.
[16] 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.
[17] Zeger, S. L., & Liang, K. Y. (1986). Longitudinal data analysis for discrete and continuous outcomes. Biometrics, 42(1), 121-130.
[18] Zeger, S. L., Liang, K. Y., & Albert, P. S. (1988). Models for longitudinal data: a generalized estimating equation approach. Biometrics, 1049-1060.
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  • APA Style

    Renhao Jin, Tao Liu, Fang Yan, Jie Zhu. (2015). A Simple Conditional Approach for Generating Spatial Correlated Binary Data. American Journal of Theoretical and Applied Statistics, 4(4), 305-311. https://doi.org/10.11648/j.ajtas.20150404.21

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    ACS Style

    Renhao Jin; Tao Liu; Fang Yan; Jie Zhu. A Simple Conditional Approach for Generating Spatial Correlated Binary Data. Am. J. Theor. Appl. Stat. 2015, 4(4), 305-311. doi: 10.11648/j.ajtas.20150404.21

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    AMA Style

    Renhao Jin, Tao Liu, Fang Yan, Jie Zhu. A Simple Conditional Approach for Generating Spatial Correlated Binary Data. Am J Theor Appl Stat. 2015;4(4):305-311. doi: 10.11648/j.ajtas.20150404.21

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  • @article{10.11648/j.ajtas.20150404.21,
      author = {Renhao Jin and Tao Liu and Fang Yan and Jie Zhu},
      title = {A Simple Conditional Approach for Generating Spatial Correlated Binary Data},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {4},
      number = {4},
      pages = {305-311},
      doi = {10.11648/j.ajtas.20150404.21},
      url = {https://doi.org/10.11648/j.ajtas.20150404.21},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20150404.21},
      abstract = {Generating a spatial random field in which the observations are binary random variables with a particular covariance function may be impossible, because there are restrictions on the parameters of Bernoulli variables. This paper develops a conditional method based from spatial GLMM for generating spatial correlated binary data, which can generate spatial correlated binary data, with the variograms of the simulated data are similar to the variograms of the corresponding latent Gaussian random field. However, the closed form for their spatial correlation is not available specifically.},
     year = {2015}
    }
    

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    T1  - A Simple Conditional Approach for Generating Spatial Correlated Binary Data
    AU  - Renhao Jin
    AU  - Tao Liu
    AU  - Fang Yan
    AU  - Jie Zhu
    Y1  - 2015/07/17
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    DO  - 10.11648/j.ajtas.20150404.21
    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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    EP  - 311
    PB  - Science Publishing Group
    SN  - 2326-9006
    UR  - https://doi.org/10.11648/j.ajtas.20150404.21
    AB  - Generating a spatial random field in which the observations are binary random variables with a particular covariance function may be impossible, because there are restrictions on the parameters of Bernoulli variables. This paper develops a conditional method based from spatial GLMM for generating spatial correlated binary data, which can generate spatial correlated binary data, with the variograms of the simulated data are similar to the variograms of the corresponding latent Gaussian random field. However, the closed form for their spatial correlation is not available specifically.
    VL  - 4
    IS  - 4
    ER  - 

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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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