Some Effects of Spatial Aggregation on Multivariate Regression Parameters

  • Harold Reynolds
  • Carl Amrhein
Part of the Advanced Studies in Theoretical and Applied Econometrics book series (ASTA, volume 35)


The Modifiable Area Unit Problem (MAUP), a term introduced in Openshaw and Taylor’s (1979) classic paper, has long been recognized as a potentially troublesome feature of spatially aggregated data, such as census data. Aggregation of unit-level (or other high-resolution) data to lower resolution areas is an almost unavoidable feature of large spatial datasets due to the requirements of privacy and/or data manageability. When the original data are aggregated, the values for the various univariate, bivariate, and multivariate parameters will change because of the loss of information. This phenomenon is called the scale effect. The N spatial units to which the higher-resolution data are aggregated, such as census enumeration areas or tracts, postal code districts, or political divisions of various levels, are arbitrarily created by some decision-making process and represent only one of an almost infinite number of ways to partition a region into N zones. Each partitioning will result in different values for the aggregated statistics; this variation in values is known as the zoning effect. The two effects are not independent, because the lower-resolution spatial structure may be built from contiguous higher-resolution units, such as census tracts from enumeration areas, and the resulting aggregate statistics will be different for each aggregation.


Spatial Autocorrelation Linear Regression Model Voronoi Tessellation Spatial Dataset Zoning Effect 
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  1. Amrhein, C. G. (1993). “Searching for the elusive aggregation effect: Evidence from statistical simulations.” Environment and Planning A, 27, 105–119.CrossRefGoogle Scholar
  2. Amrhein, C. G., and H. Reynolds. (1996). “Using spatial statistics to assess aggregation effects.” Geographical Systems, 2, 83–101.Google Scholar
  3. Amrhein, C. G., and H. Reynolds. (1997). “Using the Getis statistic to explore aggregation effects in Metropolitan Toronto Census data.” The Canadian Geographer, (forthcoming).Google Scholar
  4. Amrhein, C. G., and R. Flowerdew. (1993). “Searching for the elusive aggregation effect: Evidence from British census data.” Unpublished manuscript available from the authors.Google Scholar
  5. Fotheringham, A. S., and D. W. S. Wong. (1991). “The modifiable area unit problem in multivariate analysis.” Environment and Planning A, 23, 1025–1044.CrossRefGoogle Scholar
  6. Okabe, A., B. Boots, and K. Sugihara. (1992). Spatial Tessellations: Concepts and Applications of Voronoi Diagrams. London: Wiley.Google Scholar
  7. Openshaw, S., and P. Taylor. (1979). “A million or so correlation coefficients: Three experiments on the modifiable area unit problem.” In Statistical Applications in the Spatial Sciences, edited by N. Wrigley, pp. 127–144. London: Pion.Google Scholar
  8. Steel, D. G., and D. Holt. (1996). “Rules for random aggregation.” Environment and Planning A, 28, 957–978.CrossRefGoogle Scholar

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© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Harold Reynolds
  • Carl Amrhein

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