응용통계연구 (The Korean Journal of Applied Statistics)

  • 제28권2호
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  • Pages.353-360
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  • 2015
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  • 1225-066X(pISSN)
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  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
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공간적 상관관계가 존재하는 이산형 자료를 위한 일반화된 공간선형 모형 개관

Review of Spatial Linear Mixed Models for Non-Gaussian Outcomes

  • 투고 : 2015.04.01
  • 심사 : 2015.04.06
  • 발행 : 2015.04.30
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⟨ 이전 논문 다음 논문 ⟩

초록

공간적으로 관측되는 연속형 자료를 분석하는 모형으로 공간적 상관관계를 고려한 다양한 정규모형이 지난 수십 년간 제안되었다. 그 중에서 공간효과를 랜덤효과로 모형화하는 공간선형모형(Spatial Linear Mixed Model; SLMM)이 가장 널리 활용되는 모형 중 하나일 것이다. 연결함수(link function)을 사용하면 SLMM을 비정규 데이터도 적용할 수 있는 일반화된 공간선형모형(Spatial Generalized Linear Mixed Model; SGLMM)으로 자연스럽게 확장할 수 있다. 이 논문에서는 가장 널리 활용되는 SGLMM을 알아보고 실제 데이터 적용사례를 R 패키지를 활용하여 제시하고자 한다.

Various statistical models have been proposed over the last decade for spatially correlated Gaussian outcomes. The spatial linear mixed model (SLMM), which incorporates a spatial effect as a random component to the linear model, is the one of the most widely used approaches in various application contexts. Employing link functions, SLMM can be naturally extended to spatial generalized linear mixed model for non-Gaussian outcomes (SGLMM). We review popular SGLMMs on non-Gaussian spatial outcomes and demonstrate their applications with available public data.

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참고문헌

  1. Banerjee, S., Gelfand, A. E., Finley, A. O. and Sang, H. (2008). Gaussian predictive process models for large spatial data sets, Journal of the Royal Statistical Society B, 70, 825-848. https://doi.org/10.1111/j.1467-9868.2008.00663.x
  2. Besag, J. (1974). Spatial interaction and the statistical analysis of lattice systems, Journal of the Royal Statistical Society, Series B, 36, 192-236.
  3. Caragea, P. and Kaiser, M. (2009). Autologistic models with interpretable parameters, Journal of Agricul-tural, Biological, and Environmental Statistics, 14, 281-300. https://doi.org/10.1198/jabes.2009.07032
  4. Cressie, N. A. C. (1993). Statistics for Spatial Data, 2nd edition, Wiley, New York.
  5. Diggle, P. J., Tawn, J. A. and Moyeed, R. A. (1998). Model-based geostatistics, Journal of the Royal Statistical Society: Series C (Applied Statistics), 47, 299-350.
  6. Hartman, L. and Hossjer, O. (2008). Fast kriging of large data sets with Gaussian Markov random fields, Computational Statistics and Data Analysis, 52, 2331-2349. https://doi.org/10.1016/j.csda.2007.09.018
  7. Hughes, J. and Haran, M. (2013). Dimension reduction and alleviation of confounding for spatial generalized linear mixed models, Journal of the Royal Statistical Society: Series B, 75, 139-159. https://doi.org/10.1111/j.1467-9868.2012.01041.x
  8. Hughes, J. and Cui, X. (2015). ngspatial: Fitting the centered autologistic and sparse spatial generalized linear mixed models for areal data. R package.
  9. Kammann, E. E. and Wand, M. P. (2003). Geoadditive models, Applied Statistics, 52, 1-18.
  10. Lin, X., Wahba, G., Xiang, D., Gao, F., Klein, R. and Klein, B. (2000). Smoothing spline ANOVA models for large datasets with Bernoulli observations and the randomized GACV, The Annals of Statistics, 28, 1570-1600. https://doi.org/10.1214/aos/1015957471
  11. Lindgren, F., Lindstrom, J. and Rue, H. (2011). An explicit link between Gaussian fields and Gaussian Markov random fields: The stochastic partial differential equation approach, Journal of the Royal Statistical Society B, 73, 423-498. https://doi.org/10.1111/j.1467-9868.2011.00777.x
  12. Paciorek, C. J. (2007). Computational techniques for spatial logistic regression with large datasets, Computational Statistical Data Analysis, 51, 3631-3653. https://doi.org/10.1016/j.csda.2006.11.008
  13. Reich, B., Hodges, J. and Zadnik, V. (2006). Effects of residual smoothing on the posterior of the fixed effects in disease-mapping models, Biometrics, 62, 1197-1206. https://doi.org/10.1111/j.1541-0420.2006.00617.x
  14. Rue, H. and Held, L. (2005). Gaussian Markov Random Fields: Theory and Applications, Chapman & Hall/CRC, Boca Raton.
  15. Rue, H., Martino, S. and Chopin, N. (2009). Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations, Journal of the Royal Statistical Society B, 71, 319-392. https://doi.org/10.1111/j.1467-9868.2008.00700.x
  16. Rue, H., Martino, S., Finn, L., Simpson, D., Riebler, A. and Krainski, E. T. (2014). INLA: Functions which allow to perform full Bayesian analysis of latent Gaussian models using integrated nested Laplace approximation. R package, version 0.0-1404466478.
  17. Rue, H. and Tjelmeland, H. (2002). Fitting Gaussian Markov random fields to Gaussian field, Scandinavian Journal of Statistics, 29, 31-49. https://doi.org/10.1111/1467-9469.00058
  18. Wikle, C. and Cressie, N. (1999). A dimension-reduced approach to space-time Kalman filtering, Biometrika, 86, 815-829. https://doi.org/10.1093/biomet/86.4.815