Maintainer: | Gergely Daróczi <daroczig@rapporter.net> |
License: | AGPL-3 |
BugReports: | https://github.com/daroczig/migration.indices/issues |
Title: | Migration Indices |
LazyData: | no |
Type: | Package |
Author: | Lajos Bálint <balint@demografia.hu> and Gergely Daróczi <daroczig@rapporter.net> |
Description: | Calculate various indices, like Crude Migration Rate, different Gini indices or the Coefficient of Variation among others, to show the (un)equality of migration. |
Version: | 0.3.1 |
Imports: | calibrate |
URL: | https://github.com/daroczig/migration.indices |
Date: | 2022-06-13 |
Encoding: | UTF-8 |
RoxygenNote: | 7.1.1 |
NeedsCompilation: | no |
Packaged: | 2022-06-13 13:12:47 UTC; daroczig |
Repository: | CRAN |
Date/Publication: | 2022-06-13 15:10:09 UTC |
Check Migration Matrix
Description
Checks if provided R object looks like a migration matrix.
Usage
check.migration.matrix(m)
Arguments
m |
R object to check |
Details
A migration matrix is a symmetric matrix with the exact same row and column names. The diagonal equals to zero. The upper triangle shows the in- and the lower triangle shows the out-migration.
Value
(invisibly) TRUE
Aggregated System-wide Coefficient of Variation
Description
The Aggregated System-wide Coefficient of Variation is simply the sum of the Aggregated In-migration (migration.acv.in
) and the Aggregated Out-migration Coefficient of Variation (migration.acv.out
).
Usage
migration.acv(m)
Arguments
m |
migration matrix |
Value
A number where a higher (\neq 0
) shows more spatial focus.
References
Andrei Rogers and Stuart Sweeney (1998) Measuring the Spatial Focus of Migration Patterns. The Professional Geographer 50, 232–242
See Also
migration.cv.in
migration.cv.out
migration.acv.in
migration.acv.out
Examples
data(migration.hyp)
migration.acv(migration.hyp) # 0.3333333
migration.acv(migration.hyp2) # 0.375
Aggregated In-migration Coefficient of Variation
Description
The Aggregated In-migration Coefficient of Variation is the weighted average of the In-migration Coefficient of Variation (migration.cv.in
).
Usage
migration.acv.in(m)
Arguments
m |
migration matrix |
Value
A number where a higher (\neq 0
) shows more spatial focus.
References
Andrei Rogers and Stuart Sweeney (1998) Measuring the Spatial Focus of Migration Patterns. The Professional Geographer 50, 232–242
See Also
migration.cv.in
migration.cv.out
migration.acv.out
migration.acv
Examples
data(migration.hyp)
migration.acv.in(migration.hyp) # 0.3333333
migration.acv.in(migration.hyp2) # 0.25
Aggregated Out-migration Coefficient of Variation
Description
The Aggregated Out-migration Coefficient of Variation is the weighted average of the Out-migration Coefficient of Variation (migration.cv.out
).
Usage
migration.acv.out(m)
Arguments
m |
migration matrix |
Value
A number where a higher (\neq 0
) shows more spatial focus.
References
Andrei Rogers and Stuart Sweeney (1998) Measuring the Spatial Focus of Migration Patterns. The Professional Geographer 50, 232–242
See Also
migration.cv.in
migration.cv.out
migration.acv.in
migration.acv
Examples
data(migration.hyp)
migration.acv.out(migration.hyp) # 0
migration.acv.out(migration.hyp2) # 0.125
Crude Migration Rate
Description
Crude Migration Rate
Usage
migration.cmr(m, PAR, k = 100)
Arguments
m |
migration matrix |
PAR |
population at risk (estimated average population size) |
k |
scaling constant (set to |
Value
percentage (when k=100
)
References
Philip Rees, Martin Bell, Oliver Duke-Williams and Marcus Blake (2000) Problems and Solutions in the Measurement of Migration Intensities: Australia and Britain Compared. Population Studies 54, 207–222
Examples
data(migration.world)
migration.cmr(migration.world, 6e+9)
Migration Connectivity Index
Description
The Migration Connectivity Index measures "the proportion of the total number of potential interregional flows which are not zero":
I_{MC} = \sum_i \sum_{j \neq i} \frac{MC_{ij}}{n(n-1)}
where MC_{ij}
is 0 if the flow from i
to j
is zero and let it be 1 otherwise.
