PopChange and geostatistical ways of looking at segregation

Transcript

1. PopChange and geostatistical ways of
   looking at segregation
   Nick Bearman
   Project team: Chris Lloyd, Gemma Catney and
   Paul Williamson, University of Liverpool, UK
   Email: nick@geospatialtrainingsolutions.co.uk / nick.bearman@ucl.ac.uk
   @nickbearmanuk #RMF18
   ESRC Research Methods Festival, Bath, 4th July 2018
   

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2. Outline
   1. Population Change and Geographic
   Inequalities in the UK, 1971-2011: ESRC
   project outline
   2. Creating population surfaces
   3. Geostatistical analysis of deprivation
   

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3. PopChange project outline
   • Identifcation of comparable variables from the UK
   Censuses of 1971, 1981, 1991, 2001 and 2011
   • Creation of population surfaces for Britain for all
   comparable variables (1km cells nationally and 100m cells
   for urban areas; in Northern Ireland grid square counts for
   1971-2011 are already available)
   • Provision of population surfaces, code in R programming
   language to manipulate data and an online atlas of
   population change
   

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4. Creating population surfaces
   • Selected comparable variables for 1971, 1981, 1991,
   2001 and 2011
   • Create intensity 1km grid using postcodes
   • Overlay enumeration districts or output areas with 1km
   postcode intensity grid
   • Use areal weighting to estimate populations of each
   overlapping area with postcode intensities as weights
   • Aggregate counts within grid cells
   • Smooth grid cells to make neighbouring cells similar
   

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5. Gridded data
   • Benefts are that all units are of the same size and shape
   and this makes it easier to assess scale efects without the
   need to account for zones whose size and shape difers
   • With grid cells, there are holes
   where there are no people; this
   is conceptually more sensible
   than zones (e.g., output areas or
   wards) which cover the land
   area completely
   

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6. Population change 1971-2011
   • Population surfaces generated for 1971 and 2011 for
   - Total persons
   - Unemployed persons (% of employed and
   unemployed)
   - Non owner occupied households (%)
   - Households without access to a car or van (%)
   - Households with more than one person per room (%)
   • From the latter four, z scores were derived (percentage-
   mean / standard deviation) and these were summed to
   derive a deprivation score (following Townsend)
   

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7. https://popchange.liverpool.ac.uk
   

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8. Population change 1971-2011
   • Gridded counts and diference maps (2011-1971)
   - Total persons, Unemployed persons (%), Townsend score
   • Analysis of population spatial distribution using index of
   dissimilarity and Moran’s I autocorrelation coefcient
   • Correlations between counts/percentages/scores for 1971
   and 2011
   

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9. Total persons in 2011 Total persons 2011-1971
   

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10. Unemployed persons (%) in 2011 Unemployed persons 2011-1971
    

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11. Townsend score in 2011 Townsend score 2011-1971
    

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12. Unevenness: 1971-2011
    Index of dissimilarity for Townsend input counts
    Example: unevenness in owner occupation reduced 1981
    to 2011 – partly a function of ‘right to buy’ scheme,
    resulting in mixed tenures in areas formally dominated by
    social housing
    Index of dissimilarity, D (1 = uneven, 0 = % identical)
    Unemployed
    Non owner
    occupied
    No car van
    access Overcrowded
    1971 0.22 0.40 0.29 0.32
    1981 0.26 0.41 0.30 0.36
    1991 0.25 0.36 0.31 0.33
    2001 0.25 0.33 0.31 0.38
    2011 0.22 0.32 0.32 0.40
    Cells with > 0.5 persons/HH for all 4 variables for
    specific year
    

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13. Variograms
    Most multi-scale analyses of segregation are based on
    • An a priori idea of the scales we are interested in
    - e.g., spatial segregation measures for bandwidths
    (neighbourhood) of 500m and 5km
    • Nested hierarchy
    - e.g., output area > middle layer super output area > local
    authorities
    Using variograms (part of geostatistics),
    ●
    the spatial scales of variation are determined from the data &
    ●
    the range parameter(s) of a model ftted to the variogram provide
    information on the dominant scale(s) of spatial variation.
    Variograms are a multi-scale measure of the clustering domain of
    segregation
    

