Modelling Areal Data

  • Roger S. Bivand
  • Edzer Pebesma
  • Virgilio Gómez-Rubio
Part of the Use R! book series (USE R, volume 10)


Spatial data are often observed on polygon entities with defined boundaries. The polygon boundaries are defined by the researcher in some fields of study, may be arbitrary in others and may be administrative boundaries created for very different purposes in others again. The observed data are frequently aggregations within the boundaries, such as population counts. The areal entities may themselves constitute the units of observation, for example when studying local government behaviour where decisions are taken at the level of the entity, for example setting local tax rates. By and large, though, areal entities are aggregates, bins, used to tally measurements, like voting results at polling stations. Very often, the areal entities are an exhaustive tessellation of the study area, leaving no part of the total area unassigned to an entity. Of course, areal entities may be made up of multiple geometrical entities, such as islands belonging to the same county; they may also surround other areal entities completely, and may contain holes, like lakes.


Spatial Autocorrelation Census Tract Spatial Weight Spatial Weight Matrix Spatial Error Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Roger S. Bivand
    • 1
  • Edzer Pebesma
    • 2
  • Virgilio Gómez-Rubio
    • 3
  1. 1.Norwegian School of EconomicsBergenNorway
  2. 2.Westfälische Wilhelms-UniversitätMünsterGermany
  3. 3.Department of MathematicsUniversidad de Castilla-La ManchaAlbaceteSpain

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