Usage
migration.connectivity(m)
Arguments
m |
migration matrix |
Value
A number between 0 and 1 where zero shows no connections between regions.
References
M. Bell, M. Blake, P. Boyle, O. Duke-Williams, P. Rees, J. Stillwell and G. Hugo (2002) Cross-National Comparison of Internal Migration. Issues and Measures. Journal of the Royal Statistical Society. Series A (Statistics in Society) 165, 435–464
Examples
data(migration.hyp)
migration.connectivity(migration.hyp)
data(migration.world)
migration.connectivity(migration.world)
In-migration Coefficient of Variation
Description
As "the coefficient of variation is defined as the standard deviation to mean ratio of a distribution", the In-migration Coefficient of Variation is computed by dividing the standard deviation (with the nominator being n
instead of n-1
) of the in-migration flows by the mean.
Usage
migration.cv.in(m)
Arguments
m |
migration matrix |
Value
A numeric vector of standardized values where a higher (\neq 0
) shows more spatial focus.
References
Andrei Rogers and Stuart Sweeney (1998) Measuring the Spatial Focus of Migration Patterns. The Professional Geographer 50, 232–242
See Also
migration.cv.out
migration.acv.in
migration.acv.out
migration.acv
Examples
## Not run:
data(migration.hyp)
migration.cv.in(migration.hyp) # 0.2000000 0.5000000 0.3333333
migration.cv.in(migration.hyp2) # 0.2000000 0.0000000 0.4285714
## End(Not run)
Out-migration Coefficient of Variation
Description
As "the coefficient of variation is defined as the standard deviation to mean ratio of a distribution", the Out-migration Coefficient of Variation is computed by dividing the standard deviation (with the nominator being n
instead of n-1
) of the out-migration flows by the mean.
Usage
migration.cv.out(m)
Arguments
m |
migration matrix |
Value
A numeric vector of standardized values where a higher (\neq 0
) shows more spatial focus.
References
Andrei Rogers and Stuart Sweeney (1998) Measuring the Spatial Focus of Migration Patterns. The Professional Geographer 50, 232–242
See Also
migration.cv.in
migration.acv.in
migration.acv.out
migration.acv
Examples
## Not run:
data(migration.hyp)
migration.cv.out(migration.hyp) # 0 0 0
migration.cv.out(migration.hyp2) # 0.00 0.25 0.00
## End(Not run)
Migration Effectiveness Index
Description
The Migration Effectiveness Index "measures the degree of (a)symmetry or (dis)equilibrium in the network of interregional migration flows":
MEI = 100\frac{ \sum_i |D_i - O_i| }{ \sum_i |D_i + O_i| }
where D_i
is the total inflows to zone i
and O_i
is the total outflows from zone i
.
Usage
migration.effectiveness(m)
Arguments
m |
migration matrix |
Value
A number between 0 and 100 where the higher number shows an efficient mechanism of population redistribution.
References
Martin Bell and Salut Muhidin (2009) Cross-National Comparisons of Internal Migration. Research Paper. UNDP. https://hdr.undp.org/content/cross-national-comparisons-internal-migration
Examples
data(migration.hyp)
migration.effectiveness(migration.hyp)
data(migration.world)
migration.effectiveness(migration.world)
Joint plot for in and out-migration fields
Description
This migration field diagram makes easy to visualize both direction of migration. E.g. points above the diagonal "are outward redistributors, while those below that line are inward redistributors."
Usage
migration.field.diagram(
m,
method = c("gini", "acv"),
title = "Migration field diagram",
xlab = "Out-migration",
ylab = "In-migration"
)
Arguments
m |
migration matrix |
method |
measurement of in and out-migration |
title |
plot title |
xlab |
label for x axis |
ylab |
label for y axis |
References
Source code was adopted from Michael Ward and Kristian Skrede Gleditsch (2008) Spatial Regression Models. Thousand Oaks, CA: Sage. with the permission of the authors.
