Generalized linear models for small-area estimation

Journal of the American Statistical Association

Volumn 93, Issue 441, 1998, Pages 273-282

  Ghosh, Malay ^a   Natarajan, Kannan ^b   Stroud, T W F ^c   Carlin, Bradley P ^d  

^a University of Florida   (United States)

^b BRISTOL MYERS SQUIBB PHARMACEUTICAL RESEARCH INSTITUTE   (United States)

^c QUEEN S UNIVERSITY   (Canada)

^d UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Hierarchical model; Markov chain Monte Carlo; Posterior propriety; Spatial statistics

Indexed keywords

EID: 0032360457     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1998.10474108     Document Type: Article

References (40)

1. Albert, J. H. (1988), "Computational Methods Using a Bayesian Hierarchical Generalized Linear Model," Journal of the American Statistical Association, 83, 1037-1044.
2. Bemardinelli, L., and Montomoli, C. (1992), "Empirical Bayes Versus Fully Bayesian Analysis of Geographical Variation in Disease Risk," Statistics in Medicine, 11, 983-1007.
3. Besag, J., Green, R, Higdon, D., and Mengersen, K. (1995), "Bayesian Computation and Stochastic Systems" (with discussion), Statistical Science, 10, 3-66.
4. Besag, J., York, J. C., and Mollie, A. (1991), "Bayesian Image Restoration, With Two Applications in Spatial Statistics" (with discussion). Annals of the Institute of Statistical Mathematics, 43, 1-59.
5. Best, N. G., Cowles, M. K., and Vines, K. (1995), "CODA: Convergence Diagnosis and Output Analysis Software for Gibbs Sampling Output, Version 0.30," technical report, Cambridge University, Institute of Public Health, Medical Research Council Biostatistics Unit.
6. Breslow, N. E., and Clayton, D. G. (1993), "Approximate Inference in Generalized Linear Mixed Models," Journal of the American Statistical Association, 88, 9-25.
7. Brooks, R. J. (1984), "Approximate Likelihood Ratio Tests in the Analysis of Beta-Binomial Data," Applied Statistics, 33, 285-289.
8. Clayton, D. G., and Kaldor, J. (1987), "Empirical Bayes Estimates of Age-Standardized Relative Risks for Use in Disease Mapping," Biometrics, 43, 671-681.
9. Datta, G. S., and Ghosh, M. (1991), "Bayesian Prediction in Linear Models: Applications to Small Area Estimation," The Annals of Statistics, 19, 1748-1770.
10. Dellaportas, P., and Smith, A. F. M. (1993), "Bayesian Inference for Generalized Linear and Proportional Hazards Models via Gibbs Sampling," Applied Statistics, 42, 443-459.
11. Dempster, A. P., and Tomberlin, T. J. (1980), "The Analysis of Census Undcrcount From a Post-Enumeration Survey," in Proceedings of the Conference on Census Undercouru, pp. 88-94.
12. Farrell, P., MacGibbon, B., and Tomberlin, T. J. (in press), "Empirical Bayes Estimators of Small Area Proportions in Multistage Designs," submitted to Statistica Sinica.
13. Fay, R. E., and Herriot, R. (1979), "Estimates of Income for Small Places: An Application of James-Stein Procedures to Census Data," Journal of the American Statistical Association, 74, 269-277.
14. Gclfand, A. E., and Ghosh, S. K. (in press), "Model Choice: A Minimum Posterior Predictive Loss Approach," submitted to Biometrika.
15. Gelfand, A. E., and Smith, A. F. M. (1990), "Sampling-Based Approaches to Calculating Marginal Densities," Journal of the American Statistical Association, 85, 398-409.
16. Gelman, A., and Rubin, D. B. (1992), "Inference From Iterative Simulation Using Multiple Sequences," Statistical Science, 7, 457-511.
17. Genian, S., and Geman, D. (1984), "Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images," IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.
18. Ghosh, M., and Lahiri, P. (1987), "Robust Empirical Bayes Estimation of Means From Stratified Samples," Journal of the American Statistical Association, 82, 1153-1162.
