Natural Resources Research

, Volume 19, Issue 1, pp 33–44 | Cite as

A Spatially Autocorrelated Weights of Evidence Model

  • Minfeng DengEmail author


One of the most important features of spatial datasets is that they often exhibit spatial autocorrelation, where locational similarities are observed jointly with similarities in values. Both logistic regression (LR) modelling and weights of evidence (WE) modelling are methods commonly applied in binary pattern recognition. While a spatially autocorrelated variant of the LR model, the so-called autologistic regression (ALR) model, exists in the literature, a spatially autocorrelated variant of the WE model does not exist. In this paper, a spatially autocorrelated weights of evidence (SACWE) model will be proposed. It will be demonstrated that the new model contains the same amount of spatial information as does an ALR model, and it is easy to program and implement. Via a simulation study, it will be shown that, in the presence of spatial autocorrelation, both in terms of in-sample fit and out-of-sample predictions the SACWE model is on par with the ALR model, while significantly outperforming the conventional WE model.


Logistic regression simulation autologistic regression spatial prediction 



The author thanks Jerry Jensen and the reviewers for their insightful comments.


  1. Agterberg, F. P., 1992, Combining indicator patterns in weights of evidence modelling for resource evaluation: Nonrenew. Res., v. 1, no. 1, p. 35–50.Google Scholar
  2. Agterberg, F. P., and Bonham-Carter, G. F., 1999, Logistic regression and weights of evidence modelling in mineral exploration, in Computer Applications in the Mineral Industries: Golden, CO, p. 483–490.Google Scholar
  3. Agterberg, F. P., Bonham-Carter, G. F., and Wright, D. F., 1990, Statistical pattern integration for mineral exploration, in Gaál, G., and Merriam, D. F., eds., Computer Applications in Resource Exploration Prediction and Assessment for Metals and Petroleum: Oxford, Pergamon, p. 1–21.Google Scholar
  4. Agterberg, F. P., Bonham-Carter, G. F., Wright, D. F., and Cheng, Q., 1993, Weights of evidence modelling and weighted logistic regression for mineral potential mapping, in Davis, J. C., and Herzfeld, U. C., eds., Computers in Geology, 25 Years of Progress: Oxford University Press, New York, p. 13–32.Google Scholar
  5. Amemiya, T., 1981, Qualitative response models: a survey: J. Econ. Lit., v. 19, p. 1483–1536.Google Scholar
  6. Anselin, L., 1980, Estimation methods for spatial autoregressive structures: a study in spatial econometrics: Regional Science Dissertation and Monograph Series 8, Program in Urban and Regional Studies, Cornell University, Ithaca, New York, 273 p.Google Scholar
  7. Anselin, L. 1988, Spatial econometrics: methods and models: Kluwer Academic Publishers, Dordrecht, 284 p.Google Scholar
  8. Augustin, N. H., Mugglestone, M. A., and Buckland, S. T., 1996, An autologistic model for the spatial distribution of wildlife: J. Appl. Ecol., v. 33, p. 339–347.CrossRefGoogle Scholar
  9. Augustin, N. H., Mugglestone, M. A., and Buckland, S. T., 1998, The role of simulation in modelling spatially correlated data: Environmetrics, v. 9, p. 175–196.CrossRefGoogle Scholar
  10. Besag, J., 1972, Nearest-neighbour systems and the auto-logistic model for binary data: J. R. Stat. Soc. B, v. 34, p. 75–83.Google Scholar
  11. Besag, J., 1974, Spatial interaction and the statistical analysis of lattice systems (with discussion): J. R. Stat. Soc. B, v. 36, p. 192–236.Google Scholar
  12. Besag, J., 1975, Statistical analysis of non-lattice data: Statistician, v. 24, p. 179–195.CrossRefGoogle Scholar
  13. Bonham-Carter, G. F., 1994, Geographic Information Systems for geoscientists: Oxford, Pergamon, 398 p.Google Scholar
  14. Bonham-Carter, G. F., Agterberg, F. P., and Wright, D. F., 1988, Integration of geological datasets for gold exploration in Nova Scotia: Photogram. Remote Sens., v. 54, no. 11, p. 1585–1592.Google Scholar
