Statistical Methods & Applications

, Volume 23, Issue 2, pp 283–305 | Cite as

Estimates for geographical domains through geoadditive models in presence of incomplete geographical information

Article

Abstract

The paper deals with the matter of producing geographical domains estimates for a variable with a spatial pattern in presence of incomplete information about the population units location. The spatial distribution of the study variable and its eventual relations with other covariates are modeled by a geoadditive regression. The use of such a model to produce model-based estimates for some geographical domains requires all the population units to be referenced at point locations, however typically the spatial coordinates are known only for the sampled units. An approach to treat the lack of geographical information for non-sampled units is suggested: it is proposed to impose a distribution on the spatial locations inside each domain. This is realized through a hierarchical Bayesian formulation of the geoadditive model in which a prior distribution on the spatial coordinates is defined. The performance of the proposed imputation approach is evaluated through various Markov Chain Monte Carlo experiments implemented under different scenarios.

Keywords

Hierarchical Bayesian models Imputation Penalized splines  Linear mixed model Sample representativeness 

References

  1. Crainiceanu C, Ruppert D, Wand MP (2005) Bayesian analysis for penalized spline regression using WinBUGS. J Stat Softw 14(14):1–24Google Scholar
  2. Cressie N (1993) Statistics for spatial data. Waley, New YorkGoogle Scholar
  3. Diggle PJ (1983) Statistical analysis of spatial point patterns. Academic Press, LondonMATHGoogle Scholar
  4. Fahrmeir L, Lang S (2001) Bayesian inference for generalized additive mixed models based on markov random field priors. Appl Stat 50(2):201–220MathSciNetGoogle Scholar
  5. Fotheringham AS, Brunsdon C, Charlton ME (2002) Geographically weighted regression: the analysis of spatially varying relationships. Wiley, ChichesterGoogle Scholar
  6. Gamerman D, Moreira ARB, Rue H (2003) Space-varying regression models: specifications and simulation. Comput Stat Data Anal 42(3):513–533CrossRefMATHMathSciNetGoogle Scholar
  7. Kammann EE, Wand MP (2003) Geoadditive models. Appl Stat 52:1–18MATHMathSciNetGoogle Scholar
  8. Kaufman L, Rousseeuw PJ (1990) Finding groups in data: an introduction to cluster analysis. Wiley, New YorkCrossRefGoogle Scholar
  9. Ligges U, Thomas A, Spiegelhalter D, Best N, Lunn D, Rice K, Sturtz S (2009) BRugs 0.5-3. R package. http://www.cran.r-project.org/
  10. Little RJA, Rubin DB (1987) Statistical analysis with missing data. Wiley, New YorkMATHGoogle Scholar
  11. Lunn D, Thomas A, Best N, Spiegelhalter D (2000) WinBUGS—a Bayesian modelling framework: concepts, structure, and extensibility. Stat Comput 10:325–337CrossRefGoogle Scholar
  12. Marley J, Wand MP (2010) Non-standard semiparametric regression via BRugs. J Stat Softw 37(5):1–30Google Scholar
  13. Opsomer JD, Claeskens G, Ranalli MG, Kauermann G, Breidt FJ (2008) Non-parametric small area estimation using penalized spline regression. J R Stat Soc B 70:265–286CrossRefMATHMathSciNetGoogle Scholar
  14. R Development Core Team (2011) R: a language and environment for statistical computing. R foundation for statistical computing, Vienna, Austria. http://www.R-project.org/, ISBN 3-900051-07-0
  15. Ruppert D, Wand MP, Carroll RJ (2003) Semiparametric regression. Cambridge University Press, CambridgeCrossRefMATHGoogle Scholar
  16. Ruppert D, Wand MP, Carroll RJ (2009) Semiparametric regression during 2003–2007. Electron J Stat 3:1193–1256CrossRefMATHMathSciNetGoogle Scholar
  17. Salvati N, Chandra H, Ranalli MG, Chambers R (2010) Small area estimation using a nonparametric model-based direct estimator. Comput Stat Data Anal 54:2159–2171CrossRefMATHMathSciNetGoogle Scholar
  18. Spiegelhalter D, Thomas A, Best N, Gilks W, Lunn D (2003) BUGS: Bayesian inference using Gibbs sampling. MRC Biostatistics Unit, Cambridge, England. http://www.mrc-bsu.cam.ac.uk/bugs/
  19. Venables WN, Ripley BD (2002) Modern applied statistics with S, 4th edn. Springer, New YorkCrossRefMATHGoogle Scholar
  20. Wand MP (2003) Smoothing and mixed models. Comput Stat 18:223–249MATHGoogle Scholar
  21. Wand MP, Jones MC (1993) Comparison of smoothing parameterizations in Bivariate Kernel density estimation. J Am Stat Assoc 88:520–528CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.IRPET - Regional Institute for Economic Planning of TuscanyFirenzeItaly
  2. 2.Department of Statistics, Informatics, Applications “G. Parenti” (DiSIA)University of FlorenceFirenzeItaly

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