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Optimal models of segregation

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There has been long and wide-ranging debate in the social science literature about how best to conceptualise and to measure segregation (see, inter alia, Allen and Vignoles, 2007; Johnston and Jones, 2010; Harris, 2011). A popular measure is the dissimilarity index, usually attributed to Duncan and Duncan (1955). This is somewhat ironic because in another paper published in the same year, the same two authors were much more cautious about advocating any one index as preferable to others and were wise to the geographical limitations: "all of the segregation indexes have in common the assumption that segregation can be measured without regard to the spatial patterns of white and nonwhite residence in a city" (p.215). Whilst one response to this shortcoming has been the development of spatial measures of segregation (Wong, 1993; Reardon and O'Sullivan, 2004; Harris, 2012), a number of papers from the 1980s and 90s treated the measurement of segregation as a (spatial) optimisation problem (Jakubs 1981; Morgan 1983; Waldorf 1993). In this paper I revisit that optimisation literature, substituting geographical distances between places with ‘nearest-neighbour distances’ to determine the cost function. Applying this method to the 2011 Census data and to England, I consider claims of “white flight” that have appeared in the media.

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Optimal models of segregation

  1. 1. + Optimal models of segregation Richard Harris
  2. 2. + Classic segregation index I = k obsi −expii∑ D = 0.5 ai aii ∑ − bi bii ∑i∑
  3. 3. + Classic segregation index n Literally the sum of its parts n And those parts are places (locations within the overall study region) n Which means they can be georeferenced i (xi, yi)
  4. 4. + Classic segregation index n The georeference is superfluous n Only need to know that i is within the study region n Really just the average difference between two variables n Hence…
  5. 5. + Classic segregation index n … all these have the same index value (D = 1) n “the checkerboard problem”
  6. 6. + Same lived experience of residential segregation?
  7. 7. + Five dimensions of residential segregation (Massey & Denton, 1988) n (Un-)Evenness n which is what the classic segregation index measures n Exposure n Probabilistic measures n Concentration n Centralization n Clustering n Concerns the “checkerboard problem”
  8. 8. + Clustering n Jakubs (1981) and Morgan (1983) propose distance-based measures based on linear optimization. n Recall, for example, n For each location (i) determining whether obs > exp or obs < exp and therefore whether it has a surplus or deficit of the target population. I = k obsi −expii∑
  9. 9. + The optimization n Minimise the distance the target population would have to travel between (between the georeferences, i.e. centroids) to achieve an even distribution. n Both Jakubs and Morgan then calculate Dmin / D* where d* is the minimum distance under some hypothetical condition of maximum segregation.
  10. 10. + A problem n “After some initial experimentation … we quickly discovered that computing costs and machine requirements quickly became prohibitive for large urban areas” n Massey and Denton (1988, p.296) n But that was then… n … well before the R optimization package lpSolve became available (for free)
  11. 11. + Some tweaks n I am not convinced by the need to construct a ratio (i.e. Dmin / D*) n Instead, use Dmin / Σa – the average distance a person in group a would have to travel to create evenness (with group b) n Dmin is a function of the distances between zone centroids.Try: n Use nth nearest neighbour instead of Euclidean distance and minimise that instead n (Dmin / Σa) / meandc where meandc is the mean inter-centroid distance
  12. 12. + Some Pearson correlations D Dsp (nn) Dsp (Euc) N D 0.415 0.763 0.210 Dsp (nn) 0.356 0.788 Dsp (Euc) -0.045 D is the standard index of dissimilarity (Asian Vs White British for the 75 authorities with greater than 5% population Asian*) Dsp (nn) is the Spatial Dissimilarity index using nearest neighbour distance. Dsp uses Euclidean distances (but divides by mean inter- centroid distances) N is the number of Output Areas in the authority * Asian here defined as Pakistani + Indian + Bangladeshi (largest groups)
  13. 13. + Blackburn with Darwen
