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Using hierarchical centering to facilitate a reversible jump MCMC algorithm for random effects models

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Date
06/2016
Author
Oedekoven, Cornelia Sabrina
King , R.
Buckland, Stephen Terrence
MacKenzie, Monique Lea
Evans, K. O.
Burger Jr., L. W
Funder
EPSRC
Grant ID
EP/C522702/1
Keywords
Combined likelihood
"Metropolis-Hastings"
Point transect sampling
Random effects
Reparameterization
GE Environmental Sciences
QA75 Electronic computers. Computer science
DAS
BDC
R2C
Metadata
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Abstract
Hierarchical centering has been described as a reparameterization method applicable to random effects models. It has been shown to improve mixing of models in the context of Markov chain Monte Carlo (MCMC) methods. A hierarchical centering approach is proposed for reversible jump MCMC (RJMCMC) chains which builds upon the hierarchical centering methods for MCMC chains and uses them to reparameterize models in an RJMCMC algorithm. Although these methods may be applicable to models with other error distributions, the case is described for a log-linear Poisson model where the expected value λλ includes fixed effect covariates and a random effect for which normality is assumed with a zero-mean and unknown standard deviation. For the proposed RJMCMC algorithm including hierarchical centering, the models are reparameterized by modelling the mean of the random effect coefficients as a function of the intercept of the λλ model and one or more of the available fixed effect covariates depending on the model. The method is appropriate when fixed-effect covariates are constant within random effect groups. This has an effect on the dynamics of the RJMCMC algorithm and improves model mixing. The methods are applied to a case study of point transects of indigo buntings where, without hierarchical centering, the RJMCMC algorithm had poor mixing and the estimated posterior distribution depended on the starting model. With hierarchical centering on the other hand, the chain moved freely over model and parameter space. These results are confirmed with a simulation study. Hence, the proposed methods should be considered as a regular strategy for implementing models with random effects in RJMCMC algorithms; they facilitate convergence of these algorithms and help avoid false inference on model parameters.
Citation
Oedekoven , C S , King , R , Buckland , S T , MacKenzie , M L , Evans , K O & Burger Jr. , L W 2016 , ' Using hierarchical centering to facilitate a reversible jump MCMC algorithm for random effects models ' , Computational Statistics and Data Analysis , vol. 98 , pp. 79-90 . https://doi.org/10.1016/j.csda.2015.12.010
Publication
Computational Statistics and Data Analysis
Status
Peer reviewed
DOI
https://doi.org/10.1016/j.csda.2015.12.010
ISSN
0167-9473
Type
Journal article
Rights
© 2015, Elsevier B.V. All rights reserved. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://dx.doi.org/10.1016/j.csda.2015.12.010
Description
The first author was supported by a studentship jointly funded by the University of St Andrews and EPSRC, through the National Centre for Statistical Ecology (EPSRC grant EP/C522702/1), with subsequent funding from EPSRC/NERC grant EP/I000917/1.
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/10035

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