Comparing Internal Migration Around the GlobE (IMAGE):

The Effects of Scale and Pattern

Martin Bell, Elin Charles Edwards 1

John Stillwell, Konstantinos Daras 2

Marek Kupiszewski3, Dorota Kupiszewska4

and Yu Zhu5

International Conference on Population Geographies, 25- 28 June 2013

1. The University of Queensland, Australia 2. The University of Leeds, UK3. Institute of Geography and Spatial Organization, PAS, Poland4. International Organization for Migration, Poland5. Fujian Normal University, China

1. The University of Queensland, Australia 2. The University of Leeds, UK3. Institute of Geography and Spatial Organization, PAS, Poland4. International Organization for Migration, Poland5. Fujian Normal University, China

The IMAGE Project

An international collaborative program

which aims to provide a robust basis

for comparing internal migration

between countries around the world

Funded by Australian Research

Council Discovery Project

Project duration: 2011-2014

http://www.gpem.uq.edu.au/image

The IMAGE Global Inventory of Internal

Migration data

The IMAGE Repository of Internal

Migration data

The IMAGE Studio• Computes internal migration metrics

• Addresses key methodological issues

Outline

� Update on the IMAGE Inventory

� Update on IMAGE Repository

� Introduction to the IMAGE Studio

� Comparison of metrics for 15 countries with a

focus on intensity, distance and impact

� Investigation of the MAUP – scale effects and

pattern effects

� Conclusions and next steps

IMAGE Inventory of Internal Migration Data

Meta-data Values

Collection Instrument Census/Register/Survey

Form of data Transitions/Events/Duration

Time interval 1,2,5,other, undefined

Spatial framework All moves, # of zones

Characteristics Age, sex

• Sources

� Systematic mining of census forms, surveys and websites

� Review of published papers and reports

� Advice from IMAGE project collaborators and country experts

� Survey of national statistical agencies

Summary of Countries Collecting Internal Migration Data by Region and Source

Region CountriesData sources

Census Register Survey

Africa 50 47 0 41

Asia 40 37 14 24

Europe 42 32 28 35

Latin America 31 31 0 14

North America 3 3 2 2

Oceania 13 13 1 2

TOTAL 179 163 45 118

Building the IMAGE Repository of Internal Migration Data Collections

� Data assembled in the Repository

• National counts of all moves (by age)

• Origin-destination matrices (aggregate)

• Marginal totals (aggregate)

• Populations at risk

• Digital boundaries

Number of zones Countries

<20 26

20-49 21

50-99 19

>100 28

TOTAL 94

The IMAGE Studio

The IMAGE studio is a flexible suite of software

adaptable to a range of country-specific data inputs

organized as a set of four linked subsystems:

i. Data Preparation,

ii. Spatial Aggregation,

iii. Computation of Internal Migration

Indicators,

iv.Spatial Interaction Modelling

IMAGE Studio: Framework

IMAGE Studio – Subsystem InterfacesData Preparation Spatial Aggregation

Internal Migration Indicators Spatial Interaction Modelling

Why spatial aggregation?� Every country has unique Basic Spatial Units (BSUs) –

different size (area and population) and shape

(boundaries)

� Migration indicators depend upon how space is divided:

MAUP (Openshaw 1984)

� Scale component: How does the indicator vary according to

the number of Aggregated Spatial Regions (ASRs)?

� Pattern component: How does the indicator vary according to

the configuration of ASRs at any spatial scale?

� We address the MAUP using a system which

aggregates BSUs in a stepwise manner to identify the

scale effect

� At each step, a series of random configurations of ASRs

are produced to capture the pattern effect

Aggregation procedure

� Prepare boundary data,

migration flow matrix

and populations at risk

for BSUs

� Generate a contiguity

matrix for BSUs

F

Original Data

Data preparation

Clean Data

Manual Input

Set step size, number of

configurations and

spatial aggregation

methodStore

Data

Run Spatial Aggregation

Algorithm

For Each

level

For Each

conf.

