Zhiqiang Feng1,2 and Paul Boyle1

1School of Geography & GeosciencesUniversity of St Andrews2The Centre for Census Interaction Date Estimation and Research (CIDER)Estimating Spatially Consistent Interaction Flows

IntroductionCensus 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 levelThe census interaction data were severely under-usedThese data sets produced at large expense

Use of interaction data in analysis of demographic and social changeTheoretical implications counter-urbanisation depopulation Policy implications energy consumption environmental pollution

ProblemsChanges in census questionsChanges in definitionChanges in themesChanges in coverageChanges in disclosure control and imputationChanges in geographical boundaries

Changes in geography

Research objectivesDevelop a standard methodology for integrating migration and commuting flow matrices for different geographical unitsSpecifically, 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

Special Migration Statistics1981 Set 1: Many tables, but complex geography

Set 2:Ward-level (10,0002) 1 table2 matrices (male, female) 1991 Set 1:(Equivalent to 1981 Set 2)Ward-level (10,0002) 1 table12 matrices (age by sex)

Set 2:Many tables, at district-level

Special Workplace Statistics1981Set A & Set B Ward and district level By residence and workplace (not matrices)Set C:Ward-level (10,0002) 5 tables172 matrices1991Set A & Set B Ward and district level By residence and workplace (not matrices)Set CWard-level (10,0002) 9 tables274 matrices

Areal InterpolationPiPj=1/2*PiPk=1/2*Piijk

Interpolation for interaction flows12

Integrating strategyUse 1981 interaction data estimating for 1991 geography as an exampleGravity model of 1981 ward flowsParameter estimates from this model used to estimate 1981 ED flows (130,0002) Aggregate ED flows to 1991 wardsConstrained ED flows so they sum to known intra- and inter-ward flows

Integrating strategy

MethodologyMij=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; =parameters to be estimatedMigration:Commuting:Mij=commuting between 1981 wards i and j; Pi=workers in 1981 ward i; dij=distance between ward i and j;Models at the ward level

Methodology0-3= parameters derived from ward-level modelCommuting: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; AB= commuting between 1981 EDs A and B; PA=employees in 1981 ED A; dAB= distance between ED A and B; Estimating 1981 ED flows

Population and grid reference data extracted from Small Area Statistics (SAS)

Distance measurements:

Euclidean?Network?Mixed : Euclidean and network?

Measuring distance

Estuary problem

Island effectAssume Euclidean distance results in over-estimates offlows between, into and out of islands.

In fact, the model for all Scottish wardsshows these flows are under-estimated.

Comparison between migration model results with different distance measuresData source: 1991 SMS Set 1, Scotland

Euclidean distance

Mixed distance

Deviance

921422

922090

Degree of freedom

1002998

1002998

Proportion explained

0.5811

0.5801

Constant

1.3390

1.1811

Logged distance

-1.3888

-1.3644

Logged origin population

0.7144

0.7124

Logged destination population

0.6714

0.6697

Intra-ED flowsIntra-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 flowProportion of intra-ED flow = f (logged average population)

Estimating flows with unstated originsDestination is always knownOrigin district and ward entirely unknown

Select from all wards in Britain

Origin district known

Select from wards with flows within the district

Estimated flowsproportional to actual flowsDistrict ??ward ??DistrictwardDistrictward ??Districtwardorigindestinationorigindestination

Model results

1981 migration data

Male

Female

Deviance

7565418

7402517

Degree of freedom

105036234

105036234

Proportion explained

0.6083

0.6222

Constant

1.8654

2.3167

Logged distance

-1.6554

-1.6761

Logged population at origin

0.6072

0.5755

Logged population at destination

0.4960

0.4829

Re-estimated Datasets on WICIDMigration dataData sets 1991 2001wardST ward 1981 SMS (set 2) X X

1981 SMS (set 2) X Xincl. pro-rate migrants origin unstated1991 SMS (set 1) X

1991 SMS (set 1) Xincl. pro-rate migrants origin unstated

Commuting dataData sets 1991 2001geographygeography

1981 SWS (set c) X X

1981 SWS (set c) X Xincl. pro-rate commuters workplace unstated1991 SWS (set c) X

1991 SWS (set c) Xincl. pro-rate commuters workplace unstated

Re-estimated Datasets on WICID

Case Study - Commuting change in Liverpool

ConclusionAn innovative and model-based method has been developed for the areal interpolation of large interaction data setsThe estimated data sets have been loaded into WICID for academic use in analysis of spatio-temporal variationsMethods could be applied to other interaction data sets

Notes: the first question is why do we do the work? Or why bother to integrate the interaction data at all?A person is a migrant if he had different address one year ago to that at the date of census Most migrants move a short distance. Local level migration is thus very important phenomenon. This has theoretical and applied implications. Can be used to investigate counter-urbanisation, housing problemsthere is no time-series comparison between migration at local level. Cause it is un-comparable