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Estimation of Spatially Correlated Random Scaling Factors based on Markov Random Field Priors

Author

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  • Alexander Razen
  • Stefan Lang
  • Judith Santer

Abstract

Multiplicative random effects allow for cluster-specific scaling of covariate effects. In many applications with spatial clustering, however, the random effects additionally show some geographical pattern, which usually can not sufficiently be captured with existing estimation techniques. Relying on Markov random fields, we present a fully Bayesian inference procedure for spatially correlated scaling factors. The estimation is based on highly efficient Markov Chain Monte Carlo (MCMC) algorithms and is smoothly incorporated into the framework of distributional regression. We run a comprehensive simulation study for different response distributions to examine the statistical properties of our approach. We also compare our results to those of a general estimation procedure for independent random scaling factors. Furthermore, we apply the method to German real estate data and show that exploiting the spatial correlation of the scaling factors further improves the performance of the model.

Suggested Citation

  • Alexander Razen & Stefan Lang & Judith Santer, 2016. "Estimation of Spatially Correlated Random Scaling Factors based on Markov Random Field Priors," Working Papers 2016-33, Faculty of Economics and Statistics, Universität Innsbruck.
    • Handle: RePEc:inn:wpaper:2016-33
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    References listed on IDEAS

    as
    1. W. Brunauer & S. Lang & P. Wechselberger & S. Bienert, 2010. "Additive Hedonic Regression Models with Spatial Scaling Factors: An Application for Rents in Vienna," The Journal of Real Estate Finance and Economics, Springer, vol. 41(4), pages 390-411, November.
    2. Alexander Razen & Stefan Lang, 2016. "Random Scaling Factors in Bayesian Distributional Regression Models with an Application to Real Estate Data," Working Papers 2016-30, Faculty of Economics and Statistics, Universität Innsbruck.
    3. Ludwig Fahrmeir & Stefan Lang, 2001. "Bayesian inference for generalized additive mixed models based on Markov random field priors," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(2), pages 201-220.
    4. Julian Besag & Jeremy York & Annie Mollié, 1991. "Bayesian image restoration, with two applications in spatial statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 43(1), pages 1-20, March.
    5. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    6. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    Full references (including those not matched with items on IDEAS)

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    Keywords

    distributional regression; iteratively weighted least squares proposals; MCMC; multiplicative random effects; spatial smoothing; structured additive predictors;
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