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Fan, Y.; Leslie, D. S.; Wand, M. P.

Generalised linear mixed model analysis via sequential Monte Carlo sampling. (English) Zbl 1320.62178

Electron. J. Stat. 2, 916-938 (2008).
Summary: We present a sequential Monte Carlo sampler algorithm for the Bayesian analysis of generalised linear mixed models (GLMMs). These models support a variety of interesting regression-type analyses, but performing inference is often extremely difficult, even when using the Bayesian approach combined with Markov chain Monte Carlo (MCMC). The Sequential Monte Carlo sampler (SMC) is a new and general method for producing samples from posterior distributions. In this article we demonstrate use of the SMC method for performing inference for GLMMs. We demonstrate the effectiveness of the method on both simulated and real data, and find that sequential Monte Carlo is a competitive alternative to the available MCMC techniques.

Cited in 3 Documents

MSC:

62J12 Generalized linear models (logistic models)
62G08 Nonparametric regression and quantile regression
65C05 Monte Carlo methods

Keywords:

generalised additive models; longitudinal data analysis; nonparametric regression; sequential Monte Carlo sampler

Software:

MASS (R); SemiPar
PDF BibTeX XML Cite
\textit{Y. Fan} et al., Electron. J. Stat. 2, 916--938 (2008; Zbl 1320.62178)
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References:

[1] Besag, J., Green, P.J., Higdon, D. and Mengersen, K. (1995). Bayesian computation and stochastic systems., Statistical Science , 10 , 3-66. · Zbl 0955.62552
[2] Breslow, N.E. and Clayton, D.G. (1993). Approximate inference in generalized linear mixed models., Journal of the American Statistical Association , 88 , 9-25. · Zbl 0775.62195
[3] Breslow, N.E. and Lin X. (1995). Bias correction in generalised linear mixed models with a single component of dispersion., Biometrika , 82 , 81-91. · Zbl 0823.62059
[4] Carpenter, J., Clifford, P. and Fearnhead, P. (1999). An improved particle filter for non-linear problems., IEE proceedings - Radar, Sonar and Navigation , 146 , 2-7.
[5] Chopin, N. (2002). A Sequential Particle Filter for Static Models., Biometrika , 89 , 539-551. · Zbl 1036.62062
[6] Clayton, D. (1996). Generalized linear mixed models, pp. 275-301. In, Markov Chain Monte Carlo in Practice , eds. Gilks, W.R., Richardson, S. and Spiegelhalter, D. J. London: Chapman & Hall. · Zbl 0841.62059
[7] Cowles, M. K. and Carlin, B. P. (1996). Markov chain Monte Carlo convergence diagnostics: A comparative review., Journal of American Statistics Association , 91 , 883-904. · Zbl 0869.62066
[8] Del Moral, P., Doucet, A. and Jasra, A. (2006). Sequential Monte Carlo samplers., Journal of the Royal Statistical Society, Series B , 68 , 411-436. · Zbl 1105.62034
[9] Del Moral, P., Doucet, A. and Jasra, A. (2007). Sequential Monte Carlo for Bayesian computation. In, Bayesian Statistics 8, eds. J. M. Bernardo, M. J. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith and M. West. · Zbl 1252.62016
[10] Diggle, P., Liang, K-L. and Zeger, S. (1995)., Analysis of Longitudinal Data. Oxford: Oxford University Press. · Zbl 1031.62002
[11] Douc, R., Cappé, O. and Moulines, E. (2005). Comparison of resampling schemes for particle filtering., Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis , 64-69.
[12] Doucet, A., Godsill, S. and Andrieu C. (2000). On sequential Monte Carlo sampling methods for Bayesian filtering., Statistics and Computing , 10 , 197-208.
[13] Fearnhead, P. (2004). Particle filters for mixture models with an unknown number of components., Statistics and Computing , 14 , 11-21.
[14] Frigessi, A. (2003). On Some Current Research in MCMC, pp. 172-178. In, Highly Structured Stochastic Systems , eds. Green, P.J., Hjort, N.L. and Richardson, S. Oxford University Press.
[15] Gamerman, D. (1997)., Markov chain Monte Carlo: Stochastic simulation for Bayesian inference. Chapman & Hall. · Zbl 0881.62002
[16] Gelfand, A.E., Sahu, S.K. and Carlin, B.P. (1995). Efficient parameterisations for normal linear mixed models., Biometrika , 82 , 479-488. · Zbl 0832.62064
[17] Gelfand, A.E. and Smith, A. F. M. (1990). Sampling Based Approaches to Calculating Marginal Densities., Journal of the American Statistical Association , 85 , 398-409. · Zbl 0702.62020
[18] Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models., Bayesian Analysis , 1 , 515-533. · Zbl 1331.62139
[19] Gilks, W. R. and Berzuini, C. (2001). Following a moving target-Monte Carlo inference for dynamic Bayesian models., Journal of the Royal Statistical Society, Series B , 63 , 127-146. · Zbl 0976.62021
[20] Kong, A., Liu, J.S., and Wong, W.H. (1994). Sequential imputations and Bayesian missing data problems., Journal of American Statistics Association , 89 (425), 278-288. · Zbl 0800.62166
[21] Kitagawa, G. (1996). Monte Carlo filter and smoother for non-Gaussian, non-linear state space models., Journal of Computational and Graphical Statistics , 5 , 1-25.
[22] Lin, X. and Carroll, R.J. (2001) Semiparametric regression for clustered data., Biometrika , 88 , 1179-1865. · Zbl 0994.62031
[23] McCulloch, C.E., and Searle, S.R. (2000)., Generalized, Linear, and Mixed Models . New York: John Wiley & Sons. · Zbl 0964.62061
[24] Neal, R. (2001). Annealed importance sampling., Statistics and Computing , 11 , 125-139.
[25] Roberts, G. O., Gelman, A. and Gilks, W. R. (1997). Weak convergence and optimal scaling of random walk Metropolis algorithms., Annals of Applied Probability , 7 , 110-120. · Zbl 0876.60015
[26] Roberts, G. O. and Sahu, S. K. (1997). Updating schemes, covariance structure, blocking and parameterisation for the Gibbs sampler., Journal of the Royal Statistical Society, Series B , 59 , 291-317. · Zbl 0886.62083
[27] Ruppert, D., Wand, M. P. and Carroll, R.J. (2003)., Semiparametric Regression . New York: Cambridge University Press. · Zbl 1038.62042
[28] Skrondal, A. and Rabe-Hesketh, S. (2004)., Generalized Latent Variable Modeling: Multilevel, Longitudinal and Structural Equation Models. Boca Raton, Florida: Chapman & Hall. · Zbl 1097.62001
[29] Venables, W. & Ripley, B.D. (2005). MASS. R package within the bundle VR 7.2-24., http://cran.r-project.org.
[30] Zhao, Y., Staudenmayer, J., Coull, B.A. and Wand, M.P. (2006). General design Bayesian generalized linear mixed models., Statistical Science , 21 , 35-51. · Zbl 1129.62063
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