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Modelling Areal Data

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Book cover Applied Spatial Data Analysis with R

Part of the book series: Use R! ((USE R,volume 10))

Abstract

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.

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Notes

  1. 1.

    The BARD package for automated redistricting and heuristic exploration of redistricter revealed preference is an example of the use of R for studying this problem.

  2. 2.

    The boundaries have been projected from geographical coordinates to UTM zone 18.

  3. 3.

    http://geodacenter.asu.edu/, Anselin et al. (2006).

  4. 4.

    http://www.spatial-econometrics.com

  5. 5.

    In spatial econometrics, the abbreviation SAR means Spatial Autoregressive, and refers to the spatial lag model defined later in this chapter on p. 81.

  6. 6.

    The fitted coefficient values of the weighted CAR model do not exactly reproduce those of Waller and Gotway (2004, p. 379), although the spatial coefficient is reproduced.

  7. 7.

    Full details of the test procedures can be found in the references to the function documentation in lmtest and sandwich.

  8. 8.

    One expects the spatial lag model and its extensions to propose a hypothesis of spillover between observations of the response variable, such as contagion or competition, which is not the case for these leukemia incidence rates; the hypothesised spatial process is modelled by distances from TCE sites (the PEXPOSURE variable).

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Authors and Affiliations

  1. Norwegian School of Economics, Bergen, Norway

    Roger S. Bivand

  2. Westfälische Wilhelms-Universität, Münster, Germany

    Edzer Pebesma

  3. Department of Mathematics, Universidad de Castilla-La Mancha, Albacete, Spain

    Virgilio Gómez-Rubio

Authors
  1. Roger S. Bivand
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  2. Edzer Pebesma
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  3. Virgilio Gómez-Rubio
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Bivand, R.S., Pebesma, E., Gómez-Rubio, V. (2013). Modelling Areal Data. In: Applied Spatial Data Analysis with R. Use R!, vol 10. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7618-4_9

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