Inference of Spatial Generalized Linear Mixed Models using Integrated Laplace Nested Approximation

Document Type : Original Paper

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Department of Statistics, University of Semnan

Abstract

Spatial generalized linear mixed models are used for modeling geostatistical discrete spatial responses and spatial correlation of the data is considered via latent variables. The most important interest in these models is estimation of the model parameters and the prediction of the latent variables. In this paper, first a prediction method is presented and then, Bayesian approach and MCMC algorithms are intrpretation. Since these models are complex and in the Bayes inference of these models, are used Monte Carlo sampling, computation time is long. The Approximatin Baysian methods are considered for solving this problem. Finally, the proposed methods are applied to a case study on rainfall data observed in the weather stations of Semnan in 1391.

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References

[1] Nelder, J.A., and Wedderburn, R.W.M. (1972). Generalized Linear Mixed Models, Journal of the Royal Statistical Association,Ser. A, 135, 370-384. [2] McCulloch, P. and Nelder, J.A. (1989), Generalized Linear Models, London, Chapman and
Hall. [3] Breslow, N.E. and Clayton, D.G. (1993). Approximate Inference in Generalized Linear Mixed Models, Journal of the American Statistical Association, 88, 9-25. [4] Diggle, P., Tawn, J.A. and Moyeed, R.A. (1998). Model-Based Geostatistic, Journal
of the Royal Statistical Society, Series C. Applied Statistics, 47, 299-350. [5] McCulloch, C. (1997). Maximum Likelihood
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Thompson, R. (2007). Quasi-Monte Carlo Estimation in Generalized Linear Mixed Models, Computational Statistics and Data Analysis,51, 5765-5775.

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History

  • Receive Date: 15 June 2014
  • Revise Date: 14 September 2014
  • Accept Date: 25 September 2014

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