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Estimating Spatially Consistent Interaction Flows

Estimating Spatially Consistent Interaction Flows. Zhiqiang Feng 1,2 and Paul Boyle 1 1 School of Geography & Geosciences University of St Andrews 2 The Centre for Census Interaction Date Estimation and Research (CIDER).

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Estimating Spatially Consistent Interaction Flows

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  1. Estimating Spatially Consistent Interaction Flows Zhiqiang Feng1,2 and Paul Boyle1 1School of Geography & Geosciences University of St Andrews 2The Centre for Census Interaction Date Estimation and Research (CIDER) Research Methods Festival 2008

  2. Census interaction data include the Special Migration Statistics and Special Workplace Statistics(2001 Special Travel Statistics for Scotland) A major source of migration and journey to work information and the only source at a local level The census interaction data were severely under-used These data sets produced at large expense Introduction Research Methods Festival 2008

  3. Use of interaction data in analysis of demographic and social change • Theoretical implications • counter-urbanisation • depopulation • Policy implications • energy consumption • environmental pollution Research Methods Festival 2008

  4. Changes in census questions Changes in definition Changes in themes Changes in coverage Changes in disclosure control and imputation Changes in geographical boundaries Problems Research Methods Festival 2008

  5. Changesingeography Research Methods Festival 2008

  6. Research Methods Festival 2008

  7. Develop a standard methodology for integrating migration and commuting flow matrices for different geographical units Specifically, how do we re-estimate interaction matrices derived for the 1981, 1991 ward geographies (10,0002) for the different 1991 and 2001 ward geographies? Deliver reliable time series (1981-2001) interaction data for academic use Research objectives Research Methods Festival 2008

  8. Special Migration Statistics • 1981 • Set 1: • Many tables, but complex geography • Set 2: • Ward-level (10,0002) • 1 table • 2 matrices (male, female) • 1991 • Set 1: • (Equivalent to 1981 Set 2) • Ward-level (10,0002) • 1 table • 12 matrices (age by sex) • Set 2: • Many tables, at district-level Research Methods Festival 2008

  9. 1981 Set A & Set B Ward and district level By residence and workplace (not matrices) Set C: Ward-level (10,0002) 5 tables 172 matrices 1991 Set A & Set B Ward and district level By residence and workplace (not matrices) Set C Ward-level (10,0002) 9 tables 274 matrices Special Workplace Statistics Research Methods Festival 2008

  10. ArealInterpolation j i k Pj=1/2*Pi Pi Pk=1/2*Pi Research Methods Festival 2008

  11. A A B B C C Interpolation for interaction flows 1 2 Research Methods Festival 2008

  12. Use 1981 interaction data estimating for 1991 geography as an example Gravity model of 1981 ward flows Parameter estimates from this model used to estimate 1981 ED flows (130,0002) Aggregate ED flows to 1991 wards Constrained ED flows so they sum to known intra- and inter-ward flows Integrating strategy Research Methods Festival 2008

  13. 1991 wards 1981 ward flows I81 J81 I81 J81 J91 I91 1981 estimated ED flows Aggregate to 91 wards 1991 ward flows A A C C J91 I91 D D B B Integrating strategy Research Methods Festival 2008

  14. Methodology Models at the ward level Migration: Mij=migration between 1981 wards i and j; Pi=population in 1981 ward i; Pj=population in 1981 ward j; dij=distance between ward i and j; Commuting: Mij=commuting between 1981 wards i and j; Pi=workers in 1981 ward i; dij=distance between ward i and j; =parameters to be estimated Research Methods Festival 2008

  15. Methodology Estimating1981 ED flows Migration: AB= migration between 1981 EDs A and B; PA= population in 1981 ED A; PB= population in 1981 ED B; dAB= distance between ED A and B; Commuting: AB= commuting between 1981 EDs A and B; PA=employees in 1981 ED A; dAB= distance between ED A and B; β0-3= parameters derived from ward-level model Research Methods Festival 2008

  16. Measuring distance • Population and grid reference data • extracted from Small Area Statistics (SAS) • Distance measurements: • Euclidean? • Network? • Mixed : Euclidean and network? Research Methods Festival 2008

  17. Estuary problem Research Methods Festival 2008

  18. Island effect Assume Euclidean distance results in over-estimates of flows between, into and out of islands. In fact, the model for all Scottish wards shows these flows are under-estimated. Research Methods Festival 2008

  19. Comparison between migration model results with different distance measures Data source: 1991 SMS Set 1, Scotland Research Methods Festival 2008

  20. Intra-ED flows Intra-ED flows are excluded in the model because there is no intra-ED distance for 1981 EDs A linear regression was used to estimate the proportion of intra-ED flow compared to the total flow Proportion of intra-ED flow = f (logged average population) Research Methods Festival 2008

  21. Destination is always known Origin district and ward entirely unknown Select from all wards in Britain Origin district known Select from wards with flows within the district Estimated flows proportional to If there are no observed flows from the same district select from all wards from that district Estimating flows with unstated origins origin destination District ?? ward ?? District ward Estimated flows proportional to actual flows origin destination District ward ?? District ward Research Methods Festival 2008

  22. Model results Research Methods Festival 2008

  23. Migrationdata Data sets 1991 2001 ward ST ward 1981 SMS (set 2) X X 1981 SMS (set 2) X X incl. pro-rate migrants origin unstated 1991 SMS (set 1) X 1991 SMS (set 1) X incl. pro-rate migrants origin unstated Re-estimated Datasets on WICID Research Methods Festival 2008

  24. Commuting data Data sets 1991 2001 geography geography 1981 SWS (set c) X X 1981 SWS (set c) X X incl. pro-rate commuters workplace unstated 1991 SWS (set c) X 1991 SWS (set c) X incl. pro-rate commuters workplace unstated Re-estimated Datasets on WICID Research Methods Festival 2008

  25. Case Study - Commuting change inLiverpool Research Methods Festival 2008

  26. Research Methods Festival 2008

  27. Research Methods Festival 2008

  28. An innovative and model-based method has been developed for the areal interpolation of large interaction data sets The estimated data sets have been loaded into WICID for academic use in analysis of spatio-temporal variations Methods could be applied to other interaction data sets Conclusion Research Methods Festival 2008

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