Understanding the Modifiable Areal Unit Proble

Understanding the modifiable areal unit problem Robin Flowerdew School of Geography and Geosciences, University of St Andrews March 2009 Acknowledgements • Mick Green (Lancaster) and David Steel • • • • (Wollongong), statisticians ESRC / JISC for purchase of Census data (Crown copyright) for UK academic community David Martin (Southampton) for use of AZTool University of Canterbury for Erskine Visiting Fellowship Clive Sabel, Jamie Pearce and David Manley for help with data manipulation • What is the Modifiable Areal Unit Problem (MAUP)? • Investigating neighbourhood boundaries and health • Why does it happen? • • • – Local and regional effects – Spatial autocorrelation – Local processes Identifying processes – scales and areal zones Deriving data to reflect the processes Where does this leave us? What is the MAUP? The same basic data yield different results when aggregated in different ways •First identified by Gehlke and Biehl (1934) •Affects many types of analysis, including correlation and regression •Applies where data are aggregated to areal units which could take many forms e.g. postcode sectors, local government units, store catchment areas, grid squares •Work by (among others) Openshaw (1984), Fotheringham & Wong (1991), Tranmer & Steel (2001), on how and why the MAUP exists, and what can be done about it. The MAUP – scale and zonation issues • Two aspects – the scale effect, showing major analytical differences depending on the size of units used (generally correlations more pronounced for bigger units) • - the zonation effect (Openshaw calls it the aggregation effect), showing major differences depending on how the study area is divided up, even at the same scale Zonation effect • Simple example shows how different zonal systems give very different results from same data without major variations in zone sizes or elongated shapes Variables X and Y are defined for a 3x3 grid Zonation 1: X X Y 7 8 9 13 9 6 4 1 12 10 3 5 2 10 10 10 16 20 15 10 5 0 0 4 5 6 Y 9 8 1 2 7 3 r(X,Y) = .700 r1(X,Y) = -.642 r2(X,Y) = .913 Zonation 2: X Y 16 15 17 17 5 3 7 10 5 10 15 20 5 10 15 20 20 15 10 5 0 0 The MAUP in practice • Taylor and Openshaw (1979) found that correlations in Iowa between Republican voting and percentage of old people could vary from -.97 to +.99 depending on how counties were aggregated. Openshaw and Rao (1995) achieved correlations between unemployment and ‘no car households’ in Merseyside from -1.00 to +1.00 But shapes are convoluted and sizes variable Much less variation for more realistic zonal schemes Shape and the MAUP All shapes and sizes But shapes are convoluted and sizes variable Much less variation for more realistic zonal schemes Manley (2006) took pairs of census variables and correlated them at ward and ED level – statistically significant differences in almost all cases Example: the neighbourhood effect in health geography • Often suggested health may be affected by • contextual effects – health in the neighbourhood may affect individuals’ health But how big is a neighbourhood? Does it matter where we draw the boundaries? Recent research (Flowerdew, Sabel and Manley 2008) looks at this and finds, for the case investigated, that the MAUP is not too worrying Wards as neighbourhoods • Ward-level and ED-level figures calculated for % limiting long-term illness (pcllti) • ED-level pcllti then modelled as a function of other % variables • Then ward-level pcllti added as a contextual effect • Models weighted by population Results – ward system • Ward-level • • • Pcllti = .956 + .363 pcpens + .032 pcnonw + .334 pcmunem R2 = .870 ED-level (without neighbourhood effect) Pcllti = 1.136 + .385 pcpens + .058 pcnonw +.262 pcmunem R2 = .733 ED-level (with neighbourhood effect) Pcllti = -.465 + .351 pcpens + .037 pcnonw + .228 pcmunem + .225 pclltiwd R2 = .747 Designing new zonal systems • So far, assumed ‘neighbourhood’ = ‘ward’ • But what if the boundaries were different? • Zone design software will generate sets of pseudo-wards, based on several criteria: • Pop. threshold • Pop. target (e.g. average ward pop.) • Shape (perimeter squared / area) • Homogeneity Northamptonshire example • Study area needed – Has to be reasonably sized – No coastline – Range of settlement sizes – Knowledge of places The zonal systems • Differences in overall patterns, based on: a) the effect of constraints b) random variation (process starts from randomly selected ‘seeds’) c) often, whether zones of different types happen to be grouped together Regression results • Run • • • • • • • • • • • 3 4 5 6 8 11 14 15 16 17 21 R2 .789 .789 .787 .790 .793 .787 .788 .788 .786 .788 .789 Pseudo-ward Standard Sig. .168 .168 .136 .179 .201 .120 .140 .145 .117 .157 .162 .030 .031 .031 .031 .028 .031 .029 .032 .032 .032 .031 yes yes yes yes yes yes yes yes yes yes yes coefficient error Further analysis - Thamesdown • District of 170,000 around Swindon • 21 wards, urban centre, rural periphery • Thamesdown wards, 1991 • Limiting longterm illness • Thamesdown EDs, 1991 Limiting longterm illness Pseudo-ward systems • Pseudo-ward systems can be