Multilevel generalized linear models

Handbook of Multilevel Analysis

Volumn , Issue , 2008, Pages 335-376

  Rodríguez, Germán ^a  

^a PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 59649094258     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-0-387-73186-5_9     Document Type: Chapter

References (95)

1. O. O. Aalen. Heterogeneity in survival analysis. Statistics in Medicine, 7: 1121-1137, 1988.
2. M. Abramowitz and I. A. Stegun, editors. Handbook of Mathematical Functions. Number 55 in National Bureau of Standards Applied Mathematics Series. U.S. Government Printing Office, Washington, DC, 1964.
3. M. Aitkin, D. Anderson, B. Francis, and J. Hinde. Statistical Modelling in GLIM. Clarendon Press, Oxford, 1989.
4. M. Aitkin and D. G. Clayton. The fitting of exponential, Weibull and extreme value distributions to complex censored survival data using GLIM. Applied Statistics, 29:156-163, 1980.
5. P. D. Allison. Discrete-time methods for the analysis of event histories. Sociological Methodology, 13:61-98, 1982.
6. D. A. Anderson and M. Aitkin. Variance component models with binary response: Interviewer variability. Journal of the Royal Statistical Society, Series B, 47:203-210, 1985.
7. J. S. Barber, S. A. Murphy, W. G. Axinn, and J. Maples. Discrete-time multilevel hazard analysis. Sociological Methodology, 30:201-235, 2000.
8. S. Bennet and J. Whitehead. Fitting logistic and log-logistic regression models to censored data using GLIM. GLIM Newsletter, 4:12-19, 1981.
9. N. G. Best, M. K. Cowles, and S. K. Vines. CODA: Convergence Diagnosis and Output Analysis Software for Gibbs Sampling Output, version 0.40. Medical Research Council Biostatistics Unit, Cambridge, UK, 1997.
10. J. G. Booth, J. P. Hobert, and W. Jank. A survey of Monte Carlo algorithms for maximizing the likelihood of a two-stage hierarchical model. Statistical Modelling, 1:333-349, 2001.
11. N. E. Breslow and D. G. Clayton. Approximate inference in generalized linear mixed models. Journal of the American Statistical Association, 88:9-25, 1993.
12. N. E. Breslow and X. Lin. Bias correction in generalised linear mixed models with a single component of dispersion. Biometrika, 82:81-91, 1995.
13. W. J. Browne and D. Draper. A comparison of Bayesian and likelihood-based methods for fitting multilevel models. Bayesian Analysis, 1:473-549, 2006. (with discussion)
14. D. G. Clayton. A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Biometrika, 65:141-151, 1978.
15. D. G. Clayton. The analysis of event history data: Review of progress and outstanding problems. Statistics in Medicine, 7:819-841, 1988.
16. D. G. Clayton. Generalized linear mixed models. In W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, editors, Markov Chain Monte Carlo in Practice, pages 275-301. Chapman & Hall, London, 1996.
17. D. G. Clayton and J. Cuzick. The EM algorithm for Cox's regression model using GLIM. Applied Statistics, 34:148-156, 1985.
18. D. G. Clayton and J. Cuzick. Multivariate generalizations of the proportional hazards model. Journal of the Royal Statistical Society, Series B, 148:82-117, 1985. (with discussion)
19. C. Corcoran, B. Coull, and A. Patel. Egret for Windows User Manual. Cytel Software Corporation, Cambridge, MA, 1999.
20. D. R. Cox. Regression models and life tables. Journal of the Royal Statistical Society, Series B, 34:187-220, 1972. (with discussion)
21. D. R. Cox. Partial likelihood. Biometrika, 62:269-276, 1975.
22. D. R. Cox and D. Oakes. Analysis of Survival Data. Chapman & Hall, London, 1984.
23. M. J. Crowder. Beta-binomial Anova for proportions. Applied Statistics, 27: 34-37, 1978.
24. M. Davidian and D. M. Giltinan. Nonlinear Models for Repeated Measurement Data. Chapman & Hall, London, 1995.
25. P. J. Diggle, K.-Y. Liang, and S. L. Zeger. Analysis of Longitudinal Data. Oxford University Press, Oxford, UK, 1994.