  15. Bonham-Carter, G. F., Agterberg, F. P., and Wright, D. F., 1989, Weights of evidence modelling: a new approach to mapping mineral potential, in Agterberg, F. P. and Bonham-Carter, G. F., eds., Statistical Applications in the Earth Sciences: Geological Survey Canada Paper 9-9, p. 171–183.Google Scholar
  16. Cliff, A. D., and Ord, J. K., 1973, Spatial autocorrelation: Pion, London, 178 p.Google Scholar
  17. Comets, F., 1992, On consistency of a class of estimators for exponential families of Markov random fields on the lattice: Ann. Stat., v. 20, no. 1, p. 445–568.CrossRefGoogle Scholar
  18. Cressie, N. A. C., 1993, Statistics for spatial data, revised edition: Wiley, New York, 900 p.Google Scholar
  19. Dahal, R. K., Hasegawa, S., Nonomura, A., Yamanaka, M., Masuda, T., and Nishino, K., 2008, GIS-based weights-of-evidence modelling of rainfall-induced landslides in small catchments for landslide susceptibility mapping: Environ. Geol., v. 54, p. 311–324.CrossRefGoogle Scholar
  20. Deng, M., 2009, A conditional dependence adjusted weights of evidence model: Nat. Resour. Res. doi: 10.1007/s11053-009-9101-5.
  21. Emelyanova, I. V., Donald, G. E., Miron, D. J., Henry, D. A., and Garner, M. G., 2008, Probabilistic modelling of cattle farm distribution in Australia: Environ. Model. Assess., v. 14, p. 449–465.CrossRefGoogle Scholar
  22. Haining, R., 1985, The spatial structure of competition and equilibrium price dispersion: Geograph. Anal., v. 17, p. 231–242.Google Scholar
  23. Hansen, D. T., 2000, Describing GIS applications: spatial statistics and weights of evidence extension to ArcView in the analysis of the distribution of archeology sites in the landscape: Proceedings of the 20th Annual ESRI International User Conference, San Diego, CA.Google Scholar
  24. Hansen, D. T., West, J., Simpson, B., and Welch, P., 2002, Modeling spatial uncertainty in analysis of archeological site distribution: Proceedings of the 22nd Annual ESRI International User Conference, San Diego, CA.Google Scholar
  25. Huffer, F. W., and Wu, H., 1998, Markov Chain Monte Carlo for autologistic regression models with application to the distribution of plant species: Biometrics, v. 54, p. 509–524.CrossRefGoogle Scholar
  26. Johnston, J., and Dinardo, J., 1997, Econometric methods, 4th ed.: McGraw-Hill, New York, 531 p.Google Scholar
  27. Mathew, J., Jha, V. K., and Rawat, G. S., 2007, Weights of evidence modelling for landslide hazard zonation mapping in part of Bhagirathi valley, Uttarakhand: Curr. Sci., v. 92, no. 5, p. 628–638.Google Scholar
  28. Ord, J. K., 1975, Estimation methods for models of spatial interaction: J. Am. Stat. Assoc., v. 70, p. 120–126.CrossRefGoogle Scholar
  29. Romero-Calcerrada, R., and Luque, S., 2006, Habitat quality assessment using Weights-of-Evidence based GIS modelling: the case of Picoides tridactylus as species indicator of the biodiversity value of the Finnish forest: Ecol. Modell., v. 196, p. 62–76.CrossRefGoogle Scholar
  30. Tobler, W. R., 1970, A computer movie simulating urban growth in the Detroit Region: Econ. Geogr., v. 46, p. 234–240.CrossRefGoogle Scholar
  31. Vining, D. J., and Gladish, G. W., 1992, Receiver operating characteristic curves: a basic understanding: RadioGraphics, v. 12, p. 1147–1154.Google Scholar
  32. Wintle, B. A., and Bardos, D. C., 2006, Modeling species-habitat relationships with spatially autocorrelated observation data: Ecol. Appl., v. 16, no. 5, p. 1945–1958.CrossRefGoogle Scholar
  33. Wu, H., and Huffer, F. W., 1997, Modelling the distribution of plant species using the autologistic regression model: Environ. Ecol. Stat., v. 4, p. 49–64.CrossRefGoogle Scholar
  34. Zweig, M. H., and Cambell, G., 1993, Receiver operator characteristic plots: a fundamental evaluation tool in clinical medicine: Clin. Chem., v. 39, p. 561–577.Google Scholar

Copyright information

© International Association for Mathematical Geology 2009

Authors and Affiliations

  1. 1.Department of Econometrics and Business StatisticsMonash UniversityClaytonAustralia

Personalised recommendations