Statistics for cities

Transcription

1 Statistics for cities More than statistics about cities Jean-Luc LIPATZ INSEE «Territorial studies» August 2010

2 An argument that started with the urban audit adventure but no offense is meant : bad examples on NB : Anything that follows is related to analysis, not to reporting. Page 2

3 Man vs. wild (geography) Part I beasts awaiting! What makes spatial statistics more than statistics with and added geographical reference? Native (spatial) autocorrelation between objects Inner structure of the objects Chess board problem Ecological fallacy Modifiable Area Unit Problem Page 3

4 Spatial autocorrelation Ally or enemy? Waldo Tobler (1979) «everything is related to everything else, but near things are more related than distant things» + Without it, there will be no map + Substitute for unobservable variables - Classical tools often give biased or incorrect results Classical less squares regressions, logit regressions, etc Page 4

5 Urban audit, next round : is it possible to interpret data for each city separately? (classifications of cities as they were independent from each other?) Page 5

6 Ecological fallacy Consists in drawing conclusion at individual level from aggregated data at zone level. It is possible to get an inverted conclusion! Example (Baccaini, Courgeau 1996) : in Norway, people living in agricultural regions have the best chance to emigrate but not people working in agriculture! Page 6

7 Chessboard problem The simple list of the spatial inner components of some zone doesn t describe the zone Switching round the components will give the same description. We must introduce the links between the components (common boundaries, distance ) Page 7

8 City of Niort, standard statistical output areas Total population Population with low income High rates of low income Low rates of low income It doesn t give a picture of social segregation in the city! Page 8

9 The «Modifiable Area Unit Problem» (MAUP) Page 9

10 The MAUP A standard classification problem : conclusions depend on the classification used Aggravated by the lack of consensus about a unique territorial classification, because of Different territorial classifications coming from a multiplicity of designers, applying a multiplicity of rules At Europe level : a common denomination is not a common definition Within France (e.g. census output areas designed by municipalities) Possible mismatch design/use, coming from the intention of designing zones respectfully of some characteristics : it is not possible to fulfill all possible constraints Page 10

11 A G G R E G A T I O N E F F E C T Loss of variance ZONING EFFECT Multiple possibilities Page 11 AGGREGATION + ZONING = MAUP

12 The trap SCD 1 SCD 2 IRIS inhabitants Unemployment 10 % IRIS inhabitants Unemployment 10 % IRIS habitants Unemployment 20 % IRIS habitants Unemployment 20 % Page 12

13 A true life example : Duncan index for social categories morphological cities, 1999 census Different rankings: zoning effect Page 13 Standard output areas (IRIS) about 2000 inh. Super output areas (TRIRIS) about 5000 inh. City Inde x Ra nk Inde x Ra nk R o ue n 0,51 1 0,31 13 Lille 0,47 2 0,38 2 P a ris 0,44 3 0,39 1 Ca e n 0,42 4 0,32 9 Me tz 0,42 5 0,29 23 Le Ha vre 0,42 6 0,30 18 Lyo n 0,42 7 0,30 17 Gre no b le 0,41 8 0,29 22 Ma rs e ille 0,40 9 0,34 3 S tra s bourg 0, ,34 5 Lower values : aggregation effect

14 A true life example : Different stories in the city of Gennevilliers Aggregation effect Zoning effect Page 14

15 Urban audit analysis : segregation is higher in French cities but there, SCD are small and designed to show the inner differences of the French cities while in most other countries they were just (possibly large) administrative units! Page 15

16 Finding a way out Page 16

17 Grids Since the human made zonings are too clever (local definitions, thematic definitions), replace them by something more rude : a regular tessellation (mosaic) Anyway, nobody would have done an histogram like that! Page 17

18 Grids + Easy to build, easy to explain + Not related to a specific phenomenon = usable in the same conditions for analyzing any phenomenon + Same definition everywhere = an unique thermometer + Same definition in time - The zoning effect of the MAUP disappears but not the aggregation one : which size for the cells? - Chess board problem is still possible : there is still a need for appropriate analysis tools Page 18

19 An advertising poster for another approach, source DG-REGIO before after Page 19

20 Not only a question of detailed data Households with reference person above 65 Data on 1km² grid cells Source : Geostat++(FR) project Standard data at municipality level location : centroid of municipality Less than the average More than the average Risk estimates using kernel density probability estimation Page 20 (same processing, results mapped on a 5km wide grid)