26. P. Feigl and M. Zelen. Estimation of exponential survival probabilities with concomitant information. Biometrics, 21:826-838, 1967.
27. A. Gelman and D. B. Rubin. Inference from iterative simulation using multiple sequences. Statistical Science, 7:457-511, 1992. (with discussion)
28. J. Geweke. Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments. In J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, editors, Bayesian Statistics 4, pages 169-194. Oxford University Press, Oxford, UK, 1992.
29. W. R. Gilks and P. Wild. Adaptive rejection sampling for Gibbs sampling. Applied Statistics, 41:337-348, 1992.
30. H. Goldstein. Nonlinear multilevel models, with an application to discrete response data. Biometrika, 78:45-51, 1991.
31. H. Goldstein. Multilevel models and generalised estimating equations. Multilevel Modelling Newsletter, 5(2):2, 1993.
32. H. Goldstein. Multilevel unit specific and population average generalised linear models. Multilevel Modelling Newsletter, 7(3):4-5, 1995.
33. H. Goldstein. Consistent estimators for multilevel generalised linear models using an iterated bootstrap. Multilevel Modelling Newsletter, 8(1):3-6, 1996.
34. H. Goldstein and J. Rasbash. Improved approximations for multilevel models with binary responses. Journal of the Royal Statistical Society, Series A, 159: 505-513, 1996.
35. C. Gouriéroux and A. Monfort. Simulation-Based Econometric Methods. Oxford University Press, Oxford, UK, 1996.
36. P. J. Green. Penalized likelihood for general semi-parametric regression models. International Statistical Review, 55:245-259, 1987.
37. G. Guo and G. Rodríguez. Estimating a multivariate proportional hazards model for clustered data using the EM algorithm, with an application to child survival in Guatemala. Journal of the American Statistical Association, 87: 969-976, 1992.
38. D. Hedeker and R. D. Gibbons. A random-effects ordinal regression model for multilevel analysis. Biometrics, 50:933-944, 1994.
39. D. Hedeker and R. D. Gibbons. MIXOR: A computer program for mixed-effects ordinal regression analysis. Computer Methods and Programs in Biomedicine, 49:157-176, 1996.
40. T. R. Holford. The analysis of rates and survivorship using log-linear models. Biometrics, 36:299-306, 1980.
41. P. Hougaard. Life table methods for heterogeneous populations: Distributions describing the heterogeneity. Biometrika, 71:75-83, 1984.
42. P. Hougaard. Survival models for heterogeneous populations derived from stable distributions. Biometrika, 73:387-396, 1986.
43. J. D. Kalbfleisch and R. L. Prentice. The Statistical Analysis of Failure Time Data, 2nd edition. Wiley, New York, 2002.
44. M. P. Keane. Simulation estimation for panel data models with limited dependent variables. In G. S. Maddala, C. R. Rao, and H. D. Vinod, editors, Handbook of Statistics, volume 11, pages 545-571. North-Holland, Amsterdam, 1993.
45. A. Y. C. Kuk. Asymptotically unbiased estimation in generalized linear models with random effects. Journal of the Royal Statistical Society, Series B, 57: 395-407, 1995.
46. N. M. Laird. Empirical Bayes methods for two-way contingency tables. Biometrika, 65:581-590, 1978.
47. N. M. Laird and D. Olivier. Covariance analysis of censored survival data using log-linear analysis techniques. Journal of the American Statistical Association, 76:231-240, 1981.
48. J. F. Lawless. Regression methods for Poisson process data. Journal of the American Statistical Association, 82:808-815, 1987.
49. Y. Lee and J. A. Nelder. Hierarchical generalized linear models. Journal of the Royal Statistical Society, Series B, 58:619-678, 1996.
