:: Volume 14, Issue 2 (3-2018) ::
JSRI 2018, 14(2): 157-169 Back to browse issues page
Parameter Estimation in Spatial Generalized Linear Mixed Models with Skew Gaussian Random Effects using Laplace Approximation
Seyed Reza Hosseini Shojaei , Yadollah Waghei * , Mohsen Mohammadzadeh
, ywaghei@birjand.ac.ir
Abstract:   (1049 Views)
 Spatial generalized linear mixed models are used commonly for modelling non-Gaussian discrete spatial responses. We present an algorithm for parameter estimation of the models using Laplace approximation of likelihood function. In these models, the spatial correlation structure of data is carried out by random effects or latent variables. In most spatial analysis, it is assumed that random effects have Gaussian distribution, but the assumption is questionable. This assumption is replaced in the present work, using a skew Gaussian distribution for the latent variables, which is more flexible and includes Gaussian distribution. We examine the proposed method using a real discrete data set.
 
Keywords: Laplace approximation, multivariate skew Gaussian, random effects, SGLM, spatial data.
Full-Text [PDF 493 kb]   (178 Downloads)    
Type of Study: Research | Subject: General
Received: 2016/08/5 | Accepted: 2017/10/16 | Published: 2018/03/17
References
1. Allard, D. and Naveau, P. (2007). A New Spatial Skew-normal Random Field Model. Communications in Statistics - Theory and Methods, 36, 1821-1834. [DOI:10.1080/03610920601126290]
2. Arellano-Valle, R. and Azzalini, A. (2006). On the Unification of Families of Skew Gaussian Distributions. Scandinavian Journal of Statistics, 33, 561-574. [DOI:10.1111/j.1467-9469.2006.00503.x]
3. Azzalini, A. (1985). A Class of Distributions which Includes the Gaussian Ones. Scandinavian Journal of Statistics, 12, 171-178.
4. Azzalini, A. and Capitanio, A. (2014). The Skew Gaussian and Related Families. Cambridge University Press, New York.
5. Azzalini, A. and Dalla-Valle, A. (1996). The Multivariate Skew Gaussian Distribution. Biometrika, 83, 715-726. [DOI:10.1093/biomet/83.4.715]
6. Baghishani, H. and Mohammadzadeh, M. (2011). A Data Cloning Algorithm for Computing Maximum Likelihood Estimates in Spatial Generalized Linear Mixed Models. Computational Statistics and Data Analysis, 55, 1748-1759. [DOI:10.1016/j.csda.2010.11.004]
7. Bonat, W.H. and Ribeiro, P.J. (2015). Practical Likelihood Analysis for Spatial Generalized Linear Mixed Models. Environmetrics, 27, 83-89. [DOI:10.1002/env.2375]
8. Breslow, N.E. and Clayton, D.G. (1993). Approximate Inference in Generalized Linear Mixed Models. Journal of the American Statistical Association, 88, 9-25.
9. Chan, K.S. and Ledolter, J. (1995). Monte Carlo EM Estimation for Time Series Models Involving Counts. Journal of the American Statistical Association, 90, 242-252. [DOI:10.1080/01621459.1995.10476508]
10. Cressie, N. (1993). Statistics for Spatial Data. John Wiley and Sons, Inc, New York.
11. Christensen, O.F. (2004). Monte Carlo Maximum Likelihood in Model-based Geostatistics. Journal of Computational and Graphical Statistics, 13, 702-718. [DOI:10.1198/106186004X2525]
12. Christensen, O.F. and Waagepetersen, R. (2002). Bayesian Prediction of Spatial Count Data using Generalized Linear Mixed Models. Biometrics, 58, 280-286. [DOI:10.1111/j.0006-341X.2002.00280.x]
13. Diggle, P.J., Tawn, J.A. and Moyeed, R.A. (1998). Model-based Geostatistics (with Discussion). Journal of the Royal Statistical Society: Series C, 47, 299-326. [DOI:10.1111/1467-9876.00113]
14. Gonz'{a}lez-Far'{i}as, G., Dom'{i}nguez-Molina, J. and Gupta, A. (2004). Additive Properties of Skew Normal Random Vectors. Journal of Statistical Planning and Inference, 126, 521-534. [DOI:10.1016/j.jspi.2003.09.008]
15. Goovaerts, P. (2005). Geostatistical Analysis of Disease Data: Estimation of Cancer Mortality Risk from Empirical Frequencies Using Poisson Kriging. International Journal of Health Geographics, 4, 31. [DOI:10.1186/1476-072X-4-31]
16. Kim, H.M. and Mallick, B.K. (2004). A Bayesian Prediction Using the Skew Gaussian Distribution. Journal of Statistical Planning and Inference, 120, 85-101. [DOI:10.1016/S0378-3758(02)00501-3]
17. Lele, S.R., Nadeem, K. and Schmuland, B. (2010). Estimability and Kikelihood Inference for Generalized Linear Mixed Models Using Data Cloning. Journal of the American Statistical Association, 105, 1617-1625. [DOI:10.1198/jasa.2010.tm09757]
18. McCulloch, C.E. (1997). Maximum Likelihood Algorithms for Generalized Linear Mixed Models. Journal of the American Statistical Association, 92, 162-170. [DOI:10.1080/01621459.1997.10473613]
19. McCullagh, P. and Nelder, J.A. (1989). Generalized Linear Models. 2nd ed., Chapman and Hall, London. [DOI:10.1007/978-1-4899-3242-6]
20. Mohammadzadeh, M. and Hosseini, F. (2011). Maximum Likelihood Estimation for Spatial GLM Models. Procedia Environmental Sciences, 3, 63-68. [DOI:10.1016/j.proenv.2011.02.012]
21. Hosseini, F., Eidsvik, J. and Mohammadzadeh, M. (2011). Approximate Bayesian Inference in Spatial GLMM with Skew Gaussian Latent Variables. Computational Statistics and Data Analysis, 55, 1791-1806. [DOI:10.1016/j.csda.2010.11.011]
22. Torabi, M. (2015). Likelihood Inference for Spatial Generalized Linear Mixed Models. Communications in Statistics - Simulation and Computation, 44, 1692-1701. [DOI:10.1080/03610918.2013.824099]
23. Zhang, H. (2002). On Estimation and Prediction for Spatial Generalized Linear Mixed Models. Biometrics, 58, 129-136. [DOI:10.1111/j.0006-341X.2002.00129.x]
24. Zhang, H. and El-Shaarawi, A. (2010). On Spatial Skew-Gaussian Processes and Applications. Environmetrics, 21, 33-47.



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