1 Research Methods Festival 2008 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) Estimating Spatially Consistent Interaction Flows

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

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

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

5 Research Methods Festival 2008 Census Ward England Wales Scotland excluding shipping wards England Wales Scotland Changes in geography

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7 Research objectives 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 (10,000 2 ) for the different 1991 and 2001 ward geographies? Deliver reliable time series ( ) interaction data for academic use

8 Research Methods Festival 2008 Special Migration Statistics 1981 Set 1: Many tables, but complex geography Set 2: Ward-level (10,000 2 ) 1 table 2 matrices (male, female) 1991 Set 1: (Equivalent to 1981 Set 2) Ward-level (10,000 2 ) 1 table 12 matrices (age by sex) Set 2: Many tables, at district-level

9 Research Methods Festival 2008 Special Workplace Statistics 1981 Set A & Set B Ward and district level By residence and workplace (not matrices) Set C: Ward-level (10,000 2 ) 5 tables 172 matrices 1991 Set A & Set B Ward and district level By residence and workplace (not matrices) Set C Ward-level (10,000 2 ) 9 tables 274 matrices

10 Research Methods Festival 2008 Areal Interpolation PiPi P j =1/2*P i P k =1/2*P i i j k

11 Research Methods Festival 2008 Interpolation for interaction flows 12 ABCABC

12 Research Methods Festival 2008 Integrating strategy 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 (130,000 2 ) Aggregate ED flows to 1991 wards Constrained ED flows so they sum to known intra- and inter-ward flows

13 Research Methods Festival 2008 Integrating strategy 1981 ward flows I 81 J wards I 81 J 81 I 91 J estimated ED flows A B C D Aggregate to 91 wards A B C D 1991 ward flows I 91 J 91

14 Research Methods Festival 2008 Methodology M ij =migration between 1981 wards i and j; P i =population in 1981 ward i; P j =population in 1981 ward j; d ij =distance between ward i and j; =parameters to be estimated Migration: Commuting: M ij =commuting between 1981 wards i and j; P i =workers in 1981 ward i; d ij =distance between ward i and j; Models at the ward level

15 Research Methods Festival 2008 Methodology β 0-3 = parameters derived from ward-level model Commuting: Migration: AB = migration between 1981 EDs A and B; P A = population in 1981 ED A; P B = population in 1981 ED B; d AB = distance between ED A and B; AB = commuting between 1981 EDs A and B; P A =employees in 1981 ED A; d AB = distance between ED A and B; Estimating 1981 ED flows

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

17 Research Methods Festival 2008 Estuary problem

18 Research Methods Festival 2008 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.

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

20 Research Methods Festival 2008 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)

21 Research Methods Festival 2008 Estimating flows with unstated origins 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 actual flows District ??ward ??Districtward District ward ?? Districtward origindestination origin destination Estimated flows proportional to If there are no observed flows from the same district select from all wards from that district

22 Research Methods Festival 2008 Model results

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

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

25 Research Methods Festival 2008 Case Study - Commuting change in Liverpool

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28 Research Methods Festival 2008 Conclusion 1.An innovative and model-based method has been developed for the areal interpolation of large interaction data sets 2.The estimated data sets have been loaded into WICID for academic use in analysis of spatio- temporal variations 3.Methods could be applied to other interaction data sets