The Modifiable Areal Unit Problem
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The Modifiable Areal Unit Problem (MAUP) is a potential source of error that can affect spatial studies which utilise aggregate data sources (Unwin, 1996). Geographical data is often aggregated in order to present the results of a study in a more useful context, and spatial objects such as enumeration districts or police beat boundaries are examples of the type of aggregating zones used to show results of some spatial phenomena. These zones are often arbitrary in nature and different areal units can be just as meaningful in displaying the same base level data. For example, it could be argued that enumeration districts containing comparable numbers of houses are better sources of aggregation than police beats (which are often based on ancient parish boundaries in the UK) when displaying burglary rates. Large amounts of source data require a careful choice of aggregating zones to display the spatial variation of the data in a comprehensible manner. It is this variation in acceptable areal solution that generates the term 'modifiable'. Only recently (well, the last 20 years!) has this problem been addressed in the area of spatial crime analysis, where 'the areal units (zonal objects) used in many geographical studies are arbitrary, modifiable, and subject to the whims and fancies of whoever is doing, or did, the aggregating.' (Openshaw, 1984 p.3).
As the study area for crime incident locations has effectively infinite resolution, there exists a potentially infinite number of different options for aggregating the data. Numerous administrative boundaries exists, such as enumeration districts, wards, counties, health authority areas, etc. Within modern GIS, it is an elementary task to automatically generate a huge variety of non-overlapping boundaries. Regular, often square, grids are common, though polygons have been used in other studies of crime distribution (Hirschfield et al., 1997). The number of different combinations of areal unit available to aggregate data is staggering. Openshaw (1984) calculated that if one was to attempt to aggregate 1,000 objects into 20 groups, you would be faced with 101,260 different solution combinations. Although there are a large number of different spatial objects and ways in which a large geographical area can be sub-divided, the choices of areal units tend to be dominated by what is available rather than what is best. Police crime data is often mapped to police beats, even when the information is passed to outside agencies such as neighbourhood watches or local councils who might benefit from more relevant boundary structures.
The MAUP consists of both a scale and an aggregation problem, and the concept of the ecological fallacy should also be considered (Bailey and Gatrell, 1995). The scale problem is relatively well known. It is the variation which can occur when data from one scale of areal units is aggregated into more or less areal units. For example, much of the variation in enumeration districts changes or is lost when the data is aggregated to the ward or county level. The aggregation problem is less well known and becomes apparent when faced with the variety of different possible areal units for aggregation. Although geographical studies tend towards aggregating units which have a geographical boundary, it is possible to aggregate spatial units which are spatially distinct. Aggregating neighbours improves the problem to a small degree but does not get round the quantity of variation in possibilities which remains.
For a paper that discusses the MAUP and possible solutions, see:
Ratcliffe, J. H. and McCullagh, M. J. 1999 'Hotbeds of crime and the search for spatial accuracy'
Geographical Systems 1(4): 385-398.
Also see the Ecological Fallacy.
Bailey, T. C. and Gatrell, A. C. 1995 Interactive Spatial Data Analysis, Second Edition: Longman.
Hirschfield, A., Yarwood, D. and Bowers, K. 1997 'Crime Pattern Analysis, Spatial Targeting and GIS: The development of new approaches for use in evaluating Community Safety initiatives.', in N. Evans-Mudie (ed) Crime and health data analysis using GIS, Sheffield: SCGISA.
Openshaw, S. 1984 'The modifiable areal unit problem', Concepts and Techniques in Modern Geography 38: 41.
Unwin, D. J. 1996 GIS, spatial analysis and spatial statistics', Progress in Human Geography 20(4): 540-441.