Standard errors of prediction in generalized linear mixed models

Journal of the American Statistical Association

Volumn 93, Issue 441, 1998, Pages 262-272

  Booth, James G ^a   Hobert, James P ^a  

^a University of Florida ^*  (United States)

Author keywords

Best linear unbiased predictor; Bias correction; Bootstrap; Laplace approximation; Small area estimation; Taylor series

Indexed keywords

EID: 0032336512     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1998.10474107     Document Type: Article

References (46)

1. Battese, G. E., Harter, R. M., and Fuller, W. A. (1988), "An Enror-Components Model for Prediction of County Crop Areas Using Survey and Satellite Data," Journal of the American Statistical Association, 83, 28-36.
2. Beitler, P. J., and Landis, J. R. (1985), "A Mixed-Effects Model for Categorical Data," Biometrics, 41, 991-1000.
3. Breslow, N. E., and Clayton, D. G. (1993), "Approximate Inference in Generalized Linear Mixed Models," Journal of the American Statistical Association, 88, 9-25.
4. Butler, R. W. (1986), "Predictive Likelihood Inference With Applications" (with discussion), Journal of the Royal Statistical Society, Ser. B, 48, 1-38.
5. Butler, R. W. (1989), "Approximate Predictive Pivots and Densities," Biometrika, 76, 489-501.
6. Carlin, B. P., and Gelfand, A. E. (1990), "Approaches for Empirical Bayes Confidence Intervals," Journal of the American Statistical Association, 85, 105-114.
7. Carlin, B. P., and Gelfand, A. E. (1991). "A Sample Reuse Method for Accurate Parametric Empirical Bayes Confidence Intervals," Journal of the Royal Statistical Society, Ser. B. 53, 189-200.
8. Davison, A. C. (1986), "Approximate Predictive Likelihood," Biometrika. 73, 323-332.
9. de Bruijn, N. G. (1981), Asymptotic Methods in Analysis, New York: Dover.
10. Dempster, A. P. (1983), "Comments on 'Parametric Empirical Bayes Inference: Theory and Applications' by C. N. Morris," Journal of the American Statistical Association, 78, 57-58.
11. Efron, B. (1987), "Comments on 'Empirical Bayes Confidence Intervals Based on Bootstrap Samples' by N. M. Laird and T. A. Louis," Journal of the American Statistical Association, 82, 754.
12. Efron, B., and Hinkley, D. V. (1978), "Assessing the Accuracy of the Maximum Likelihood Estimator: Observed Versus Expected Fisher Information," Biometrika, 65, 457-481.
13. Fuller, W. A., and Harter, R. M. (1987). "The Multivariate Components of Variance Model for Small Area Estimation," in Small Area Statistics: An International Symposium, eds. R. Platek, J. N. K. Rao, C. E. Samdal, and M. P. Singh, New York: Wiley, pp. 103-123.
14. Ghosh, M., and Rao, J. N. K. (1994), "Small Area Estimation: An Appraisal," Statistical Science, 9, 55-76.
15. Goldstein, H. (1991), "Nonlinear Multilevel Models. With an Application to Discrete Response Data" Biometrika, 78, 45-51.
16. Hill, J. R. (1986), "Empirical Bayes Statistics: A Comprehensive Theory for Data Analysis," unpublished Ph.D. thesis, University of Texas at Austin.
17. Hinkley, D. (1979), "Predictive Likelihood," The Annals of Statistics, 7, 718-728.
18. Hobert, J. P., and Casella, G. (1996), "The Effect of Improper Priors on Gibbs Sampling in Hierarchical Linear Mixed Models," Journal of the American Statistical Association, 91, 1461-1473.
19. Kackar, R. N., and Harville, D. A. (1984), "Approximations for Standard Errors of Estimates of Fixed and Random Effects in Mixed Linear Models," Journal of the American Statistical Association, 79, 853-862.
20. Kass, R. E., and Steffey, D. (1989), "Approximate Bayesian Inference in Conditionally Independent Hierarchical Models (Parametric Empirical Bayes Models)," Journal of the American Statistical Association, 84, 717-726.
21. Kass, R. E., and Wasserman, L. (1996), "The Selection of Prior Distributions by Formal Rules," Journal of the American Statistical Association, 91, 1343-1370.