Store

Data

True

False

True

False

� Set step size and number of

configurations at each level

� Choose spatial aggregation

method

IRA-wave Algorithm

12

3

11

6

4

1213

16

14

109

15

5

78

12

3

11

6

4

1213

16

14

109

15

5

78

12

3

11

6

4

1213

16

14

109

15

5

78

12

3

11

6

4

1213

16

14

109

15

5

78

12

3

11

6

4

1213

16

14

109

15

5

78

2) Select all neighbouring

areas

3) Assign the selected areas to

region

Final Aggregation to Aggregate Spatial Regions (2 ASRs)

Basic Spatial Units (16 BSUs) 1) Select 2 random seeds

Example of aggregation: Germany

412 BSUs 200 ASRs 150 ASRs

100 ASRs 50 ASRs 10 ASRs

Comparisons between countries

� Sample of 15 countries with larger numbers of Basic

Spatial Units

� Cross-national comparisons on three dimensions using

six indicators

� Analysis of scale effects and pattern effects on each

indicator

� Spatial aggregation using IRA wave with steps of 10 and

100 iterations at each step

� At each scale step, we take the indicator mean of the 100

configurations but also capture variation from the

coefficient of variation or the maximum and minimum

values for each set of ASRs

Sample countriesCountry Data type Year # BSU

1 Ghana 5yr Transition 2000 110

2 Brazil 5yr Transition 2000 558

3 Chile 5yr Transition 2002 342

4 Ecuador 5yr Transition 2001 995

5 Honduras 5yr Transition 2001 298

6 Mexico 5yr Transition 2000 2,439

7 Philippines 5yr Transition 2000 1,622

8 Canada 5yr Transition 2006 288

9 South Korea 5yr Transition 2006 232

10 Australia 1yr/5yr Transition 2011 333

11 United Kingdom 1yr Transition/Event 2001,2010 406

12 Belgium Event 2005 589

13 Finland Event 2011 336

14 Germany Event 2009 412

15 Sweden Event 2008 290

Total Migrants

0

0.5

1

1.5

2

2.5

3

0 50 100 150 200 250 300 350 400 450

Mig

ran

ts(M

illi

on

s)

Number of ASRs

1Y transition

Australia UK

0

2

4

6

8

10

12

0 50 100 150 200 250 300 350 400 450 500 550

Mig

ran

ts(M

illi

on

s)

Number of ASRs

5Y transition

Australia BrazilCanada ChileMexico EcuadorGhana HondurasPhilippines S Korea

0

0.5

1

1.5

2

2.5

3

0 50 100 150 200 250 300 350 400 450

Mig

ran

ts(M

illi

on

s)

Number of ASRs

Events

Belgium*

Finland

Germany

Sweden

Indicators of Internal Migration• Dimensions identified in Bell et al. (2002) Journal of

the Royal Statistical Society A

1 Crude Migration Intensity

2 Standardized Migration Intensity

3 Gross Migraproduction Rate

4 Migration Expectancy

5 Courgeau’s ‘K’

6 Peak Migration Intensity

7 Age at Peak Intensity

8 Mean/Median Distance Moved

9 Distance Decay Parameter

10 Index of Migration Connectivity

11 Index of Migration Inequality

12 Migration Weighted Gini

13 Coefficient of Variation

14 Migration Effectiveness Index

15 Aggregate Net Migration Rate

Migration Intensity

Migration Distance

Migration Connectivity

Migration Impact

Comparing Migration Intensities

� A migration intensity is the proportion of a

population changing residence in a specified time

interval

� Encompasses both migration rates and probabilities

� Crude migration Intensity (CMI) is the migration

count (M) divided by the population at risk (P):

CMIR = MR / P

where R is the number of ASRs

� Prior work (Long 1991; Bogue et al. 2010; Courgeau

1973)

