Double hierarchical generalized linear models

Journal of the Royal Statistical Society. Series C: Applied Statistics

Volumn 55, Issue 2, 2006, Pages 139-185

  Lee, Youngjo ^a   Nelder, John A ^b  

^a Seoul National University   (South Korea)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Generalized linear models; h likelihood; Heavy tailed distribution; Hierarchical generalized linear models; Hierarchical likelihood; Joint generalized linear models; Random effect models; Restricted maximum likelihood estimator; Stochastic volatility models

Indexed keywords

EID: 33644629431     PISSN: 00359254     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1467-9876.2006.00538.x     Document Type: Article

References (68)

1. Aalen, O. O. (1988) Heterogeneity in survival analysis. Statist.Med., 7, 1121-1137.
2. Barndorff-Nielsen, O. E. (1983) On a formula for the distribution of the maximum likelihood estimator. Biometrika, 70, 343-365.
3. Barndorff-Nielsen, O. E. and Shephard, N. (2001) Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics (with discussion). J. R. Statist. Soc. B, 63, 167-241.
4. Bayarri, M. J., DeGroot, M. H. and Kadane, J. B. (1988) What is the likelihood function (with discussion)? In Statistical Decision Theory and Related Topics IV, vol. 1 (eds S. S. Gupta and J. O. Berger). New York: Springer.
5. Bellio, R. and Varin, C. (2005) A pairwise likelihood approach to generalized linear models with crossed random effects. Statist. Modllng, 5, 217-227.
6. Birnbaum, A. (1962) On the foundations of statistical inference (with discussion). J. Am. Statist. Ass., 57, 269-306.
7. Bjørnstad, J. F. (1996) On the generalization of the likelihood function and likelihood principle. J. Am. Statist. Ass., 91, 791-806.
8. Breslow, N. E. and Clayton, D. G. (1993) Approximate inference in generalized linear mixed models. J. Am. Statist. Ass., 88, 9-25.
9. Breslow, N. E. and Lin, X. (1995) Bias correction in generalised linear mixed models with a single component of dispersion. Biometrika, 82, 81-91.
10. Browne, W. J. (1998) Applying MCMC methods to multi-level models. PhD Thesis. University of Bath, Bath.
11. Browne, W. J., Draper, D., Goldstein, H. and Rasbash, J. (2002) Bayesian and likelihood methods for fitting multilevel models with complex level-1 variation. Computnl Statist. Data Anal., 39, 203-225.
12. Carlin, B. P. and Louis, T. A. (2000) Bayesian and Empirical Bayesian Methods for Data Analysis. London: Chapman and Hall.
13. Chen, K., Hu, I. and Ying, Z. (1999) Strong consistency of maximum quasi-likelihood estimators in generalized linear models with fixed and adaptive designs. Ann. Statist., 27, 1155-1163.
14. Cox, D. R. and Reid, N. (1987) Parameter orthogonality and approximate conditional inference. J. R. Statist. Soc. B, 49, 1-18.
15. Cox, D. R. and Reid, N. (2004) A note on pseudo-likelihood constructed from marginal densities. Biometrika, 91, 729-737.
16. Duffie, D. and Singleton, K. (1993) Simulated moments estimation of Markov models of asset prices. Econometrica, 61, 929-952.
17. Eberlein, E. and Keller, U. (1995) Hyperbolic distributions in finance. Bernoulli, 1, 281-299.
18. Efron, B. (1986) Double exponential families and their use in generalized linear regression. J. Am. Statist. Ass., 81, 709-721.
19. Gallant, A. and Tauchen, G. (1996) Which moments to match. Econometr. Theory, 12, 657-681.
20. Goldstein, H. (1986) Multilevel mixed linear model analysis using iterative generalised least squares. Biometrika, 73, 43-56.
