Maximum likelihood estimation of regression parameters with spatially dependent discrete data

Journal of Agricultural, Biological, and Environmental Statistics

Volumn 14, Issue 4, 2009, Pages 375-391

  Madsen, L ^a  

^a OREGON STATE UNIVERSITY   (United States)

Author keywords

Continuous extension; Correlated count data; Dependent count data; Gaussian copula; Spatial copula

Indexed keywords

BEETLE; BIOMETRY; COMPUTER SIMULATION; CONFIDENCE INTERVAL; CORRELATION; ESTIMATION METHOD; GAUSSIAN METHOD; GEOSTATISTICS; MAXIMUM LIKELIHOOD ANALYSIS; NUMERICAL MODEL; PARAMETERIZATION; REGRESSION ANALYSIS; SAMPLING BIAS; SOIL ORGANIC MATTER; SPATIAL DATA;

COLEOPTERA; POPILLIA JAPONICA;

EID: 77951714350     PISSN: 10857117     EISSN: 15372693     Source Type: Journal    
DOI: 10.1198/jabes.2009.07116     Document Type: Article

References (35)

1. Albert, P. S., and McShane, L. M. (1995), "A Generalized Estimating Equations Approach for Spatially Correlated Binary Data: Applications to the Analysis of Neuroimaging Data," Biometrics, 51, 627-638.
2. Berger, J. O., de Oliveira, V., and Sansó, B. (2001), "Objective Bayesian Analysis of Spatially Correlated Data," Journal of the American Statistical Association, 96, 1361-1374.
3. Cressie, N. A. C. (1993), Statistics for Spatial Data (revised ed.), New York: Wiley.
4. Dalthorp, D. (2004), "The Generalized Linear Model for Spatial Data: Assessing the Effects of Environmental Covariates on Population Density in the Field," Entomologia Experimentalis et Applicata, 111, 117-131.
5. Dalthorp, D., Nyrop, J., and Villani, M. (2000), "Spatial Ecology of the Japanese Beetle, Popillia japonica," Entomologia Experimentalis et Applicata, 96, 129-139.
6. Denuit, M., and Lambert, P. (2005), "Constraints on Concordance Measures in Bivariate Discrete Data," Journal of Multivariate Analysis, 93, 40-57.
7. Diggle, P. J., Tawn, J. A., and Moyeed, R. A. (1998), "Model-Based Geostatistics," Applied Statistics, 47, 299-350.
8. Fisher, N. (1997), "Copulas," in Encyclopedia of Statistical Sciences, Vol. 1, New York: Wiley, pp. 159-163.
9. Gotway, C. A., and Stroup, W. W. (1997), "A Generalized Linear Model Approad to Spatial Data Analysis and Prediction," Journal of Agricultural, Biological, and Environmental Statistics, 2, 157-178.
10. Hilbe, J. M. (2007), Negative Binomial Regression, New York: Cambridge University Press.
11. Hoeffding, W. (1940), "Masstabinvariante Korrelationstheorie," Schriften des Matematischen Instituts and des Instituts für Angewandte Matematik de Universität Berlin, 5, 179-233.
12. Hoff, P. D. (2007), "Extending the Rank Likelihood for Semipaametric Copula Estimation," Journal of Computational and Theoretical Nanoscience, 1, 265-283.
13. Irvine, K. M., Gitelman, A. I., and Hoeting, J. A. (2007), "Spatial Designs and Properties of Spatial Correlation: Effects on Covariance Estimation," Journal of Agricultural, Biological, and Environmental Statistics, 12, 450-469.
14. Joe, H. (2001), Multivariate Models and Dependence Concepts, London: Chapman & Hall/CRC.
15. Kruskal, W. H. (1958), "Ordinal Measures of Association," Journal of the American Statistical Association, 53, 814-861.
16. Lee, Y., Nelder, J. A., and Pawitan, Y. (2006), Generalized Linear Models With Random Effects, Unified Analysis via H-Likelihood, Boca Raton, FL: Chapman & Hall/CRC.
17. Liang, K.-Y., and Zeger, S. (1986), "Longitudinal Data Analysis Using Generalized Linear Models," Biometrika, 73, 13-22.
18. Lin, P.-S., and Clayton, M. K. (2005), "Analysis of Binary Spatial Data by Quasi-Likelihood Estimating Equations," The Annals of Statistics, 33, 542-555.
19. Madsen, L., and Dalthorp, D. (2007), "Simulating Correlated Count Data," Environmental and Ecological Statistics, 14, 129-148.
20. Mardia, K. V., and Marshall, R. J. (1984), "Maximum Likelihood Estimation of Models for Residual Covariance in Spatial Statistics," Biometrika, 71, 135-146.
21. McCullagh, P., and Nelder, J. A. (1989), Generalized Linear Models, (2nd ed.), Boca Raton, FL: Chapman & Hall/CRC.
22. McShane, L. M., Albert, P. S., and Palmatier, M. A. (1997), "A Latent Process Regression Model for Spatially Correlated Count Data," Biometrics, 53, 698-706.
23. Nelsen, R. B. (2006), An Introduction to Copulas (2nd ed.), New York: Springer.
24. Pitt, M., Chan, D., and Kohn, R. (2006), "Efficient Bayesian Inference for Gaussian Copula Regression Models," Biometrika, 93, 537-554.
25. Prentice, R. L. (1988), "Correlated Binary Regression With Covariates Specific to Each Binary Observation," Biometrics, 44, 1033-1048.
26. Schabenberger, O., and Gotway, C. A. (2005), Statistical Methods for Spatial Data Analysis, Boca Raton, FL: Chapman & Hall/CRC.
27. Solomon, D. L. (1983), "The Spatial Distribution of Butterfly Eggs," in Life Science Models, Vol. 4, eds. H. Roberts and M. Thompson, New York: Springer-Verlag, pp. 350-366.
28. Song, P. X.-K. (2000), "Multivariate Dispersion Models Generated From Gaussian Copula," Scandanavian Journal of Statistics, 27, 305-320.
29. - (2007), Correlated Data Analysis, New York: Springer.
30. Song, P. X.-K., Li, M., and Yuan, Y. (2009), "Joint Regression Analysis of Correlated Data Using Gaussian Copulas," Biometrics, 65, 60-68.
31. Taylor, L. R. (1961), "Aggregation, Variance and the Mean," Nature, 189, 732-735.
32. Venables, W., and Ripley, B. (2002), Modern Applied Statistics With S (4th ed.), New York: Springer.
33. Yasui, Y., and Lele, S. (1997), "A Regression Method for Spatial Disease Rates: An Estimating Function Approach," Journal of the American Statistical Association, 92, 21-32.
34. Zeger, S., and Liang, K.-Y. (1986), "Longitudinal Data Analysis for Discrete and Continuous Outcomes," Biometrics, 42, 121-130.
35. Zhang, H. (2004), "Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics," Journal of the American Statistical Association, 99, 250-261.