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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.