21. Goldstein, H. and Rasbash, J. (1996) Improved approximations for multilevel models with binary responses. J. R. Statist. Soc. A, 159, 505-513.
22. Gourieroux, C., Monfort, A. and Renault, E. (1993) Indirect inference. J. Appl. Econometr., 8, S85-S118.
23. Ha, I. D. and Lee, Y. (2005) Comparison of hierarchical likelihood versus orthodox BLUP approach for frailty models. Biometrika, 92, 717-723.
24. Hougaard, P. (2000) Analysis of Multivariate Survival Data. New York: Springer.
25. Lane, P. W. and Nelder, J. A. (1982) Analysis of covariance and standardization as instances of prediction. Biometrics, 38, 613-621.
26. Lee, Y. (2004) Estimating intraclass correlation for binary data using extended quasi-likelihood. Statist. Modllng, 4, 113-126.
27. Lee, Y. and Nelder, J. A. (1996) Hierarchical generalized linear models (with discussion). J. R. Statist. Soc. B, 58, 619-678.
28. Lee, Y. and Nelder, J. A. (2000) The relationship between double-exponential families and extended quasi-likelihood families, with application to modelling Geissler's human sex ratio data. Appl. Statist., 49, 413-419.
29. Lee, Y. and Nelder, J. A. (2001a) Hierarchical generalised linear models: a synthesis of generalised linear models, random effect models and structured dispersions. Biometrika, 88, 987-1006.
30. Lee, Y. and Neider, J. A. (2001b) Modelling and analysing correlated non-normal data. Statist. Modllng, 1, 3-16.
31. Lee, Y. and Nelder, J. A. (2005a) Likelihood for random-effect models (with discussion). Statist. Oper. Res. Trans., 29, 141-182.
32. Lee, Y. and Nelder, J. A. (2005b) Fitting via alternative random-effect models. Statist. Comput., to be published.
33. Leppik, I. E., Dreifuss, F. E., Porter, R., Bowman, T., Santilli, N., Jacobs, M., Crosby, C., Cloyd, J., Stackman, J. and Graves, N. (1987) A controlled study of progabide in partial seizures: methodology and results. Neurology, 37, 963-968.
34. Liang, K.-Y. and Zeger, S. L. (1986) Longitudinal data analysis using generalized linear models. Biometrika, 73, 13-22.
35. Lin, X. and Breslow, N. E. (1996) Bias correction in generalized linear mixed models with multiple components of dispersion. J. Am. Statist. Ass., 91, 1007-1016.
36. Lindsay, B. G. (1988) Composite likelihood methods. Contemp. Math., 80, 221-239.
37. Ma, R. (1999) An orthodox BLUP approach to generalized linear mixed models. PhD Thesis. University of British Columbia, Vancouver.
38. MacKenzie, G., Ha, I. D. and Lee, Y. (2006) Multivariate survival models based on the GTDL. Submitted to Biostatistics.
39. MacKenzie, G. and Pan, J. X. (2006) Optimal joint-mean covariance modelling. In Select. Proc. 2nd Int. Wrkshp Correlated Data Modelling (eds D. Gregori, G. MacKenzie, H. Friedl and R. Corradetti). Milan: Agneli. To be published.
40. Madan, D. B. and Seneta, E. (1990) The variance gamma model for share market returns. J. Bus., 63, 511-524.
41. Molenberghs, G. and Verbeke, G. (2005) Models for Discrete Longitudinal Data. New York: Springer.
42. Neider, J. A. (1965) The analysis of randomized experiments with orthogonal block structure: I, Block structure and the null analysis of variance; II, Treatment structure and the general analysis of variance. Proc. R. Soc. Lond. A, 283, 147-178.
43. Neider, J. A. and Lee, Y. (1991) Generalized linear models for the analysis of Taguchi-type experiments. Appl. Stochast. Mod. Data Anal., 7, 107-120.
