Modifiable Areal Unit Problem (MAUP)

The modifiable areal unit problem (MAUP) affects the analysis of data that have been aggregated to a set of zones or areal units. The MAUP manifests itself through two related components, known as the scaling and aggregation (or zoning) problems. It has been observed that the number of areal units in a given study region affects the outcome of an analysis. The results are conditioned on the resolution or scale of the areal units; this is the scaling problem. There are also many different ways in which a study region can be partitioned into the same number of areal units; this is the aggregation or zoning problem. Data aggregation is often used in administrative data reporting so that the characteristics of any individual cannot be derived from the data. Analysis using such data will be affected by the MAUP.

Sociologists working with census tract data in the early 1930s were the first to document this behavior. Gelhke and Biehl observed that variations in the values of the correlation coefficient seemed related to the size of the unit used, noting that smaller units tended to produce smaller correlations: the scaling effect. They questioned whether a correlation coefficient computed from aggregated data had any value in causal analysis.

In 1950, Yule and Kendall reported on research in the variation in crop yields using agricultural data for English counties. In their study of the relationship between wheat and potato yields, they also observed the scale effect. They described their spatial units as “modifiable,” which appears to have inspired Openshaw and Taylor to coin the term modifiable areal unit problem.

The ubiquity of data that have been aggregated to areal units for reporting and analysis means that the MAUP should not be taken lightly. Of the millions of correlation coefficients that have been computed since the early 1930s, many authors appear to have ignored the MAUP. However, the correlation coefficient may not be the most helpful measure of association between data reported for areal units. In 1989, Tobler asserted that analysis should be frame independent, that is, it should not depend on the spatial coordinates or spatial units that are used. He contended that the correlation coefficient, therefore, is an inappropriate measure of association with data for spatial units because of the effects of MAUP. He suggested that the spatial cross-coherence function is the appropriate measure and further noted that the association between two variables may vary with location.

The MAUP would appear to affect more than just correlations between spatial data. It has been shown that parameter estimates from regression models may [Page 289]be sensitive to variations in spatial aggregation and variations in zone definition can influence the results of location-allocation modeling. Indeed, the MAUP affects a wide range of commonly used techniques, including correlation, regression, spatial interaction modeling, location-allocation modeling, and discrete choice modeling.

If the MAUP is all-pervasive, can the prudent analyst take steps to ameliorate its effects? No satisfactory solution is applicable to all modifiable areal unit problems, but a few solutions include ignoring the problem, using disaggregate data, devising meaningful areal units, and devising unconventional forms of areal units.

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