Building on Courgeau’s k� Value of CMIn depends on the number of zones (n)

� Courgeau (1973) plotted CMI at multiple scales to

define a linear relationship (k)

� Courgeau et al. (2012) plots CMI against

ln [average households (H) per zone (n)]

� Algebraically, CMIn = a + b ln (H/n)

� When H/n = 1 (i.e. average of 1 household per zone)

then CMIn = a (representing overall mobility)

� Simultaneously addresses the scale and pattern

components of MAUP for migration intensities

Using the Courgeau et al. (2012) method

0

2

4

6

8

10

12

14

0 5 10 15 20

Cru

de

Mig

rati

on

In

ten

sity

(%

)

Ln (No of Households / No of ASRs)

1 year event

Sweden_E

Germany_E

Belgium_E

Finland_E

Estimated overall mobility (a)

CMIs using Courgeau’s method

Country

R2

Estimated

CMIs (all

moves) ranked

Observed CMIs (all

moves)

Event Finland 0.995 12.80 16.25

Event Belgium 0.991 11.08 -

Event Sweden 0.998 10.16 -

Event Germany 0.998 8.87 -

1Y transition Australia 0.999 20.93 14.58

1Y transition UK 0.994 11.50 10.73

5Y transition Australia 0.999 58.45 37.73

5Y transition Chile 0.985 41.13 -

5Y transition Canada 0.988 40.03 38.50

5Y transition South Korea 0.995 35.76 -

5Y transition Ghana 0.981 19.02 -

5Y transition Brazil 0.992 18.98 -

5Y transition Ecuador 0.913 18.24 -

5Y transition Honduras 0.967 14.30 -

5Y transition Mexico 0.888 12.94 -

5Y transition Philippines 0.990 10.47

• The relationship between CMI and distance may not

always be linear

Australia, 1 year transition

y = -1.3348x + 20.934

y = -0.0614x2 - 0.103x + 14.576

0

5

10

15

20

25

0 5 10 15 20

Cru

de

Mig

rati

on

In

ten

sity

(%

)

ln (No of Households / No of ASRs)

Australia 1Y Australia(obs)

Comparing Migration Distance

• Many studies have identified the negative influence of

distance on migration since Ravenstein’s law in 1885

indicating that

“The majority of migrants go only a short distance”

• including: Stewart (1941); Zipf (1946); Lee (1966); Lowry

(1966); Wilson (1967); Tobler (1970); Stillwell (1978);

Fotheringham (1980); Flowerdew (1982); Plane (1984);

P..

• and more recently: ODPM (2002); Fotheringham et al.

(2004); Kalogirou (2005); P. Dennett and Wilson (2011);

....

• Range of different model formulations and calibration

methods for capturing the frictional effect of distance

Spatial Interaction Model (SIM)

� Modelling would typically involve calibrating a model for a

selected set of BSUs, e.g. fitting a doubly constrained SIM:

Mij = Ai Oi Bj Dj dij-β

where Oi = the out-migration from zone i to all other zones

Dj = the in-migration to zone j from all other zones

Ai and Bj = balancing factors that ensure the

constraints are satisfied

dij- β = a linear distance decay function with

parameter β

� Mean distance migrated (MDM) is computed directly based

on inter-BSU migration flow and distance matrices

MDM = Σi≠jΣj≠iMij dij / Σi≠jΣj≠iMij

Key question

� What happens to the β parameter and MDM and

when we progressively aggregate each set of

Basic Spatial Units (BSUs) to Aggregated Spatial

Regions (ASRs)?

