Bayesian semiparametric reproductive dispersion mixed models for non-normal longitudinal data: estimation and case influence analysis

References

• Fung W-K, Zhu Z-Y, Wei B-C et al.., Influence diagnostics and outlier tests for semiparametric mixed models. J R Stat Soc Ser B. 2002;64:565–579. doi: 10.1111/1467-9868.00351
   Google Scholar
• Lombardía MJ, Sperlich S. Semiparametric inference in generalized mixed effects models. J R Stat Soc Ser B. 2008;70:913–930. doi: 10.1111/j.1467-9868.2008.00655.x
   Google Scholar
• Liang H. Generalized partially linear mixed-effects models incorporating mismeasured covariates. Ann Inst Statist Math. 2009;61:27–46. doi: 10.1007/s10463-007-0146-0
   PubMed Web of Science ®Google Scholar
• Qin GY, Zhu ZY. Robust estimation in generalized semiparametric mixed models for longitudinal data. J Multivariate Anal. 2007;98:1658–1683. doi: 10.1016/j.jmva.2007.01.006
   Web of Science ®Google Scholar
• Qin GY, Zhu ZY. Robustified maximum likelihood estimation in generalized partial linear mixed model for longitudinal data. Biometrics. 2009;65:52–59. doi: 10.1111/j.1541-0420.2008.01050.x
   PubMed Web of Science ®Google Scholar
• Chen X-D, Tang N-S. Bayesian analysis of semiparametric reproductive dispersion mixed-effects models. Comput Statist Data Anal. 2010;54:2145–2158. doi: 10.1016/j.csda.2010.03.022
   Web of Science ®Google Scholar
• Kleinman KP, Ibrahim JG. A semi-parametric Bayesian approach to generalized linear mixed models. Stat Med. 1998;17:2579–2596. doi: 10.1002/(SICI)1097-0258(19981130)17:22<2579::AID-SIM948>3.0.CO;2-P
   PubMed Web of Science ®Google Scholar
• Kleinman KP, Ibrahim JG. A semiparametric Bayesian approach to the random effects model. Biometrics. 1998;54:921–938. doi: 10.2307/2533846
   PubMed Web of Science ®Google Scholar
• Chow S-M, Tang NS, Yuan Y, et al. Bayesian estimation of semiparametric nonlinear dynamic factor analysis models using the Dirichlet process prior. British J Math Statist Psych. 2011;64:69–106. doi: 10.1348/000711010X497262
   PubMed Web of Science ®Google Scholar
• Lee S-Y, Lu B, Song X-Y. Semiparametric Bayesian analysis of structural equation models with fixed covariates. Stat Med. 2008;15:2341–2360. doi: 10.1002/sim.3098
   Web of Science ®Google Scholar
• Li YS, Müller P, Lin XH. Center-adjusted inference for a nonparametric Bayesian random effect distribution. Statist Sinica. 2011;21:1201–1223. doi: 10.5705/ss.2009.180
   Web of Science ®Google Scholar
• Yang M, Dunson DB, Baird D. Semiparametric Bayes hierarchical models with mean and variance constraints. Comput Statist Data Anal. 2010;54:2172–2186. doi: 10.1016/j.csda.2010.03.025
   PubMed Web of Science ®Google Scholar
• Weiss RE, Cook RD. A graphical case statistic for assessing posterior influence. Biometrika. 1992;79:51–55.
   Web of Science ®Google Scholar
• Peng F, Dey DK. Bayesian analysis of outlier problems using divergence measures. Canad J Statist. 1995;23:199–213. doi: 10.2307/3315445
   Web of Science ®Google Scholar
• Weiss R. An approach to Bayesian sensitivity analysis. J R Stat Soc Ser B. 1996;58:739–750.
   Google Scholar
• Bradlow ET, Zaslavsky AM. Case influence analysis in Bayesian inference. J Comput Graph Statist. 1997;6:314–331.
   Web of Science ®Google Scholar
• Cho H, Ibrahim JG, Sinha D, et al. Bayesian case influence diagnostics for survival models. Biometrics. 2009;65:116–124. doi: 10.1111/j.1541-0420.2008.01037.x
   PubMed Web of Science ®Google Scholar
• Zhu HT, Ibrahim JG, Cho H, et al. Bayesian case influence measures for statistical models with missing data. J Comput Graph Statist. 2012;21:253–271. doi: 10.1198/jcgs.2011.10139
   PubMed Web of Science ®Google Scholar
• Jorgensen B. The theory of dispersion models. London: Chapman and Hall; 1997.
   Google Scholar
• Sethuraman J. A constructive definition of Dirichlet priors. Statist Sinica. 1994;4:639–650.
   Web of Science ®Google Scholar
• Ishwaran H, Zarepour M. Markov chain Monte Carlo in approximate Dirichlet and beta two-parameter process hierarchical models. Biometrika. 2000;87:371–390. doi: 10.1093/biomet/87.2.371
   Web of Science ®Google Scholar
• Lang S, Brezger A. Bayesian P-splines. J Comput Graph Statist. 2004;13:183–212. doi: 10.1198/1061860043010
   Web of Science ®Google Scholar
• Ruppert D, Wand MP, Carroll RJ. Semiparametric regression. New York: Cambridge University Press; 2003.
   Google Scholar
• Song X-Y, Lu Z-H. Semiparametric latent variable models with Bayesian P-splines. J Comput Graph Statist. 2010;19:590–608. doi: 10.1198/jcgs.2010.09094
   Web of Science ®Google Scholar
• Lee S-Y, Tang N-S. Local influence analysis of nonlinear structural equation models. Psychometrika. 2004;69:573–592. doi: 10.1007/BF02289856
   Web of Science ®Google Scholar
• Gelman A. Inference and monitoring convergence. In: Gilks WR, Richardson S, Spiegelhalter DJ, editors. Markov chain Monte Carlo in practice. London: Chapman and Hall; 1996; p. 131–144.
   Google Scholar
• Wu HL, Zhang JT. Nonparametric regression methods for longitudinal data analysis. Hoboken: John Wiley & Sons; 2006.
   Google Scholar