  14. 14. + However… n This is not actually a measure of clustering n It conflates clustering and centralisation n Pearson correlation (Dsp, Distance between the mean centre for the entire population per local authority and the mean centre for the Asian population): 0.529
  15. 15. + Three choices n Decide what actually it is n Geographic measure of the residential separation of the White British from the Asian population with the local authorities n So, if you believe distance effects contact, it is a measure of exposure n Create a ratio against some hypothetical notion of ‘total segregation’ for the given geography n Control for the centralisation effects (e.g. using regression) …
  16. 16. P WBloss D Dsp Cl Wycombe Wolverhampton Wokingham Woking Windsor and Maidenhead Westminster Wellingborough Watford Warwick Wandsworth Waltham Forest Walsall Trafford Tower Hamlets Three Rivers Tameside Sutton Stoke-on-Trent Spelthorne South Bucks Solihull Slough Sheffield Sandwell Rochdale Redbridge Reading Preston Peterborough Pendle Oxford Oldham Oadby and Wigston Nuneaton and Bedworth Nottingham Newham Newcastle upon Tyne Milton Keynes Middlesbrough Merton Manchester Luton Leicester Leeds Kirklees Kingston upon Thames Hyndburn Hounslow Hillingdon Harrow Hackney Gravesham Enfield East Staffordshire Ealing Dudley Derby Croydon Crawley Coventry Charnwood Camden Calderdale Bury Burnley Brent Bradford Bolton Blackburn with Darwen Blaby Birmingham Bedford Barnet Barking and Dagenham Wycombe Wolverhampton Wokingham Woking Windsor and Maidenhead Westminster Wellingborough Watford Warwick Wandsworth Waltham Forest Walsall Trafford Tower Hamlets Three Rivers Tameside Sutton Stoke-on-Trent Spelthorne South Bucks Solihull Slough Sheffield Sandwell Rochdale Redbridge Reading Preston Peterborough Pendle Oxford Oldham Oadby and Wigston Nuneaton and Bedworth Nottingham Newham Newcastle upon Tyne Milton Keynes Middlesbrough Merton Manchester Luton Leicester Leeds Kirklees Kingston upon Thames Hyndburn Hounslow Hillingdon Harrow Hackney Gravesham Enfield East Staffordshire Ealing Dudley Derby Croydon Crawley Coventry Charnwood Camden Calderdale Bury Burnley Brent Bradford Bolton Blackburn with Darwen Blaby Birmingham Bedford Barnet Barking and Dagenham
  17. 17. P WBloss D Dsp Cl Wycombe Wolverhampton Wokingham Woking Windsor and Maidenhead Westminster Wellingborough Watford Warwick Wandsworth Waltham Forest Walsall Trafford Tower Hamlets Three Rivers Tameside Sutton Stoke-on-Trent Spelthorne South Bucks Solihull Slough Sheffield Sandwell Rochdale Redbridge Reading Preston Peterborough Pendle Oxford Oldham Oadby and Wigston Nuneaton and Bedworth Nottingham Newham Newcastle upon Tyne Milton Keynes Middlesbrough Merton Manchester Luton Leicester Leeds Kirklees Kingston upon Thames Hyndburn Hounslow Hillingdon Harrow Hackney Gravesham Enfield East Staffordshire Ealing Dudley Derby Croydon Crawley Coventry Charnwood Camden Calderdale Bury Burnley Brent Bradford Bolton Blackburn with Darwen Blaby Birmingham Bedford Barnet Barking and Dagenham Wycombe Wolverhampton Wokingham Woking Windsor and Maidenhead Westminster Wellingborough Watford Warwick Wandsworth Waltham Forest Walsall Trafford Tower Hamlets Three Rivers Tameside Sutton Stoke-on-Trent Spelthorne South Bucks Solihull Slough Sheffield Sandwell Rochdale Redbridge Reading Preston Peterborough Pendle Oxford Oldham Oadby and Wigston Nuneaton and Bedworth Nottingham Newham Newcastle upon Tyne Milton Keynes Middlesbrough Merton Manchester Luton Leicester Leeds Kirklees Kingston upon Thames Hyndburn Hounslow Hillingdon Harrow Hackney Gravesham Enfield East Staffordshire Ealing Dudley Derby Croydon Crawley Coventry Charnwood Camden Calderdale Bury Burnley Brent Bradford Bolton Blackburn with Darwen Blaby Birmingham Bedford Barnet Barking and Dagenham
  18. 18. + Closing Thoughts n There is no longer a technological barrier for treating the measurement of segregation as a (spatial) optimization problem. n But it is not a measure of clustering per se n It still takes a while to calculate n And the ‘most segregated’ [sic] authority based on the principal component loadings?
  19. 19. + Newham n  It is because 36% of Newham’s residential population is Asian and it also lost 37% of its White British population from 2001 – 2011 n  The next is Redbridge (33% Asian; lost 30%) n  Then Blackburn (unevenly distributed and spatially clustered Asian population) Prop. Asian 0.05 to <0.15 0.15 to <0.30 0.30 to <0.60 0.60 to 0.81 Omitted

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