Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/31094 
Year of Publication: 
2005
Series/Report no.: 
Discussion Paper No. 460
Publisher: 
Ludwig-Maximilians-Universität München, Sonderforschungsbereich 386 - Statistische Analyse diskreter Strukturen, München
Abstract: 
In this paper we present and evaluate a Gibbs sampler for a Poisson regression model including spatial effects. The approach is based on Frühwirth-Schnatter and Wagner (2004b) who show that by data augmentation using the introduction of two sequences of latent variables a Poisson regression model can be transformed into an approximate normal linear model. We show how this methodology can be extended to spatial Poisson regression models and give details of the resulting Gibbs sampler. In particular, the influence of model parameterisation and different update strategies on the mixing of the MCMC chains is discussed. The developed Gibbs samplers are analysed in two simulation studies and applied to model the expected number of claims for policyholders of a German car insurance company. The mixing of the Gibbs samplers depends crucially on the model parameterisation and the update schemes. The best mixing is achieved when collapsed algorithms are used, reasonable low autocorrelations for the spatial effects are obtained in this case. For the regression effects however, autocorrelations are rather high, especially for data with very low heterogeneity. For comparison a single component Metropolis Hastings algorithms is applied which displays very good mixing for all components. Although the Metropolis Hastings sampler requires a higher computational effort, it outperforms the Gibbs samplers which would have to be run considerably longer in order to obtain the same precision of the parameters.
Subjects: 
block updates
collapsing
data augmentation
Gibbs sampler
model parameterisation
spatial Poisson count data
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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