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Gaussian Markov random field spatial models in GAMLSS

Author

Listed:
  • Fernanda De Bastiani
  • Robert A. Rigby
  • Dimitrios M. Stasinopoulous
  • Audrey H.M.A. Cysneiros
  • Miguel A. Uribe-Opazo

Abstract

This paper describes the modelling and fitting of Gaussian Markov random field spatial components within a Generalized AdditiveModel for Location, Scale and Shape (GAMLSS) model. This allows modelling of any or all the parameters of the distribution for the response variable using explanatory variables and spatial effects. The response variable distribution is allowed to be a non-exponential family distribution. A new package developed in R to achieve this is presented. We use Gaussian Markov random fields to model the spatial effect in Munich rent data and explore some features and characteristics of the data. The potential of using spatial analysis within GAMLSS is discussed. We argue that the flexibility of parametric distributions, ability to model all the parameters of the distribution and diagnostic tools of GAMLSS provide an ideal environment for modelling spatial features of data.

Suggested Citation

  • Fernanda De Bastiani & Robert A. Rigby & Dimitrios M. Stasinopoulous & Audrey H.M.A. Cysneiros & Miguel A. Uribe-Opazo, 2018. "Gaussian Markov random field spatial models in GAMLSS," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(1), pages 168-186, January.
    • Handle: RePEc:taf:japsta:v:45:y:2018:i:1:p:168-186
    DOI: 10.1080/02664763.2016.1269728
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    References listed on IDEAS

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    1. Vlasios Voudouris & Robert Gilchrist & Robert Rigby & John Sedgwick & Dimitrios Stasinopoulos, 2012. "Modelling skewness and kurtosis with the BCPE density in GAMLSS," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(6), pages 1279-1293, November.
    2. Voudouris, Vlasios & Stasinopoulos, Dimitrios & Rigby, Robert & Di Maio, Carlo, 2011. "The ACEGES laboratory for energy policy: Exploring the production of crude oil," Energy Policy, Elsevier, vol. 39(9), pages 5480-5489, September.
    3. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
    4. J. Besag & D. Higdon, 1999. "Bayesian analysis of agricultural field experiments," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 691-746.
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    Cited by:

    1. Henning Schaak & Oliver Musshoff, 2022. "The distribution of the rent–price relationship of agricultural land in Germany [An analysis of growth of U.S. farmland prices, 1963–82]," European Review of Agricultural Economics, Oxford University Press and the European Agricultural and Applied Economics Publications Foundation, vol. 49(3), pages 696-718.
    2. Schaak, Henning & Mußhoff, Oliver, 2020. "A geoadditive distributional regression analysis of the local relationship of land prices and land rents in Germany," FORLand Working Papers 20 (2020), Humboldt University Berlin, DFG Research Unit 2569 FORLand "Agricultural Land Markets – Efficiency and Regulation".

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