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.

1Research Methods Festival 2008

Zhiqiang Feng1,2 and Paul Boyle1

1School of Geography & Geosciences

University of St Andrews2The Centre for Census Interaction

Date Estimation and Research (CIDER)

Estimating Spatially Consistent Interaction

Flows


Introduction

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


Use of interaction data in analysis of demographic and social change

•Theoretical implications

• counter-urbanisation

• depopulation

• Policy implications

• energy consumption

• environmental pollution


Problems

• Changes in census questions• Changes in definition• Changes in themes

• Changes in coverage• Changes in disclosure control and

imputation• Changes in geographical

boundaries


Census Ward 1981 1991 2001

England 8718 8822 7932

Wales 974 1108 868

Scotland 1211 1003 1176

10903 10933 9976

excluding shipping wards

1981 1991 2001

England 8357 8461 7932

Wales 932 1066 868

Scotland 1155 1002 1176

10444 10529 9976

Changes in geography



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 (10,0002) for the different 1991 and 2001 ward geographies?

• Deliver reliable time series (1981-2001) interaction data for academic use


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)


1 table

12 matrices (age by sex)

• Set 2:

Many tables, at district-level


Special Workplace Statistics

1981

• Set A & Set B

Ward and district level

By residence and workplace

(not matrices)

• Set C:


5 tables

172 matrices

1991

• Set A & Set B

Ward and district level

By residence and workplace

(not matrices)

• Set C


9 tables

274 matrices


Areal Interpolation

Pi

Pj=1/2*Pi

Pk=1/2*Pi

i j k

sntt PP *


Interpolation for interaction flows

1 2 A B CA B C


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 (130,0002) • Aggregate ED flows to 1991 wards• Constrained ED flows so they sum to known

intra- and inter-ward flows


Integrating strategy1981 ward flows

I81 J81

1991 wards

I81 J81

I91

J91

1981 estimated ED flows

A

B

C

D

Aggregate to 91 wards

A

B

C

D

1991 ward flows

I91

J91


Methodology

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;

ijij3j2i10ij ε)lndβlnPβlnPβexp(βM

30=parameters to be estimated

ijijiij dWM )lnlnexp( 210

Migration:

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


Methodology

β0-3= parameters derived from ward-level model

iA jB

ABij MM ˆ

)lnlnexp(ˆ210 ABAAB dWM Commuting:

)lnlnlnexp(ˆ3210 ABBAAB dPPM 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;

M̂

AB= commuting between 1981 EDs A and B; PA=employees in 1981 ED A;

dAB= distance between ED A and B;

M̂

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 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.


Comparison between migration model results with different distance measures

Euclideandistance

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 destinationpopulation

0.6714 0.6697

Data source: 1991 SMS Set 1, Scotland


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 flow

Proportion of intra-ED flow = f (logged average population)


Estimating flows with unstated origins

Destination 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 flows

District ?? ward ?? District ward

District ward ?? District ward

origin destination

origin destination

Estimated flows

proportional to

ij

ji

d

PP

If there are no observed flows from the same district select from all wards from that district


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 atorigin

0.6072 0.5755

Logged population atdestination

0.4960 0.4829


Re-estimated Datasets on WICIDMigration dataData sets 1991 2001

ward ST ward 1981 SMS (set 2) X X

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

1991 SMS (set 1) X

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


Commuting dataData sets 1991 2001

geography geography

1981 SWS (set c) X X

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

1991 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




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

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.

Documents

ward i

set b ward

ward geographies

ward levelmethodology0

wardlevel modelcommuting

ward j dij

ward flowsparameter

interaction data estimating