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14. Characterising spatial structure
    z(x
    i
    ) is a percentage, or score at
    location x
    i
    p(h) is the number of data pairs
    separated by the lag (distance
    and direction) h
    Variogram: spatial dependence at diferent spatial scales
    1) For each pair of data points
    a) Store the squared diference in the value
    b) And the spatial distance between them
    2) Group these value diferences into distance bins
    a) all squared diferences for pairs separated by 1-2, 2-3km, ...
    b) compute half of the average of these diferences
    3) Plot (half) average diferences (value) against distances
    4) Plot shows how diference between values changes as a function of
    distance
    2
    )
    (
    1
    )}
    (
    )
    (
    {
    )
    (
    2
    1
    )
    (
    ˆ h
    x
    x
    h
    h
    h
    
    
     
    
    i
    i
    p
    i
    z
    z
    p
    
    

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15. Provides a composite measure of clustering and polarisation: small
    nugget indicates localised clustering – with a large sill this indicates
    polarisation
    Variogram model
    Value
    differences
    Distance
    Range(s) – intra-city and inter-city
    

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16. Simulated surfaces: spherical model with range (a) = 2 and 40.
    Short range = marked diferences in neighbouring areas (intra-city)
    (LLTI, variation over small space)
    Long range = neighbouring areas are similar (inter-city)
    (Ethnicity, variation over large spaces)
    Variograms
    

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17. Variograms for Townsend score:
    1971-2011
    Decreased variation in 2011 but less spatial continuity in scores
    over regional scales (smaller ranges)
    Nugget (c
    0
    )
    Str. comp. 1 (c
    1
    )
    Range 1 (a
    1
    )
    Model 1 type
    Str. comp. 2 (c
    2
    )
    Range 1 (a
    2
    )
    Model 2 type
    Nugget/Sill
    1971 2.406 2.080 11299.7 sph. 1.154 67960.8 sph. 0.427
    1981 2.559 1.527 10452.1 sph. 0.859 42066.4 sph. 0.517
    1991 2.537 1.575 10309.6 sph. 1.127 46083.3 sph. 0.484
    2001 2.156 1.428 9956.55 sph. 1.158 42036 sph. 0.455
    2011 1.744 1.354 10066.1 sph. 1.271 44917.1 sph. 0.399
    

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18. Variograms for Townsend input variables:
    1971 and 2011
    Note the presence of two ranges highlighting major scales of
    spatial variation – these correspond to variation across (short
    range) and between (large range) urban areas
    NB. Inputs
    are log-ratio
    transformed
    percentages
    

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19. Variogram model coefficients for Townsend
    input variables: 1971 and 2011
    Nugge
    t (c0)
    Str.
    comp.
    1 (c1)
    Range 1
    (a1) m
    Model
    1 type
    Str.
    comp.
    2 (c2)
    Range 1
    (a2) m
    Model
    2 type
    Nugge
    t/Sill
    Unemployment, 1971 0.130 0.069 11548.1 sph. 0.109 117367 sph. 0.422
    Unemployment, 2011 0.154 0.041 11836.6 sph. 0.039 110811 sph. 0.658
    Non owner occupied, 1971 0.179 0.115 10815 sph. 0.045 53527.2 sph. 0.528
    Non owner occupied, 2011 0.109 0.061 10152.7 sph. 0.030 47993.5 sph. 0.545
    No car or van, 1971 0.043 0.044 11427.2 sph. 0.031 56772.5 sph. 0.364
    No car or van, 2011 0.112 0.036 9947.9 sph. 0.042 40713.8 sph. 0.589
    Overcrowded, 1971 2.578 1.132 11623.9 sph. 1.303 110897 sph. 0.514
    Overcrowded, 2011 0.410 0.145 11211.2 sph. 0.161 84762.8 sph. 0.573
    

