Modifiable areal unit problem

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MAUP distortion example
An example of the modifiable areal unit problem and the distortion of rate calculations

The modifiable areal unit problem (MAUP) is a source of

illness rates.[1][2] The resulting summary values (e.g., totals, rates, proportions, densities) are influenced by both the shape and scale of the aggregation unit.[3]

For example, census data may be aggregated into county districts, census tracts, postcode areas, police precincts, or any other arbitrary spatial partition. Thus the results of data aggregation are dependent on the mapmaker's choice of which "modifiable areal unit" to use in their analysis. A census choropleth map calculating population density using state boundaries will yield radically different results than a map that calculates density based on county boundaries. Furthermore, census district boundaries are also subject to change over time,[4] meaning the MAUP must be considered when comparing past data to current data.

Background

The issue was first recognized by Gehlke and Biehl in 1934

Michael F. Goodchild suggesting it be referred to as the "Openshaw effect."[7]

Ecological bias caused by MAUP has been documented as two separate effects that usually occur simultaneously during the analysis of aggregated data. First, the scale effect causes variation in statistical results between different levels of aggregation (radial distance). Therefore, the association between variables depends on the size of areal units for which data are reported. Generally, correlation increases as areal unit size increases. The zoning effect describes variation in correlation statistics caused by the regrouping of data into different configurations at the same scale (areal shape).[8]

Since the 1930s, research has found extra variation in statistical results because of the MAUP. The standard methods of calculating within-group and between-group variance do not account for the extra variance seen in MAUP studies as the groupings change. MAUP can be used as a methodology to calculate upper and lower limits as well as average regression parameters for multiple sets of spatial groupings. The MAUP is a critical source of error in spatial studies, whether observational or experimental. As such, unit consistency, particularly in a time-series cross-sectional (TSCS) context, is essential. Further, robustness checks of unit sensitivity to alternative spatial aggregation should be routinely performed to mitigate associated biases on resulting statistical estimates.

A hand map with different spatial patterns. Note: p is the probability of q-statistic; * denotes statistical significant at level 0.05, ** for 0.001, *** for smaller than 10−3;(D) subscripts 1, 2, 3 of q and p denotes the strata Z1+Z2 with Z3,Z1 with Z2+Z3, and Z1 and Z2 and Z3 individually, respectively; (E) subscripts 1 and 2 of q and p denotes the strata Z1+Z2 with Z3+Z4,and Z1+Z3 with Z2+Z4, respectively.

Suggested solutions

Several suggestions have been made in literature to reduce aggregation bias during regression analysis. A researcher might correct the variance-covariance matrix using samples from individual-level data.[9] Alternatively, one might focus on local spatial regression rather than global regression. A researcher might also attempt to design areal units to maximize a particular statistical result.[6] Others have argued that it may be difficult to construct a single set of optimal aggregation units for multiple variables, each of which may exhibit non-stationarity and spatial autocorrelation across space in different ways. Others have suggested developing statistics that change across scales in a predictable way, perhaps using fractal dimension as a scale-independent measure of spatial relationships. Others have suggested Bayesian hierarchical models as a general methodology for combining aggregated and individual-level data for ecological inference.

Studies of the MAUP based on empirical data can only provide limited insight due to an inability to control relationships between multiple spatial variables. Data simulation is necessary to have control over various properties of individual-level data. Simulation studies have demonstrated that the spatial support of variables can affect the magnitude of ecological bias caused by spatial data aggregation.[10]

MAUP sensitivity analysis

Using simulations for univariate data, Larsen advocated the use of a Variance Ratio to investigate the effect of spatial configuration, spatial association, and data aggregation.

spatial autocorrelation
.

This topic is of particular importance because in some cases data aggregation can obscure a strong correlation between variables, making the relationship appear weak or even negative. Conversely, MAUP can cause random variables to appear as if there is a significant association where there is not. Multivariate regression parameters are more sensitive to MAUP than correlation coefficients. Until a more analytical solution to MAUP is discovered, spatial sensitivity analysis using a variety of areal units is recommended as a methodology to estimate the uncertainty of correlation and regression coefficients due to ecological bias. An example of data simulation and re-aggregation using the ArcPy library is available.[13] [14]

In transport planning, MAUP is associated to Traffic Analysis Zoning (TAZ). A major point of departure in understanding problems in transportation analysis is the recognition that spatial analysis has some limitations associated with the discretization of space. Among them, modifiable areal units and boundary problems are directly or indirectly related to transportation planning and analysis through the design of traffic analysis zones – most of transport studies require directly or indirectly the definition of TAZs. The modifiable boundary and the scale issues should all be given specific attention during the specification of a TAZ because of the effects these factors exert on statistical and mathematical properties of spatial patterns (ie the modifiable areal unit problem—MAUP). In the studies of Viegas, Martinez and Silva (2009, 2009b)[14] the authors propose a method where the results obtained from the study of spatial data are not independent of the scale, and the aggregation effects are implicit in the choice of zonal boundaries. The delineation of zonal boundaries of TAZs has a direct impact on the reality and accuracy of the results obtained from transportation forecasting models. In this paper the MAUP effects on the TAZ definition and the transportation demand models are measured and analyzed using different grids (in size and in origin location). This analysis was developed by building an application integrated in commercial GIS software and by using a case study (Lisbon Metropolitan Area) to test its implementabiity and performance. The results reveal the conflict between statistical and geographic precision, and their relationship with the loss of information in the traffic assignment step of the transportation planning models.[14]

See also

Applications

References

  1. ISBN 0-86094-134-5
    .
  2. ^
    S2CID 255206315
    .
  3. ^ "MAUP | Definition – Esri Support GIS Dictionary". support.esri.com. Retrieved 2017-03-09.
  4. ^ Geography, US Census Bureau. "Geographic Boundary Change Notes". www.census.gov. Retrieved 2017-02-24.
  5. ^ Gehlke & Biehl 1934
  6. ^ a b Openshaw 1984, p. 3
  7. doi:10.1080/13658816.2022.2102637
    . Retrieved 24 January 2024.
  8. ISBN 978-1-4129-1082-8
    .
  9. ^ Holt D, Steel D, Tranmer M, Wrigley N. (1996). “Aggregation and ecological effects in geographically based data.” “Geographical Analysis” 28:244{261
  10. ^ a b Swift, A., Liu, L., and Uber, J. (2008) "Reducing MAUP bias of correlation statistics between water quality and GI illness." Computers, Environment and Urban Systems 32, 134–148
  11. ^ Larsen, J. (2000). "The Modifiable Areal Unit Problem: A problem or a source of spatial information?" PhD thesis, Ohio State University.
  12. ^ Reynolds, H. (1998). "The Modifiable Area Unit Problem: Empirical Analysis By Statistical Simulation." PhD thesis, Department of Geography University of Toronto, http://www.badpets.net/Thesis
  13. ^ Swift, A. (2017). "Crime mapping data simulation", https://app.box.com/s/a84w16x7hffljjvkhtlr72eisj4qiene
  14. ^
    S2CID 54840846
    .

Sources

Further reading
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