Fitting generalized linear mixed models for point-referenced spatial data

Journal of Modern Applied Statistical Methods

Volumn 2, Issue 2, 2003, Pages 497-511

  Gemperli, Armin ^a,b   Vounatsou, Penelope ^a  

^a SWISS TROPICAL AND PUBLIC HEALTH INSTITUTE   (Switzerland)

^b Biostatistics Unit   (Switzerland)

Author keywords

Geostatistics; Infant mortality; Kriging; Markov chain Monte Carlo (MCMC); Penalized quasi likelihood (PQL); Risk mapping; Sampling importance resampling (SIR)

Indexed keywords

EID: 18544379452     PISSN: 15389472     EISSN: None     Source Type: Journal    
DOI: 10.22237/jmasm/1067646180     Document Type: Article

References (36)

1. Anderson, D. A., & Hinde, J. P. (1988). Random effects in generalized linear models and the EM algorithm. Communication in Statistics: Theory and Methods, 17, 3847-3856.
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. Booth, J. G., & Hobert, J. P. (1999). Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm. Journal of the Royal Statistical Society, Series B, 61, 265-285.
4. Breslow, N. E., & Clayton, D. G. (1993). Approximate inference in generalized linear mixed models. Journal of the American Statistical Association, 88, 9-25.
5. Breslow, N. E., & Lin, X. (1995). Bias correction in generalized linear mixed models with a single component of dispersion. Biometrika, 82, 81-91.
6. Browne, W. J., & Draper, D. (2000). A comparison of Bayesian and likelihood methods for fitting multilevel models. Submitted.
7. Cleland, J., & van Ginneken, J. K. (1989). Maternal education and child survival in developing countries: The search for pathways of influence. Social Science and Medicine, 27, 1357-1368.
8. Cressie, N., & Hawkins, D. M. (1980). Robust estimation of the variogram. Mathematical Geology, 12, 115-125.
9. Dempster, A. P., Laird, N. M. & Rubin D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B, 39, 1-38.
10. Diggle, P. J., Tawn, J. A., & Moyeed, R. A. (1998). Model-based geostatistics. Journal of the Royal Statistical Society, Series C, 47, 299-350.
11. Ecker, M., & Gelfand, A. E. (1997). Bayesian variogram modeling for an isotropic spatial process. Journal of Agricultural, Biological and Environmental Statistics, 2, 347-369.
12. Farah, A. A., & Preston, S. H. (1982). Child mortality differentials in Sudan. Population and Development Review, 8, 365-383.
13. GDE Systems Inc. (1995). Geoname Digital Gazetteer, Version I, CD-ROM.
14. Gelfand, A. E., Ravishanker, N., & Ecker, M. (1999). Modeling and inference for point-referenced binary spatial data. In D. Dey, S. Ghosh & B. Mallick (Eds.), Generalized linear models: a bayesian perspective. 373-386. Marcel Dekker Inc.
15. Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In J. M. Bernardo, J. O. Berger,A.P. Dawid & A. F. M. Smith (Eds.), Bayesian statistics, 4, 169-193. Oxford University Press.
16. Gilks, W. R., & Roberts, G. O. (1996). Strategies for improving MCMC. In W. R. Gilks, S. Richardson, & D. J. Spiegelhalter (Eds.), Markov chain Monte Carlo in practice. 89-114. London: Chapman and Hall.
17. Haran, M., Hodges, J. S., & Carlin, B. P. (2001). Accelerating computation in Markov random field models for spatial data via structured MCMC. Journal of Computaional and Graphical Statistics, 12, 249-264.
18. Heagerty, P. J., & Lele, S. R. (1998). A composite likelihood approach to binary spatial data. Journal of the American Statistical Association, 93, 1099-1111.
19. Jain, A. (1988). Determinants of regional variation in infant mortality in rural India. In A. Jain, & L. Visaria (Eds.), Infant mortality in India: Differentials and determinants, 127-167. Sage Publications.
20. Kalipeni, E. (1993). Determinants of infant mortality in Malawi: a spatial perspective. Social Science and Medicine, 37, 183-198.
21. Lesaffre, E., & Spiessens, B. (2001). On the effect of the number of quadrature points in a logistic random-effects model: An example. Journal of the Royal Statistical Society, Series C, 50, 325-335.
22. Liang, K. Y., & Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13-22.
23. Matheron, G. (1963). Principles of geostatistics. Economic Geology, 58, 1246-1266.
24. McCulloch, C. E. (1997). Maximum likelihood algorithms for generalized linear mixed models. Journal of the American Statistical Association, 92, 162-170.
25. Mira, A., & Savent, D. J. (2000). Strategies for speeding Markov chain Monte Carlo algorithms. Technical Report, University of Insubria, Varese.
26. Neuhaus, J. N., & Segal, M. R. (1997). An assessment of approximate maximum likelihood estimators in generalized linear mixed models. In T. G. Gregoire, D. R. Brillinger, P. J. Diggle, E. Russek-Cohen, W. G. Warren, & R. D. Wolfinger (Eds.), Modeling longitudinal and spatially correlated data: Lecture notes in statistics, 122, 11-22.
27. Pace, K. R., & Barry, R. (1997). Quick computation of the regressions with spatially autoregressive dependent variable. Geographical Analysis, 29, 232-247.
28. Preisler, H. K. (1988). Maximum likelihood estimates for binary data with random effects. Biometrical Journal, 3, 339-350.
29. Rubin, D. B. (1987). Comment on: The calculation of posterior distributions by data augmentation, by M. A. Tanner and W. H. Wong. Journal of the American Statistical Association, 82, 543-546.
30. Rue, H. (2000). Fast sampling of gaussian markov random fields. Journal of the Royal Statistical Society, Series B, 48, 233-243.
31. Schultz, T. P. (1979, June 19-25). Interpretation of relations among mortality, economics of the household and the health environment. Proceedings of the meeting on socio-economic determinants and consequences of mortality, Mexico City. Geneva: World Health Organization.
32. Tubilla, A. (1975). Error convergence rates for estimates of multidimensional integrals of random functions. Technical Report No. 72, Department of Statistics, Stanford University, Stanford, CA.
33. Wolfinger, R., & O'Connell, M. (1993). Generalized linear mixed models: A pseudo-likelihood approach. Journal of Statistical Computation and Simulation, 48, 233-243.
34. World Resources Institute (1995) Africa Data Sampler. Edition I, CD-ROM.
35. Zeger, S. L., & Liang, K. Y. (1986). Longitudinal data analysis for discrete and continuous outcomes. Biometrika, 42, 121-130.
36. Zimmerman, D. L., & Zimmerman, M. B. (1991). A comparison of spatial semivariogram estimators and corresponding ordinary kriging predictors. Technometrics, 33, 77-91.