19. Ghosh, M., and Lahiri, P. (1992), "A Hierarchical Bayes Approach to Small Area Estimation With Auxiliary Information," in Bayesian Analysis in Statistics and Econometrics, Lecture Notes in Statistics 75, eds. P. K. Goel and N. S. Iyengar, New York: Springer-Verlag, pp. 107-125.
20. Ghosh, M., and Meeden, G. (1986). "Empirical Bayes Estimation in Finite Population Sampling," Journal of the American Statistical Association, 74, 269-277.
21. Ghosh, M., and Rao, J. N. K. (1994), "Small Area Estimation: An Appraisal" (with discussion), Statistical Science, 9, 65-93.
22. Gilks, W. R., and Wild, P. (1992), "Adaptive Rejection Sampling for Gibbs Sampling," Applied Statistics, 41, 337-348.
23. Leonard, T., and Novick, M. R. (1986), "Bayesian Full Rank Marginalization for Two-Way Contingency Tables," Journal of Educational Statistics, 11. 33-56.
24. MacGibbon, B., and Tomberlin, T. J. (1989), "Small Area Estimates of Proportions via Empirical Bayes Techniques," Survey Methodology, 15, 237-252.
25. Maiti, T. (1997), "Hierarchical Bayes Estimation of Mortality Rates for Disease Mapping," Technical Report 546, University of Florida, Dept, of Statistics.
26. Malec, D., Sedransk, J., and Tompkins, L. (1993), "Bayesian Predictive Inference for Small Areas for Binary Variables in the National Health Interview Survey," in Case Studies in Bayesian Statistics, eds. C. Gat-sonis, J. S. Hodges, R. E. Kass, and N. D. Singpurwalla, New York: Springer-VerJag. pp. 377-389.
27. McCullagh, P., and Nelder, J. A. (1989), Generalized Linear Models (2nd ed.), London: Chapman and Hall.
28. Nandram, B., and Sedransk, J. (1993), "Bayesian Predictive Inference for a Finite Population Proportion: Two-Stage Cluster Sampling," Journal of the Royal Statistical Society, Ser. B. 55, 399-408.
29. Prasad, N. G. N., and Rao, J. N. K. (1990), "The Estimation of the Mean Squared Error of Small-Arca Estimators," Journal of the American Statistical Association, 85, 163-171.
30. Spiegelhalter, D. J., Thomas, A., Best, N., and Gilks, W. R. (1995), "BUGS: Bayesian Inference Using Gibbs Sampling, Version 0.50," technical report, Cambridge University, Institute of Public Health, Medical Research Council Biostatistics Unit.
31. Statistics Canada (1992), "The 1991 General Social Survey-Cyclc 6: Health," in Public Use Microdata File Documentation and User's Guide, Ottawa: Statistics Canada.
32. Stroud, T. W. F. (1987), "Bayes and Empirical Bayes Approaches to Small Area Estimation of Small Area Statistics," in International Symposium on Small Area Statistics, eds. R. Platek, J. N. K. Rao, C. E. Saerndal, and M. P. Singh, New York: Wiley, pp. 124-140.
33. Stroud, T. W. F (1991), "Hierarchical Bayes Predictive Means and Variances With Application to Sample Survey Inference," Communications in Statistics, Part A-Theory and Methods, 20, 13-36.
34. Stroud, T. W. F (1994), "Bayesian Inference From Categorical Survey Data," Canadian Journal of Statistics, 22, 33-45.
35. Tierney, L., and Kadane, J. B. (1986), "Accurate Approximations for Posterior Moments and Marginal Densities," Journal of the American Statistical Association, 81, 82-86.
36. Tsutakawa, R. K. (1985), "Estimation of Cancer Mortality Rates: A Bayesian Analysis of Small Frequencies," Biometrics, 41, 69-79.
37. Tsutakawa, R. K (1988), "Mixed Model for Analyzing Geographic Variability in Mortality Rates," Journal of the American Statistical Association, 83, 37-42.
38. Tsutakawa, R. K., Shoop, G. L., and Marienfeld, C. J. (1985), "Empirical Bayes Estimation of Cancer Mortality Rates," Statistics in Medicine, 4, 201-212.
39. Waller, L. A., Carlin, B. P., Xia, H., and Gelfand, A. E. (1997), "Hierarchical Spatio-Temporal Mapping of Disease Rates," Journal of the American Statistical Association, 92, 607-617.
40. Zeger, S. L., and Karim, M. R. (1991), "Generalized Linear Models With Random Effects: A Gibbs Sampling Approach," Journal of the American Statistical Association, 86, 79-86.