� At each scale step, we take the mean β and MDM

values of the 100 configurations but also capture

variation from the maximum and minimum values

for each set of ASRs

� These sets of values for different spatial levels tell

us more about the inverse migration v distance

relationship than values for single geographies

50

100

150

200

250

300

350

0 50 100 150 200 250 300 350 400 450

Me

an

Dis

tan

ce

Mig

rate

d (

Km

)

Number of ASRs

UK

Germany

Finland

Sweden

50

250

450

650

850

1050

1250

1450

0 50 100 150 200 250 300 350 400 450

Me

an

Dis

tan

ce

Mig

rate

d (

Km

)

Number of ASRs

Finland

Germany

Sweden

UK

Australia

Mean Migration Distance by number of ASRs

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

0 50 100 150 200 250 300 350 400 450

Be

ta V

alu

e

Number of ASRs

UK

Germany

Sweden

Finland

Australia

Decay parameter by number of ASRs

GR

OU

P

A/A Country Data type # BSU

Mean Beta Value

All BSUs200

ASRs

100

ASRs50 ASRs

MD

M <

20

0 k

m 1 Ecuador 5yr Transition 995 6.31 1.67 1.75 1.80

2 South Korea 5yr Transition 232 1.30 1.32 1.35 1.35

3 Ghana 5yr Transition 110 1.25 - 1.26 1.35

4 Philippines 5yr Transition 1,622 - 1.15 1.10 1.07

5 Honduras 5yr Transition 298 1.04 1.04 1.03 1.03

MD

M >

20

0 k

m 6 Brazil 5yr Transition 558 1.63 1.67 1.66 1.59

7 Mexico 5yr Transition 2,439 2.45 1.59 1.63 1.67

8a Australia 5yr Transition 333 1.01 1.05 1.08 1.13

9 Chile 5yr Transition 342 1.03 1.03 1.01 1.03

10 Canada 5yr Transition 288 0.90 0.93 0.96 1.00

1yr 11 United Kingdom 1yr Transition 406 1.58 1.56 1.55 1.53

8b Australia 1yr Transition 333 1.07 1.08 1.12 1.16

Eve

nt

12 Belgium Event 589 - 3.09 3.13 3.35

13 Germany Event 412 1.77 1.79 1.79 1.79

14 Finland Event 336 2.13 1.83 1.73 1.69

15 Sweden Event 290 1.66 1.52 1.42 1.39

Decay parameters using SIM

Comparing migration impact

� The most significant aspect of internal migration is

how it alters the spatial distribution of populations

� Does impact vary at different spatial scales and

between countries?

� How do we measure this impact?

� Aggregate net migration rate

� ANMR represents the net system-wide redistribution

per 100 persons

ANMR = 100 * 0.5 ∑i |Di-Oi| / PDi = inflows to i, Oi = outflows from i, P = total population

Aggregate Net Migration Rate by number of ASRs

0

0.05

0.1

0.15

0.2

0.25

0 100 200 300 400 500

Ag

gre

ga

te N

et

Mig

rati

on

Ra

te

Number of ASRs

Finland Germany

1 year events

0

0.05

0.1

0.15

0.2

0.25

0.3

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Ag

gre

gate

Ne

t M

igra

tio

n R

ate

ln (Number of ASRs)

1 year events

Belgium

Finland

Germany

Sweden

0

0.5

1

1.5

2

2.5

3

3.5

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Ag

gre

gate

Ne

t M

iga

tio

n R

ate

ln (Number of ASRs)

5 year transition

Australia

Ghana

Honduras

Brazil

Mexico

Ecuador

Chile

Philippines

Aggregate Net Migration Rate by ln (number of ASRs)

Determinants of ANMR

ANMR = MEI * CMI / 100

where Migration Effectiveness Index (MEI) measures the overall

degree of symmetry between inflows and outflows within a

migration system

MEI captures the net system-wide redistribution per 100 migrants

MEI = 100 * ∑i |Di-Oi| / ∑i (Di+Oi)

