A Simple Conditional Approach for Generating Spatial Correlated Binary Data

Renhao Jin; Tao Liu; Fang Yan; Jie Zhu

doi:doi:10.11648/j.ajtas.20150404.21

| Peer-Reviewed

A Simple Conditional Approach for Generating Spatial Correlated Binary Data

Renhao Jin, Tao Liu, Fang Yan, Jie Zhu

Published in American Journal of Theoretical and Applied Statistics (Volume 4, Issue 4)

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

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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

[1]	Al Osh, M. A., & Lee, S. J. (2001). A simple approach for generating correlated binary variates. Journal of Statistical Computation and Simulation, 70(3), 231-255.
[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.

Cite This Article

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
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
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.20150404.21
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
SP  - 305
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  -

Copy | Download

Author Information

Renhao Jin

School of Information, Beijing Wuzi University, Beijing, China
Tao Liu

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

Download PDF

Sections

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
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
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.20150404.21
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
SP  - 305
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  -

Copy | Download