A consistent simulation-based estimator in generalized linear mixed models

References

• Laird , N. M. and Wair , J. H. 1982 . Random-effects models for longitudinal data . Biometrics , 38 : 963 – 974 .
   PubMed Web of Science ®Google Scholar
• Zeger , S. L. , Liang , K. Y. and Albert , P. S. 1988 . Models for longitudinal data: A generalized estimating equation approach . Biometrics , 44 : 1049 – 1060 .
   PubMed Web of Science ®Google Scholar
• Breslow , N. E. and Clayton , D. G. 1993 . Approximate inference in generalized linear mixed models . J. Amer. Statist. Assoc. , 88 : 9 – 25 .
   Web of Science ®Google Scholar
• Rabe-Hesketh , S. , Skrondal , A. and Pickles , A. 2002 . Reliable estimation of generalized linear mixed models using adaptive quadrature . Stata J. , 2 : 1 – 21 .
   Web of Science ®Google Scholar
• Durbin , J. and Koopman , S. J. 1997 . Monte Carlo maximum likelihood estimation for non-Gaussian state space models . Biometrika , 84 : 669 – 684 .
   Web of Science ®Google Scholar
• Joe , H. 2008 . Accuracy of Laplace approximation for discrete response mixed models . Comput. Stat. Data Anal. , 52 : 5066 – 5074 .
   Web of Science ®Google Scholar
• 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 .
   Web of Science ®Google Scholar
• Jiang , J. M. 1998 . Consistent estimators in generalized linear mixed models . J. Amer. Statist. Assoc. , 93 : 720 – 729 .
   Web of Science ®Google Scholar
• Sutradhar , B. C. 2004 . On exact quasilikelihood inference in generalized linear mixed models . Sankhya Indian J. Stat. , 66 : 261 – 289 .
   Google Scholar
• Wang , L. 2007 . A unified approach to estimation of nonlinear mixed effects and Berkson measurement error models . Can. J. Stat. , 35 : 233 – 248 .
   Web of Science ®Google Scholar
• Gouriéroux , C. and Monfort , A. 1996 . Simulation-Based Econometric Methods , New York : Oxford University Press .
   Google Scholar
• McFadden , D. 1989 . A method of simulated moments for estimation of discrete response models without numerical integration . Econometrica , 57 : 995 – 1026 .
   Web of Science ®Google Scholar
• Pakes , A. and Pollard , D. 1989 . Simulation and the asymptotics of optimization estimators . Econometrica , 57 : 1027 – 1057 .
   Web of Science ®Google Scholar
• Wang , L. 2004 . Estimation of nonlinear models with Berkson measurement errors . Ann. Stat. , 32 : 2559 – 2579 .
   Web of Science ®Google Scholar
• Davidian , M. and Gallant , A. R. 1993 . The nonlinear mixed effects model with a smooth random effects density . Biometrika , 80 : 475 – 488 .
   Web of Science ®Google Scholar
• Zhang , D. and Davidian , M. 2001 . Linear mixed models with flexible distributions of random effects for longitudinal data . Biometrics , 57 : 795 – 802 .
   PubMed Web of Science ®Google Scholar
• Field , C. A. and Genton , M. G. 2006 . The multivariate g-and-h distribution . Technometrics , 48 : 104 – 111 .
   Web of Science ®Google Scholar
• Huber , P. J. 2004 . Robust Statistics , New York : Wiley .
   Google Scholar
• Abarin , T. and Wang , L. 2006 . Comparison of GMM with second-order least squares estimator in nonlinear models . Far East J. Theoret. Stat. , 20 : 179 – 196 .
   Google Scholar
• Hampel , F. R. , Ronchetti , E. M. , Rousseeuw , P. J. and Stahel , W. A. 1986 . Robust Statistics: The Approach Based on Influence Functions , New York : Wiley .
   Google Scholar
• Altonji , J. G. and Segal , L. M. 1996 . Small sample bias in GMM estimation of covariance structures . J. Bus. Econ. Stat. , 14 : 353 – 366 .
   Web of Science ®Google Scholar
• Sinha , S. K. 2004 . Robust analysis of generalized linear mixed models . J. Amer. Statist. Assoc. , 99 : 451 – 460 .
   Web of Science ®Google Scholar
• Sinha , S. K. 2006 . Robust inference in generalized linear mixed models for longitudinal data . Can. J. Stat. , 34 ( 2 ) : 1 – 18 .
   Google Scholar
• Qu , A. and Song , X. K. 2004 . Assessing robustness of generalised estimating equations and quadratic inference functions . Biometrika , 91 : 447 – 459 .
   Web of Science ®Google Scholar
• Noh , M. and Lee , Y. 2007 . Robust modeling for inference from generalized linear model classes . J. Amer. Statist. Assoc. , 102 : 1059 – 1072 .
   Web of Science ®Google Scholar
• Thall , P. F. and Vail , S. C. 1990 . Some covariance models for longitudinal count data with overdispersion . Biometrics , 46 : 657 – 671 .
   PubMed Web of Science ®Google Scholar
• Amemiya , T. 1973 . Regression analysis when the dependent variable is truncated normal . Econometrica , 41 : 997 – 1016 .
   Web of Science ®Google Scholar