Abstract
BackgroundAll analyses of spatially aggregated data are vulnerable to the modifiable areal unit problem (MAUP), which describes the sensitivity of analytical results to the arbitrary choice of spatial aggregation unit at which data are measured. The MAUP is a serious problem endemic to analyses of spatially aggregated data in all scientific disciplines. However, the impact of the MAUP is rarely considered, perhaps partly because it is still widely considered to be unsolvable.ResultsIt was originally understood that a solution to the MAUP should constitute a comprehensive statistical framework describing the regularities in estimates of association observed at different combinations of spatial scale and zonation. Additionally, it has been debated how such a solution should incorporate the geographical characteristics of areal units (e.g. shape, size, and configuration), and in particular whether this can be achieved in a purely mathematical framework (i.e. independent of areal units). We argue that the consideration of areal units must form part of a solution to the MAUP, since the MAUP only manifests in their presence. Thus, we present a theoretical and statistical framework that incorporates the characteristics of areal units by combining estimates obtained from different scales and zonations. We show that associations estimated at scales larger than a minimal geographical unit of analysis are systematically biased from a true minimal-level effect, with different zonations generating uniquely biased estimates. Therefore, it is fundamentally erroneous to infer conclusions based on data that are spatially aggregated beyond the minimal level. Instead, researchers should measure and display information, estimate effects, and infer conclusions at the smallest possible meaningful geographical scale. The framework we develop facilitates this.ConclusionsThe proposed framework represents a new minimum standard in the estimation of associations using spatially aggregated data, and a reference point against which previous findings and misconceptions related to the MAUP can be understood.
Highlights
All analyses of spatially aggregated data are vulnerable to the modifiable areal unit problem (MAUP), which describes the sensitivity of analytical results to the arbitrary choice of spatial aggregation unit at which data are measured
We introduce a method to identify the range of minimal-level values (‘true effects’) that could have generated an observed set of estimates
We have shown that differences in association estimates derived from data aggregated to different zonations and at different scales can be recreated using a range of values operating at a minimal areal unit of analysis
Summary
All analyses of spatially aggregated data are vulnerable to the modifiable areal unit problem (MAUP), which describes the sensitivity of analytical results to the arbitrary choice of spatial aggregation unit at which data are measured. The consequence of the MAUP is that estimates obtained, and conclusions inferred, from analyses of data aggregated at a single zonation, are dependent on the chosen aggregation unit [1, 5, 6] This is a serious problem undermining analyses of spatially aggregated data in all scientific disciplines, including ecological studies [7], epidemiology and health research [8, 9], demography [10], the design of electoral boundaries [11], economics [12], transport and traffic modelling [13], criminology [14], and physical geography [15], among many others. In the absence of a generalized solution, sensitivity analyses investigating estimates at multiple scales and zonations are the minimum standard to examine the MAUP’s impact [4, 5], but these are rarely undertaken
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