22. Kuk, A. Y. C. (1995). "Asymptotically Unbiased Estimation in Generalized Linear Models With Random Effects," Journal of the Royal Statistical Society, Ser. B, 57, 395-407.
23. Lahiri, P., and Rao, J. N. K. (1995), "Robust Estimation of Mean Squared Error of Small Area Estimators," Journal of the American Statistical Association, 90, 758-766.
24. Laird, N. M., and Louis, T. A. (1987), "Empirical Bayes Confidence Intervals Based on Bootstrap Samples." Journal of the American Statistical Association, 82, 739-750.
25. Lejeune, M. and Faulkenberry, D. G. (1982). "A Simple Predictive Density Function," Journal of the American Statistical Association, 77, 654-657.
26. Lin, X., and Breslow, N. E. (1998), "Bias Correction in Generalized Linear Mixed Models With Multiple Components of Dispersion," Journal of the American Statistical Association, 91,1007-1016.
27. Littell, R. C., Milliken, G. A., Stroup, W. W., and Wolfinger, R. D. (1996), SAS System for Mixed Models, Cary, NC: SAS Institute Inc.
28. Longford, N. T. (1994), "Logistic Regression With Random Coefficients," Computational Statistics and Data Analysis, 17, 1-15.
29. Mardia, K. V., Kent, J. T., and Bibby, J. M. (1979), Multivariate Analysis, Boston: Academic Press.
30. McCullagh, P., and Nelder, J. A. (1989), Generalized Linear Models (2nd ed.), London: Chapman and Hall.
31. McCulloch, C. E. (1994), "Maximum Likelihood Variance Components Estimation for Binary Data," Journal of the American Statistical Association, 89, 330-335.
32. McCulloch, C. E. (in press), "Maximum Likelihood Algorithms for Generalized Linear Mixed Models," Journal of the American Statistical Association, 92, 162-170.
33. McGilchrist, C. A. (1994), "Estimation in Generalized Mixed Models," Journal of the Royal Statistical Society, Ser. B, 56, 61-69.
34. Morris, C. N. (1983), "Parametric Empirical Bayes Inference: Theory and Applications," Journal of the American Statistical Association, 78. 47-55.
35. Natarajan, R., and McCulloch, C. E. (1995), "A Note on the Existence of the Posterior Distribution for a Class of Mixed Models for Binomial Responses," Biometrika, 82, 639-643.
36. Natarajan, R., and McCulloch, C. E. (in press), "Gibbs Sampling With Diffuse Priors: A Valid Approach to Data-Driven Inference?" submitted to Journal of Computational and Graphical Statistics.
37. Piegorsch, W. W., and Casella, G. (1996), "Empirical Bayes Estimation for Logistic Regression and Extended Parametric Regression Models," Journal of Agricultural, Biological, and Environmental Statistics, 1,231-247.
38. Prasad, N. G. N., and Rao, J. N. K. (1990), 'The Estimation of the Mean Squared Error of Small-Area Estimators," Journal of the American Statistical Association, 85, 163-171.
39. Robinson, G. K. (1991), 'That BLUP is a Good Thing: The Estimation of Random Effects," Statistical Science, 6, 15-32.
40. SAS Institute Inc. (1997), SAS/STAT Software: Changes and Enhancements Through Release 6.12, Cary, NC: Author.
41. Schall, R. (1991), "Estimation in Generalized Linear Models With Random Effects," Biometrika, 78, 719-727.
42. Searle, S. R., Casella, G., and McCulloch, C. E. (1992), Variance Components, New York: Wiley.
43. Tierney, L., and Kadane, J. B. (1986), "Accurate Approximations for Posterior Moments and Marginal Densities," Journal of the American Statistical Association. 81, 82-86.
44. Waclawiw, M. A., and Liang, K.-Y. (1993), "Prediction of Random Effects in the Generalized Linear Model," Journal of the American Statistical Association, 88, 171-178.
45. Wei, G. C. G., and Tanner, M. A. (1990), "A Monte Carlo Implementation of the EM Algorithm and the Poor Man's Data Augmentation Algorithms," Journal of the American Statistical Association, 85, 699-704.
46. Wolfinger, R., and O'Connell, M. (1993), "Generalized Linear Mixed Models: A Pseudolikclihood Approach," Journal of Statistical Computation and Simulation, 48, 233-243.