generated with different constraints, of which population equality, shape and homogeneity are the main factors • All systems had 19-22 zones of reasonably equal populations and sensible shapes Variations in correlation structure • The zonation effect suggests that there could be • • • • • • • • important changes in correlation coefficients for different zonal systems X Y highest r lowest r Pcllti pcwhite .334 -.045 Pcllti pckids -.296 -.378 Pcllti pcpens .883 .828 Pcllti pcunem .863 .810 Pcllti pcoo .538 .329 Pcllti pcla .826 .701 Pcunem pcla .817 .686 Regression of illness on other variables • At ED level, • Pcllti = 9.391 - .075 pcwhite + .374 pcpens + • • • • .363 pcunem + .179 pcla (R2 = .847) Adding neighbourhood variable, gives Pcllti = 9.225 - .078 pcwhite + .368 pcpens + .298 pcunem + .179 pcla + .067 nbdpw (s.e. .049) (R2 = .847) i.e. neighbourhood variable is not significant The neighbourhood effect in other zonal systems • To date, R 2 values have ranged from .849 to .995 • In most cases, neighbourhood effect is positive and small but statistically significant • Biggest impact was to raise R2 from .980 to .995 Conclusions about neighbourhood boundaries • Possible to generate pseudo-ward zonal • • • systems, with different constraints When relevant, analysts should try different zonal systems to test robustness of results In Northamptonshire, the neighbourhood effect varies from .117 to .201 – however it’s always +ve and significant – it does not matter in this case how you draw the boundaries In Thamesdown, it varies from .084 to .731 – not always significant – perhaps it does matter here! Why does it happen? • Size of correlation coefficient r is greatly influenced by • • highest and lowest values: if high X associated with high Y (and low X with low Y), you get high positive r If high X associated with low Y (and low X with high Y) – high negative r • If aggregation groups zones with high X values (and / or • high Y values) this effect is intensified If it groups high X zones with low X zones (or with average X zones), the effect is diluted MAUP and spatial autocorrelation • If the high values of X or Y are close together • • • (positive spatial autocorrelation), grouping is likely to intensify the correlation of X and Y If high values are scattered around the study area (low spatial autocorrelation), grouping will diminish their effect MAUP effect results from interplay of these Effect of grouping may be largely a chance factor – or may come from a desire for homogeneity from people drawing the boundaries Local and regional effects • • • Processes with spatial aspects may generate the MAUP E.g. the labour market – unemployment in zone i depends on job vacancies not just in i but in surrounding zones too The housing market likewise i.e. local and regional effects Problem: identifying the region! Work assumed local = ED and regional = ward, but why should labour market respect ward boundaries? Local processes • Often our understanding of the distribution of X • • or Y reflects local knowledge – we know a housing estate is located here, a good school is located there, an ethnic enclave is over there Such information can in part explain mapped patterns and correlations, and can suggest the configuration of zones that best reflects geographical reality i.e. descriptive empirical studies can inform modelling Identifying processes – scales and areal units • Need to recognise that geographical processes • • occur at particular scales, and studying them at the wrong scale may not be very helpful Further, data are not always available at the right scale – usually impossible to disaggregate data below its scale of supply Even if data are available for very small areas, it may not be clear how to aggregate them up Finding data to reflect the processes • MAUP has a zonation effect too – even if data • • are at the right scale, they may not be configured in a way that reflects the processes going on Should we design a set of zones specifically to fit an empirical problem? (perhaps by finding a set of zones to maximise correlation) Would this be ‘cheating’? Optimal scales may vary spatially • Note also that appropriate scales may be different for different places – social segregation for example may affect whole wards in big cities but a few EDs in towns • Appropriate scales may be different even within the same study area Where does this leave us? - 1 • Scales of process are not always the same as scales for which we have data – likewise for configurations • We need to be critical of the data for these reasons as well as many others • We need to think about the processes being studied and the scales of data needed Where does this leave us? - 2 • Most statistical work using modifiable areal unit • • • data is deficient – because zonal system doesn’t fit processes - and probably underestimates the strength of relationships Statistical results are not independent of the zonal systems the data come from Probably worth analysing data at several different scales, noting the differences and using them to help identify processes Good zone design software becoming available