A Hybrid Approximation Bayesian Test of Variance Components for Longitudinal Data

References

• Breslow , N. E. , Clayton , D. G. ( 1993 ). Approximate inference in generalized linear mixed models . J. Amer. Statist. Assoc. 88 : 9 – 25 .
   Web of Science ®Google Scholar
• Chib , S. ( 1995 ). Marginal likelihood from the Gibbs output . J. Amer. Statist. Assoc. 90 : 1313 – 1321 .
   Web of Science ®Google Scholar
• Chib , S. , Greenberg , E. , Winkelmann , R. ( 1998 ). Posterior simulation and Bayes factors in panel count data models . J. Econometrics 86 : 33 – 54 .
   Web of Science ®Google Scholar
• Chib , S. , Jeliazkov , I. ( 2001 ). Marginal likelihood from the Metropolis–Hastings output . J. Amer. Statist. Assoc. 96 : 270 – 281 .
   Web of Science ®Google Scholar
• Chib , S. , Jeliazkov , I. ( 2005 ). Accept-reject Metropolis–Hastings sampling and marginal likelihood estimation . Statist. Neerl. 59 : 30 – 44 .
   Web of Science ®Google Scholar
• Chib , S. , Jeliazkov , I. ( 2006 ). Inference in semiparametric dynamic models for binary longitudinal data . J. Amer. Statist. Assoc. 101 : 685 – 700 .
   Web of Science ®Google Scholar
• Christiansen , C. L. , Morris , C. N. (1997). Hierarchical Poisson regression modeling. J. Amer. Statist. Assoc. 92:618–632.
   Web of Science ®Google Scholar
• Crainiceanu , C. M. , Ruppert , D. , Claeskens , G. , Wand , M. P. ( 2005 ). Exact likelihood ratio tests for penalized splines . Biometrika 92 : 91 – 103 .
   Web of Science ®Google Scholar
• Daniels , M. J. , Kass , R. E. ( 1999 ). Nonconjugate Bayesians estimation of covariance matrices and its use in hierarchical models . J. Amer. Statist. Assoc. 94 : 1254 – 1263 .
   Web of Science ®Google Scholar
• DiCiccio , T. J. , Kass , R. E. , Raftery , A. , Wasserman , L. ( 1997 ). Computing Bayes factor by combining simulation and asymptotic approximations . J. Amer. Statist. Assoc. 92 : 903 – 915 .
   Web of Science ®Google Scholar
• Gelfand , A. E. , Dey , D. K. ( 1994 ). Bayesian model choice: asymptotics and exact calculations . J. Roy. Statist. Soc. B. 56 : 501 – 514 .
   Google Scholar
• George , E. I. , McCulloch , R. E. ( 1993 ). Variable selection via Gibbs sampling . J. Amer. Statist. Assoc. 88 : 881 – 889 .
   Web of Science ®Google Scholar
• Geweke , J. ( 1999 ). Using simulation methods for Bayesian econometric models: inference, development, and communication . Econom. Rev. 18 : 1 – 73 .
   Google Scholar
• Huang , S. Y. , Hsiao , C. K. , Chang , C. W. ( 2003 ). Optimal volume-corrected Laplace-Metropolis method . Ann. Inst. Statist. Math. 55 : 655 – 670 .
   Web of Science ®Google Scholar
• Kass , R. E. , Raftery , A. E. ( 1995 ). Bayes factors . J. Amer. Statist. Assoc. 90 : 773 – 795 .
   Web of Science ®Google Scholar
• Kass , R. E. , Wasserman , L. ( 1995 ). A reference Bayesian test for nested hypothesis and its relationship to the Schwarz criterion . J. Amer. Statist. Assoc. 90 : 928 – 934 .
   Web of Science ®Google Scholar
• Kass , R. E. , Wasserman , L. ( 1996 ). The selection of prior distributions by formal rules . J. Amer. Statist. Assoc. 91 : 1343 – 1369 .
   Web of Science ®Google Scholar
• et al. . ( 1985 ). A double-blind crossover evaluation of progabide in partial seizures . Neurology 35 : 285 .
   Web of Science ®Google Scholar
• Lin , X. , 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
• Meng , X. L. , Schilling , S. ( 2002 ). Warp bridge sampling . J. Comput. Graph. Statist. 11 : 552 – 586 .
   Web of Science ®Google Scholar
• Meng , X. L. , Wong , W. H. ( 1996 ). Simulating ratios of normalizing constants via a simple identity: a theoretical exploration . Statist. Sinica 6 : 831 – 860 .
   Web of Science ®Google Scholar
• Newton , M. A. , Raftery , A. E. ( 1994 ). Approximate Bayesian inference by the weighted likelihood bootstrap (with discussion) . J. Roy. Statist. Soc. B 56 : 3 – 48 .
   Google Scholar
• Natarajan , R. , Kass , R. ( 2000 ). Reference Bayesian methods for generalized linear mixed models . J. Amer. Statist. Assoc. 95 : 227 – 237 .
   Web of Science ®Google Scholar
• O'Hagan , A. ( 1994 ). Kendall's Advanced Theory of Statistics: Bayesian Inference . Vol. 2B . London : Edward Arnold .
   Google Scholar
• Pauler , D. K. , Wakefield , J. C. , Kass , R. E. ( 1999 ). Bayes factors and approximations for variance component models . J. Amer. Statist. Assoc. 94 : 1242 – 1253 .
   Web of Science ®Google Scholar
• Potthoff , R. F. , Roy , S. N. ( 1964 ). A generalized multivariate analysis of variance model useful especially for growth curve problems . Biometrika 51 : 313 – 326 .
   Web of Science ®Google Scholar
• Sinharay , S. , Stern , H. S. ( 2001 ). Bayes factors for variance component testing in generalized linear mixed models. Bayesian Methods with Applications to Science, Policy and Official Statistics (ISBA 2000 Proceedings), pp. 507–516 .
   Google Scholar
• Sinharay , S. , Stern , H. S. ( 2005 ). An empirical comparison of methods for computing Bayes factors in generalized linear mixed models . J. Comput. Graph. Statist. 14 : 415 – 435 .
   Web of Science ®Google Scholar
• Tsai , M. Y. , Hsiao , C. K. ( 2008 ). Computation of reference Bayesian inference for variance components in longitudinal studies . Computat. Statist. 23 : 587 – 604 .
   Web of Science ®Google Scholar
• Wolfinger , R. D. , Kass , R. E. ( 2000 ). Nonconjugate Bayesian analysis of variance component models . Biometrics 56 : 768 – 774 .
   PubMed Web of Science ®Google Scholar