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Variational approximations in geoadditive latent Gaussian regression: mean and quantile regression

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Abstract

Geoadditive regression models define a comprehensive class of statistical models that allow to capture a variety of different effects on a response variable of interest, including nonlinear effects of continuous covariates and spatial effects as special cases. We develop variational approximations for Bayesian inference in geoadditive regression models to provide a computationally attractive, fast alternative to Markov chain Monte Carlo simulations. Therefore we consider the class of latent Gaussian regression models where the distribution of the response can be represented as a location-scale mixture of Gaussians such that the calculation of quasi-full conditionals in the variational approximations is considerably facilitated. As special cases, we consider mean and quantile regression and evaluate the novel variational Bayes approaches in a simulation study. As an application, we focus on the analysis of technical efficiencies of British and Welsh farms where the response variable of interest is the output produced by a farm given specific input covariates.

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Authors and Affiliations

  1. University of Liverpool, Liverpool, UK

    Elisabeth Waldmann

  2. Georg August University, Göttingen, Germany

    Thomas Kneib

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  1. Elisabeth Waldmann
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  2. Thomas Kneib
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Correspondence to Elisabeth Waldmann.

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Waldmann, E., Kneib, T. Variational approximations in geoadditive latent Gaussian regression: mean and quantile regression. Stat Comput 25, 1247–1263 (2015). https://doi.org/10.1007/s11222-014-9480-2

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  • DOI: https://doi.org/10.1007/s11222-014-9480-2

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