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20. Variogram model coefficients for Townsend
    input variables: 1971 and 2011
    Unemployment: spatial distribution is similar, but the magnitude of variation was greater in
    1971 than in 2011 – the places with large and small rates are similar, but the differences
    between places have reduced.
    Tenure: again, spatial distribution is similar (slightly less spatially continuous), but the
    magnitude of variation was greater in 1971 than in 2011 – the places with large and small
    rates are similar, but the differences between places have reduced.
    Car or van access: increased short range spatial variation – this suggests that there is more
    variation over rerlatively short distances – there are more pronounced distinctions between
    places with small and large rates in the same regions.
    Overcrowding: marked decrease in variation (note differences between Scotland and
    England and Wales in 1971 make comparisons difficult). Reduction in the spatial scale of
    variation – overcrowding is ‘spreading out’ of urban areas (especially London).
    

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21. Summary
    • The PopChange resource enables geographically - and
    attribute-rich - analyses of population change in the UK
    and, specifcally, the ways in which the population has
    become more or less geographically unequal
    • The variogram ofers a powerful means of characterising
    the spatial distribution of population variables
    • The spatial structure of socioeconomic variables is
    consistent across time, but the magnitude of variation has
    reduced for most variables – locations with large
    percentages of, for example, unemployment, are broadly
    the same but the diferences between locations have
    reduced
    

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22. Acknowledgements
    Support from the ESRC is acknowledged gratefully
    (Grant Ref No ES/L014769/1).
    The Ofce for National Statistics are thanked for
    provision of the data.
    Ofce for National Statistics, 2011 Census: Digitised
    Boundary Data (England and Wales) [computer fle].
    ESRC/JISC Census Programme, Census Geography
    Data Unit (UKBORDERS), EDINA (University of
    Edinburgh)/Census Dissemination Unit. Census
    output is Crown copyright and is reproduced with the
    permission of the Controller of HMSO and the
    Queen's Printer for Scotland.
    

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23. Questions?
    PopChange and geostatistical ways of looking at segregation
    Nick Bearman
    Project team: Chris Lloyd, Gemma Catney and
    Paul Williamson, University of Liverpool, UK
    ESRC Research Methods Festival, Bath, 4th July 2018
    Email: nick@geospatialtrainingsolutions.co.uk / nick.bearman@ucl.ac.uk
    Lloyd, C. D., Catney, G., Williamson, P. and Bearman, N. (2017)
    Exploring the utility of grids for analysing long term population change.
    Computers, Environment and Urban Systems, 66, 1–12.
    doi:10.1016/j.compenvurbsys.2017.07.003, Open Access
    @nickbearmanuk #RMF18
    

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24. Additional Slides
    

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25. Characterising spatial structure
    z(x
    i
    ) is a percentage, or
    score at location x
    i
    p(h) is the number of data
    pairs separated by the lag
    (distance and direction) h
    Variogram: spatial dependence at diferent spatial scales
    1. Take each data value in turn and compute its squared
    diference from each of the other values in the data set and
    store the distances between them
    2. Group these diferences into distance bins – e.g., all squared
    diferences for pairs separated by 1 to 2 km and compute half
    of the average of these diferences
    3. Plot these (half) average diferences against distances
    4. The plot shows how diference between values changes as a
    function of distance
    2
    )
    (
    1
    )}
    (
    )
    (
    {
    )
    (
    2
    1
    )
    (
    ˆ h
    x
    x
    h
    h
    h
    
    
     
    
    i
    i
    p
    i
    z
    z
    p
    
    

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26. Bounded variogram model: nugget and efect and spherical component.
    Provides a composite measure of clustering and polarisation: small
    nugget indicates localised clustering – with a large sill this indicates
    polarisation
    Variogram model
    Value
    differences
    Distance
    Range(s) – intra-city and inter-city
    

    View Slide