Migration Effectivness Indexby number of ASRs

Relationship between ANMR, CMI and MEI

ANMR = MEI * CMI / 100

=

No of ASR 50 50 50 No of ASR 100 100 100

ANMR CMI MEI ANMR CMI MEI

South Korea 0,47 9,08 5,13 South Korea 0,59 10,25 5,72

Philippines 0,51 2,80 17,95 Philippines 0,60 3,21 18,78

Mexico 0,81 4,60 17,55 Mexico 0,98 5,12 19,23

Ghana 0,90 5,26 17,02 Brazil 1,11 5,54 20,06

Brazil 0,91 4,86 18,64 Ghana 1,28 5,88 21,78

Australia 1,11 14,32 7,74 Australia 1,31 16,72 7,83

Honduras 1,26 4,81 26,26 Honduras 1,37 5,33 25,69

Ecuador 1,60 6,84 23,44 Ecuador 1,77 7,43 23,80

Chile 1,84 12,10 15,21 Chile 2,23 13,52 16,52

Canada 2,96 10,83 27,32 Canada 3,18 12,25 26,02

CMI and MEI values for 50 and 100 ASR for 5 year transition data by ANMR value

Patterns of population redistribution (BSUs)

-20

-15

-10

-5

0

5

10

15

20

0-2

5

25

-50

50

-10

0

10

0-2

00

20

0-3

00

30

0-5

00

50

0-7

00

70

0-1

00

0

10

00

-20

00

20

00

-40

00

40

00

-60

00

>6

00

0

Ne

t M

igra

tio

n R

ate

( p

er

10

00

)

Population density (persons per km2)

Belgium

-60

-40

-20

0

20

40

60

0-2

5

25

-50

50

-10

0

10

0-2

00

20

0-3

00

30

0-5

00

50

0-7

00

70

0-1

00

0

10

00

-20

00

20

00

-40

00

40

00

-60

00

Ne

t M

igra

tio

n R

ate

( p

er

10

00

)

Population density (persons per km2)

Brazil

Conclusions� “The simplest solution to the MAUP is to pretend it does

not exist and hope that the results being produced for ad

hoc zoning systems will still be meaningful or least

interpretable” (Openshaw, 1984)

Conclusions� MAUP: Scale Effect

� There are systematic regularities in the behaviour of

summary migration indicators in relation to scale

� These regularities can be useful in estimating

parameters at other spatial scales

� These regularities break down at very coarse levels of

aggregation e.g. <30 regions

� This can be problematic for countries which do not

have data at fine levels of spatial disaggregation

Conclusions

� MAUP: Pattern Effect

� The pattern effect becomes more problematic the smaller

the number of ASRs, because variability increases

� Observed values of internal migration indicators based on

standard statistical geographies may be outliers with

respect to the mean configurations of zones at equivalent

spatial scales and are therefore misleading for cross-

national comparisons

Both the scale and pattern effects of the MAUP do

matter. Our results show they impact on migration

in systematic ways. However, these manifest

differently between countries.

Conclusions� Intensity

� CMI varies systematically with spatial scale

� Scale effects can be exploited to generate a measure of aggregate

population mobility which is comparable across countries

� Distance� The frictional effect of distance varies between countries

� Countries exhibit systematic variations in the frictional effect of distance

which may rise, fall, or remain stable with increasing distance

� Impact� ANMR varies systematically with the CMI with changing scale

� The MEI is relatively stable except at low numbers of ASRs

� Differences in the ranking of countries on the ANMR compared with

their ranking on the CMI are due to variations in the MEI

Next steps

� How much closer are we to methods for cross-

national comparison?� CMI: Closer – use Courgeau given multiple data points

� Distance and Impact: Closer - as we now know that distance and

impact vary in a well behaved fashion

� MAUP: explore ASRs based on Objective Functions� Equality (e.g. ASRs with equal populations)

� Similarity (e.g. ASRs with similar population densities)

� Develop league tables based on key indicators

� Investigate how the internal migration indicators vary

for population sub-groups and over time

� We invite collaborations using the IMAGE Studio.