1991
DOI: 10.2307/2289717
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Generalized Linear Models With Random Effects; A Gibbs Sampling Approach

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Cited by 267 publications
(174 citation statements)
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“…In the following, we present the joint posterior distribution of the unknown parameters arising for a GLMM for canonical one-parameter exponential families [ 26,27 ]. Assume that conditional on a random effect δ, the responses y i are independent and follow an exponential family with conditional mean related to the linear predictor through g(μ) = Uα + Xδ = η, with δ ~ N(0, G).…”
Section: Bayesian Analysis Using the Gibbs Samplingmentioning
confidence: 99%
See 1 more Smart Citation
“…In the following, we present the joint posterior distribution of the unknown parameters arising for a GLMM for canonical one-parameter exponential families [ 26,27 ]. Assume that conditional on a random effect δ, the responses y i are independent and follow an exponential family with conditional mean related to the linear predictor through g(μ) = Uα + Xδ = η, with δ ~ N(0, G).…”
Section: Bayesian Analysis Using the Gibbs Samplingmentioning
confidence: 99%
“…Details on the use of Gibbs sampler and on the full conditional distributions in the case of generalized linear mixed models can be found in Zeger and Karim [ 26 ], Gamerman [ 29 ], and Natarajan and Kass [ 27 ]. WinBUGS [ 30 ] software was used to generate the samples and derive inferences on the parameters of interest and the WinBUGS code is supplied in the Appendix.…”
Section: Bayesian Analysis Using the Gibbs Samplingmentioning
confidence: 99%
“…The data augmentation algorithm can be used to estimate the parameters with sampling based approaches like the Gibbs sampler. The Gibbs sampler is proposed by Geman and Geman (1984), and is widely used as a general method in Bayesian computation (Gelfand and Smith, 1990;Zeger and Karim, 1991).…”
Section: Estimation Proceduresmentioning
confidence: 99%
“…A Monte Carlo approach would use an approach like Metropolis Hastings. The model can also be fit using the Gibbs sampling approach [Zeger and Karim, 1991], as done by Burton et al [2000].…”
Section: Ascertainment In a Glmmmentioning
confidence: 99%