44. Nelder, J. A. and Wedderburn, R. W. M. (1972) Generalized linear models. J. R. Statist. Soc, A, 135, 370-384.
45. Noh, M., Ha, I. D. and Lee, Y. (2006) Dispersion frailty models and HGLMs. Statist. Med., to be published.
46. Noh, M. and Lee, Y. (2005) Robust modelling for inference from GLM classes. Manuscript. To be published.
47. Noh, M., Lee, Y. and Pawitan, Y. (2005) Robust ascertainment-adjusted parameter estimation. Genet. Epidem., 29, 68-75.
48. Pan, J. X. and MacKenzie, G. (2003) On modelling mean-covariance structures in longitudinal studies. Biometrika, 90, 239-244.
49. Payne, R. W. (2004) Confidence intervals and tests for contrasts between combined effects in generally balanced designs. In COMPSTAT2004: Proc. Computational Statistics, pp. 1629-1636. Heidelberg: Physica.
50. Payne, R. W. and Tobias, R. D. (1992) General balance, combination of information and the analysis of covariance. Scand. J. Statist., 19, 3-23.
51. Pourahmadi, M. (2000) Maximum likelihood estimation of generalized linear models for multivariate normal covariate matrix. Biometrika, 87, 425-435.
52. Rao, C. R. (1965) The theory of least squares when the parameters are stochastic and its application to the analysis of growth curves. Biometrika, 52, 355-372.
53. Rasbash, J., Browne, W. J., Healy, M., Cameron, B. and Charlton, C. (2004) MLwiN (Version 2.0). London: Institute of Education.
54. Ridout, M.S., Demétrio, C. G. B. and Firth, D. (1999) Estimating intraclass correlation for binary data. Biometrics, 55, 137-148.
55. Rigby, R. A. and Stasinopoulos, D. M. (2005) Generalized additive models for location, scale and shape (with discussion). Appl. Statist., 54, 507-554.
56. Rodríguez, G. and Goldman, N. (1995) An assessment of estimation procedures for multilevel models with binary responses. J. R. Statist. Soc. A, 158, 73-89.
57. Sandmann, G. and Koopman, S. (1998) Estimation of stochastic volatility models via Monte Carlo maximum likelihood. J. Econometr., 87, 271-301.
58. Senn, S. (2000) Consensus and controversy in pharmaceutical statistics (with discussion). Statistician, 49, 135-176.
59. Smyth, G. K. and Verbyla, A. P. (1999) Adjusted likelihood methods for modelling dispersion in generalized linear models. Environmetrics, 10, 696-709.
60. Thall, P. F. and Vail, S. C. (1990) Some covariance-models for longitudinal count data with overdispersion. Biometrics, 46, 657-671.
61. Varin, C. and Vidoni, P. (2005) A note on composite likelihood inference and model selection. Biometrika, 92, 519-529.
62. Wedderburn, R. W. M. (1974) Qua si-likelihood functions, generalized linear models and the Gauss-Newton method. Biometrika, 61, 439-447.
63. Wolfinger, R. and O'Connell, M. (1993) Generalized linear mixed models: a pseudo-likelihood approach. J. Statist. Computn Simuln, 48, 233-243.
64. Xia, N. and Zhang, Z. Z. (2005a) Convergence rate of Lee-Nelder estimators in Poisson-Gamma models. Acta Math. Appl. Sin., to be published.
65. Xia, N. and Zhang, Z. Z. (2005b) Asymptotic normality of Lee-Nelder estimators in a HGLM family. Working Paper. Beijing University of Technology, Beijing.
66. Xue, X. (2001) Analysis of childhood brain tumour data in New York City using frailty models. Statist. Med., 20, 3459-3473.
67. Yates, F. and Cochran, W. G. (1938) The analysis of groups of experiments. J. Agric. Sci., 28, 556-580.
68. Yau, K. K. W. and Kuk, A. Y. C. (2002) Robust estimation in generalized linear mixed models. J. R. Statist. Soc. B, 64, 101-117.