21 Page 21 (UA) City of Rennes : 1km² grid, standard output areas Also showing built up areas and roads

22 But grids are zonings! Could we get some more exact solution? Page 22

23 Coping with the chessboard problem The Reardon and O Sullivan idea (2004) : no zoning! Zonings are just a special instance of a more general concept of neighboring Replace zoning with discs centered on each observation For the Duncan index : Duncan 1 = ~ x x P 2TP 1 P π π ~ P T x local proportion around observation x global proportion total population ( ) Extends the classical approach, but changes the concept of a neighborhood from inclusion in the same preset zone to spatial proximity. But the question is now which size for the centered discs! Should be related to some objective criterion : feeling of being a neighbor? Page spatial 23 extent of phenomena (spatial autocorrelation)?

24 Applying the Reardon and O Sullivan idea The 3 main municipalities in region»poitou- Charentes» - Segregation of aged people Duncan index 0,4000 0,3500 0,3000 0,2500 0,2000 0,1500 0,1000 0,0500 0,0000 Page 24 Census districts Standard output areas Geostat grids Ordering still differs at the different scales! UA SCDs Poitiers Niort La Rochelle Discs radius (/ 100m)

25 A maximum for a neighborhood size? Learning from spatial autocorrelation Variance between observations Maximum = no more correlation 1 γ ( h ) = var + h 2 ( Z( s) Z( s )) 1600m 1600m 2 IRIS(red boundaries) around 5000 inh. Distance between observations Municipality Page 25 of La Rochelle ( inh.) proportion of aged people (source RFL 2007) Correlation between proportions measured in 1ha grid cells

26 Urban audit sub city districts : the instructions says inhabitants is a minimum. For smaller cities it should be a maximum! Page 26

27 An optimum for a neighborhood size? Learning from non parametric density estimation Simplifying picture fˆ ( x) N = 1 x X K Nh i= 1 h i A neighborhood? Page 27

28 Non parametric probability density estimation Which value for h? With an appropriate kernel function K K( x, y) = 1 2πh h x y exp( x h x y h y 2 ) It can be demonstrated that the optimum values for h x and h y depend on the number of observations and on their spatial dispersion : Software (SAS) adds a possibility to do fine tuning, using multipliers for the theoretical optimal values. But which multiplier value to use? h x = σ N x 1 6 Page 28

29 Building a model for the urban morphology Learning from fractals Neighborhoods Blocks Houses Page 29 Dimension = log(5) log(3) 1,5

30 Fractal dimensions : an attempt to be practical The Ripley s K function gives a measure of the way space is filled K( r) = mean( number( d density <= r)) Fractal dimension D is obtained by fitting a function y = r D over the experimental function K Some results from the census address register aggregated into 50mx50m grid cells : space is relatively empty, filled in a way similar than the simplified previous model and without many disparities within the French municipalities even in the Indian Ocean Paris XVIème : D = 1.4 (Haussmann town planning in the XIXth century) Paris XVème, Strasbourg, La Rochelle : D = 1.5 Caen, Rennes, Poitiers, Bordeaux, Amiens, Reims, Nancy, Besançon, Clermont- Ferrand, Limoges : D = 1.6 Nantes, Toulouse : D = 1.7 (large old centers with small streets) Saint-Denis de la Réunion : D = 1.5 Page 30

31 Experimenting from the theoretical model Page 31 Automatically generated data

32 Experimenting from the theoretical model Playing with the multiplier of the bandwith of the probability density estimation BWM=1.0 BWM=0.6 BWM=0.5 BWM=0.3 BWM=0.2 Page 32

33 BWM=0.5 gives h=300m Angoulême ( inh.) Besançon ( inh.) Nantes ( inh.) Toulouse ( inh.) Page 33

34 Conclusion It is possible to cope with both to the MAUP and the chessboard problem, but it requires specific data and specific statistical processes France is not a country with interconnected registers : everything is matter of good will Elementary data should be detailed enough to allow viewing 300m wide spots Address based data is better, but census tracts may be sufficient, French target is 1ha grid cells. 0,4000 0,3500 0,3000 0,2500 0,2000 Poitiers>Niort>La Rochelle Page 34 0,1500 0,1000 0,0500 0,

35 Any reactions? Page 35