50. S. R. Lerman and C. F. Manski. On the use of simulated frequencies to approximate choice probabilities. In C. F. Manski and D. McFadden, editors, Structural Analysis of Discrete Data with Econometric Applications, pages 305-319. MIT Press, Cambridge, MA, 1981.
51. L. A. Lillard and C. W. A. Panis. aML: Multilevel Multiprocess Statistical Software, Version 2.0. EconWare, Los Angeles, CA, 2003.
52. X. Lin and N. E. Breslow. Bias correction in generalized linear mixed models with multiple components of dispersion. Journal of the American Statistical Association, 91:1007-1016, 1996.
53. Q. Liu and D. A. Pierce. A note on Gauss-Hermite quadrature. Biometrika, 81: 624-629, 1994.
54. N. T. Longford. A quasi-likelihood adaptation for variance component analysis. In American Statistical Association Proceedings of the Statistical Computing Section, pages 137-142. 1988.
55. N. T. Longford. VARCL: Software for Variance Component Analysis of Data with Nested Random Effects (Maximum Likelihood). Educational Testing Service, Princeton, NJ, 1988.
56. N. T. Longford. Logistic regression with random coefficients. Computational Statistics & Data Analysis, 17:1-15, 1994.
57. T. A. Louis. Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical Society, Series B, 44:226-233, 1982.
58. K. G. Manton, E. Stallard, and J. W. Vaupel. Alternative models for the heterogeneity of mortality risks among the aged. Journal of the American Statistical Association, 81:635-644, 1986.
59. P. McCullagh and J. A. Nelder. Generalized Linear Models, 2nd edition. Chapman & Hall, London, 1989.
60. C. E. McCulloch. Maximum likelihood algorithms for generalized linear mixed models. Journal of the American Statistical Association, 92:162-170, 1997.
61. D. McFadden. A method of simulated moments for estimation of discrete response models without numerical integration. Econometrica, 57:995-1026, 1989.
62. W. H. Mosley and L. C. Chen. An analytical framework for the study of child survival in developing countries. Population and Development Review, 10:25-45, 1984.
63. J. Myles and D. G. Clayton. GLMMGibbs: An R Package for Estimating Bayesian Generalised Linear Mixed Models by Gibbs Sampling. Comprehensive R Archive Network (devel section), 2001. URL http://cran.r-project.org
64. J. C. Naylor and A. F. M. Smith. Applications of a method for the efficient computation of posterior distributions. Applied Statistics, 31:214-225, 1980.
65. J. A. Nelder and R. Wedderburn. Generalized linear models. Journal of the Royal Statistical Society, Series B, 135:370-384, 1972.
66. J. M. Neuhaus, J. D. Kalbfleisch, and W. W. Hauck. A comparison of clusterspecific and population-averaged approaches to analyzing correlated binary data. International Statistical Review, 59:25-35, 1991.
67. E. S. W. Ng, J. R. Carpenter, H. Goldstein, and J.Rasbash. Estimation in generalised linear mixed models with binary outcomes by simulated maximum likelihood. Statistical Modelling, 6:23-42, 2006.
68. D. Oakes. A model for association in bivariate survival data. Journal of the Royal Statistical Society, Series B, 44:414-422, 1982.
69. A. R. Pebley, N. Goldman, and G. Rodríguez. Prenatal and delivery care and childhood immunization in Guatemala: Do family and community matter? Demography, 33:231-247, 1996.
70. J. C. Pinheiro and D. M. Bates. Approximations to the log-likelihood function in the nonlinear mixed-effects model. Journal of Computational and Graphical Statistics, 4:12-35, 1995.
71. J. C. Pinheiro and D. M. Bates. Mixed-Effects Models in S and S-PLUS. Springer, New York, 2000.
72. R. L. Prentice and L. A. Gloeckler. Regression analysis of grouped survival data with application to breast cancer data. Biometrics, 34:57-67, 1978.
73. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical Recipes in C, 2nd edition. Cambridge University Press, Cambridge, MA, 1992.
74. S. Rabe-Hesketh, A. Skrondal, and A. Pickles. Reliable estimation of generalized linear mixed models using adaptive quadrature. The Stata Journal, 2:1-21, 2002.
75. A. E. Raftery and S. M. Lewis. How many iterations in the Gibbs sampler? In J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, editors, Bayesian Statistics 4, pages 763-773. Oxford University Press, Oxford, UK, 1992.
76. A. E. Raftery and S. M. Lewis. Implementing MCMC. In W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, editors, Markov Chain Monte Carlo in Practice, pages 115-130. Chapman & Hall, London, 1996.
77. S. W. Raudenbush, M.-L. Yang, and M. Yosef. Maximum likelihood for generalized linear models with nested random effects via high-order, multivariate Laplace approximation. Journal of Computational and Graphical Statistics, 9: 141-157, 2000.
78. G. O. Roberts. Markov chain concepts related to sampling algorithms. In W. R. Gilks, S. Richardson, and D. J. Spiegelhalter, editors, Markov Chain Monte Carlo in Practice, pages 45-57. Chapman & Hall, London, 1996.
79. G. Rodríguez. Event history analysis. In S. Kotz, C. B. Read, and D. L. Banks, editors, Encyclopedia of Statistical Sciences, Update Volume, pages 222-230. Wiley, New York, 1997.
80. G. Rodríguez and I. Elo. Intra-class correlation in random-effects models for binary data. The Stata Journal, 3:32-46, 2003.
81. G. Rodríguez and N. Goldman. An assessment of estimation procedures for multilevel models with binary responses. Journal of the Royal Statistical Society, Series A, 158:73-89, 1995.
82. G. Rodríguez and N. Goldman. Improved estimation procedures for multilevel models with binary response: A case-study. Journal of the Royal Statistical Society, Series A, 164:339-355, 2001.
83. N. Sastry. A nested frailty model for survival data, with an application to the study of child survival in northeast Brazil. Journal of the American Statistical Association, 92:426-435, 1997.
84. R. Schall. Estimation in generalized linear models with random effects. Biometrika, 78:719-727, 1991.
85. S. G. Self and K.-Y. Liang. Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under non-standard conditions. Journal of the American Statistical Association, 82:605-610, 1987.
86. D. J. Spiegelhalter, A. Thomas, N. G. Best, and W. R. Gilks. BUGS: Bayesian Inference Using Gibbs Sampling. Medical Research Council Biostatistics Unit, Cambridge, UK, 1996.
87. R. Stiratelli, N. M. Laird, and J. H. Ware. Random-effects models for serial observations with binary response. Biometrics, 40:961-971, 1984.
88. D. O. Stram and J. W. Lee. Variance components testing in the longitudinal mixed-effects model. Biometrics, 50:1171-1177, 1994.
89. T. M. Therneau and P. M. Grambsch. Modeling Survival Data: Extending the Cox Model. Springer, New York, 2000.
90. R. A. Thisted. Elements of Statistical Computing: Numerical Computation. Chapman & Hall, London, 1988.
91. J. Vaupel, K. G. Manton, and E. Stallard. The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography, 16:439-454, 1979.
92. J. Vaupel and A. Yashin. Heterogeneity's ruses: Some surprising effects of selection on population dynamics. American Statistician, 39:176-185, 1985.
93. J. Whitehead. Fitting Cox's regression model to survival data using GLIM. Applied Statistics, 29:268-275, 1980.
94. G. Y. Wong and W. M. Mason. The hierarchical logistic regression model for multilevel analysis. Journal of the American Statistical Association, 80:513-524, 1985.
95. S. L. Zeger and M. R. Karim. Generalized linear models with random effects: A Gibbs sampling approach. Journal of the American Statistical Association, 86:79-86, 1991.