## Trondheim, Norway. On a Hybrid Data Cloning Method and Its Application in Generalized Linear Mixed Models

### BibTeX

@MISC{Baghishani_trondheim,norway.,

author = {Hossein Baghishani and Mohsen Mohammadzadeh and Hossein Baghishani A and H˚avard Rue B and Mohsen Mohammadzadeh A},

title = {Trondheim, Norway. On a Hybrid Data Cloning Method and Its Application in Generalized Linear Mixed Models},

year = {}

}

### OpenURL

### Abstract

Data cloning method is a new computational tool for computing maximum likelihood estimates in complex statistical models such as mixed models. The data cloning method is synthesized with integrated nested Laplace approximation to compute maximum likelihood estimates efficiently via a fast implementation in generalized linear mixed models. Asymptotic normality of the hybrid data cloning based distribution is established aided by modification of Stein’s Identity. The results are illustrated through a series of well known examples. It is shown that the proposed method as well as normal approximation perform very well and justify the theory.

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Citation Context ...ces such as biology, ecology, epidemiology and medicine. The Generalized Linear Mixed Models are flexible models for modeling these types of data. As an extension of generalized linear models (GLMs) (=-=McCullagh and Nelder, 1989-=-), a GLMM assumes that the response variable follows a distribution from the exponential family and is conditionally independent given latent variables, while the latent variables are modeled by rando... |

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Citation Context ... main aim is to compute the posterior marginals π(ψl|y), l=1,...,q and π(θv|y), v = 1,...,d. It is well known, however, that MCMC methods tend to exhibit poor performance when applied to such models (=-=Rue et al., 2009-=-). INLA is a new tool for Bayesian inference on latent Gaussian models introduced by Rue et al. (2009). The method combines Laplace approximations and numerical integration in a very efficient manner.... |

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Citation Context ... main aim is to compute the posterior marginals π(ψl|y), l=1,...,q and π(θv|y), v = 1,...,d. It is well known, however, that MCMC methods tend to exhibit poor performance when applied to such models (=-=Rue et al., 2009-=-). INLA is a new tool for Bayesian inference on latent Gaussian models introduced by Rue et al. (2009). The method combines Laplace approximations and numerical integration in a very efficient manner.... |

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Citation Context ...terior distribution, but it is constructed from two functions which are not in fact a prior distribution and a likelihood. However, considering them as prior and likelihood can be mimicked virtually (=-=Baghishani and Mohammadzadeh, 2009-=-). The trick in the DC is generating samples from a DC-based distribution constructed by duplicating the original data set enough times, k say, such that the sample mean as well as the scaled sample v... |

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Citation Context ... ℜr−j ∫ ∞ bj {hj(b1,...,bj−1,c) − hj−1(b1,...,bj−1)}e 1 − 2 e2 for −∞ <b1,...,br < ∞ and j =1,...,r.ThenletUh =(g1,...,gr) T . Following lemma states a modified version of Stein’s Identity. Lemma 1. (=-=Weng and Tsai, 2008-=-). Let s be a nonnegative integer and let dΓ =fdΦr, wheref is differentiable on ℜr such that ∫ |f|dΦr + ℜ r ∫ ℜ r (1 + ‖a‖ s )‖∇f(a)‖Φr(da) < ∞. dc, Then for all h ∈ Hs. ∫ Γh − Γ1 · Φrh = (Uh(a)) T ∇f... |

1 | Asymptotic normality of posterior distributions for generalized linear mixed models - Baghishani, Mohammadzadeh - 2010 |

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