Maximum posterior estimation of random effects in generalized linear mixed models

Statistica Sinica

Volumn 11, Issue 1, 2001, Pages 97-120

  Jiang, Jiming ^a   Jia, Haomiao ^a   Chen, Hegang ^a  

^a NONE

Author keywords

Consistency; GLMM; Maximum posterior; Small area estimation

Indexed keywords

EID: 0035635648     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (27)

1. Breslow, N. E. (1996). Comment on Lee & Nelder: hierarchical generalized linear models. J. Roy. Statist. Soc. Ser. B 58, 667.
2. Breslow, N. E. and Clayton, D. G. (1993). Approximate inference in generalized linear mixed models. J. Amer. Statist. Assoc. 88, 9-25.
3. Clayton, D. G. (1996). Comment on Lee & Nelder: hierarchical generalized linear models. J. Roy. Statist. Soc. Ser. B 58, 657-659.
4. Ghosh, M. and Rao, J. N. K. (1994). Small area estimation: an appraisal. Statist. Sci. 6, 15-51.
5. Haberman, S. J. (1977). Maximum likelihood estimates in exponential response models. Ann. Statist. 5, 815-841.
6. Henderson, C. R. (1950). Estimation of genetic parameters (abstract). Ann. Math. Statist. 21, 309-310.
7. Jiang (1996). REML estimation: asymptotic behavior and related topics. Ann. Statist. 24, 255-286.
8. Jiang, J. (1998a). Asymptotic properties of the empirical BLUP and BLUE in mixed linear models. Statist. Sinica 8, 861-885.
9. Jiang, J. (1998b). Consistent estimators in generalized linear mixed models. J. Amer. Statist. Assoc. 93, 720-729.
10. Jiang, J. (1999). On maximum hierarchical likelihood estimators, Commun. Statist. - Theory Meth. 28, 1769-1775.
11. Jiang, J. (2000). A nonlinear Gauss-Seidel algorithm for inference about GLMM. Comp. Statist. 15, 229-241.
12. Kuk, A. Y. C. (1995). Asymptotically unbiased estimation in generalized linear models with random effects. J. Roy. Statist. Soc. Ser. B 57, 395-407.
13. Lai, T. L. and Wei, C. Z. (1982). Least squares estimates in stochastic regression models with applications to identification and control of dynamic systems. Ann. Statist. 10, 154-166.
14. Lee, Y. and Nelder, J. A. (1996). Hierarchical generalized linear models. J. Roy. Statist. Soc. Ser. B 58, 619-678.
15. Lin, X. and Breslow, N. E. (1996). Bias correction in generalized linear mixed models with multiple components of dispersion. J. Amer. Statist. Assoc. 91, 1007-1016.
16. Malec, D., Sedransk, J., Moriarity, C. L. and LeClere, F. B. (1997). Small area inference for binary variables in the national health interview survey. J. Amer. Statist. Assoc. 92, 815-826.
17. McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models. 2nd edition. Chapman and Hall, New York.
18. McCullagh, P. and Tibshirani, R. (1990). A simple method for adjustment of profile likelihoods. J. Roy. Statist. Soc. Ser. B 52, 325-344.
19. McGilchrist, C. A. (1994). Estimation in generalized mixed models. J. Roy. Statist. Soc. Ser. B 56, 61-69.
20. Neyman, J. and Scott, E. (1948). Consistent estimates based on partially consistent observations. Econometrika 16, 1-32.
21. Portnoy, S. (1988). Asymptotic behavior of likelihood methods for exponential families when the number of parameters tends to infinity. Ann. Statist. 16, 356-366.
22. Rasch, G. (1960). Probabilistic Models for Some Intelligence and Attainment Tests. Danish Inst. of Edu. Research, Copenhagen.
23. Rasch, G. (1961). On general laws and the meaning of measurement in psychology. Proc. Fourth Berkeley Symp. Math. Statist. Probab. 4, 321-334, Univ. of California Press.
24. Robinson, G. K. (1991). That BLUP is a good thing: the estimation of random effects. Statist. Sci. 6, 15-51.
25. Schall, R. (1991). Estimation in generalized linear models with random effects. Biometrika 78, 719-727.
26. Searle, S. R., Casella, G. and McCulloch, C. E. (1992). Variance Components. John Wiley, New York.
27. Speed, T. (1991). Comment on Robinson: Estimation of random effects. Statist. Sci. 6, 42-44.