Case study and use case: Andrei Rogers and Stuart Sweeney (1998) Measuring the Spatial Focus of Migration Patterns. The Professional Geographer 50, 232–242
Examples
## Not run:
data(migration.world)
par(mfrow = c(2, 1))
migration.field.diagram(migration.world)
migration.field.diagram(migration.world, method = 'acv')
## End(Not run)
Spatial Gini Indexes
Description
This is a wrapper function computing all the following Gini indices:
Total Flows Gini Index (
migration.gini.total
)Rows Gini Index (
migration.gini.row
)Standardized Rows Gini Index (
migration.gini.row.standardized
)Columns Gini Index (
migration.gini.col
)Standardized Columns Gini Index (
migration.gini.col.standardized
)Exchange Gini Index (
migration.gini.exchange
)Standardized Exchange Gini Index (
migration.gini.exchange.standardized
)Out-migration Field Gini Index (
migration.gini.out
)Migration-weighted Out-migration Gini Index (
migration.weighted.gini.out
)In-migration Field Gini Index (
migration.gini.in
)Migration-weighted In-migration Gini Index (
migration.weighted.gini.in
)Migration-weighted Mean Gini Index (
migration.weighted.gini.mean
)
Usage
migration.gini(m, corrected = TRUE)
Arguments
m |
migration matrix |
corrected |
to use Bell et al. (2002) updated formulas instead of Plane and Mulligan (1997) |
Value
List of all Gini indices.
References
David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. Demography 34, 251–262
M. Bell, M. Blake, P. Boyle, O. Duke-Williams, P. Rees, J. Stillwell and G. Hugo (2002) Cross-National Comparison of Internal Migration. Issues and Measures. Journal of the Royal Statistical Society. Series A (Statistics in Society) 165, 435–464
See Also
migration.gini.col
migration.gini.row
migration.gini.exchange
migration.gini.in
migration.gini.out
Examples
data(migration.hyp)
migration.gini(migration.hyp)
migration.gini(migration.hyp2)
Columns Gini Index
Description
The Columns Gini index concentrates on the "relative extent to which the destination selections of in-migrations are spatially focused":
G^T_R = \frac{\sum_j \sum_{i \neq j} \sum_{g \neq i,j} | M_{ij} - M_{gj} | }{ (2n(n-1)-1) \sum_i \sum_{j \neq i} M_{ij}}
This implementation solves the above formula by computing the dist
matrix for each columns.
Usage
migration.gini.col(m)
Arguments
m |
migration matrix |
Value
A number between 0 and 1 where 0 means no spatial focusing and 1 shows maximum focusing.
References
David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. Demography 34, 251–262
See Also
migration.gini.row
migration.gini.col.standardized
Examples
data(migration.hyp)
migration.gini.col(migration.hyp) # 0.05555556
migration.gini.col(migration.hyp2) # 0.04166667
Standardized Columns Gini Index
Description
The standardized version of the Columns Gini Index (migration.gini.col
) by dividing that with the Total Flows Gini Index (migration.gini.total
):
G^{T*}_C = 100\frac{G^T_C}{G^T}
As this index is standardized, it "facilitate comparisons from one period to the next" of the columns indices.
Usage
migration.gini.col.standardized(m, gini.total = migration.gini.total(m, FALSE))
Arguments
m |
migration matrix |
gini.total |
optionally pass the pre-computed Total Flows Gini Index to save computational resources |
Value
A percentage range from 0% to 100% where 0% means that the migration flows are uniform, while a higher value indicates spatial focusing.
References
David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. Demography 34, 251–262
See Also
migration.gini.col
migration.gini.row.standardized
Examples
data(migration.hyp)
migration.gini.col.standardized(migration.hyp) # 25
migration.gini.col.standardized(migration.hyp2) # 22.22222
Exchange Gini Index
Description
The Exchange Gini Index "indicates the contribution to spatial focusing represented by the n(n-q)
net interchanges in the system":
G^T_{RC, CR} = \frac{\sum_i \sum_{j \neq i} | M_{ij} - M_{ji} | }{ (2n(n-1)-1) \sum_i \sum_{j \neq i} M_{ij}}
This implementation solves the above formula by simply substracting the transposed matrix's values from the original one at one go.
Usage
migration.gini.exchange(m)
Arguments
m |
migration matrix |
Value
A number between 0 and 1 where 0 means no spatial focusing and 1 shows maximum focusing.
References
David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. Demography 34, 251–262
See Also
migration.gini
migration.gini.exchange.standardized
Examples
data(migration.hyp)
migration.gini.exchange(migration.hyp) # 0.05555556
migration.gini.exchange(migration.hyp2) # 0.04166667
Standardized Exchange Gini Index
Description
The standardized version of the Exchange Gini Index (migration.gini.exchange
) by dividing that with the Total Flows Gini Index (migration.gini.total
):
G^{T*}_{RC, CR} = 100\frac{G^T_{RC, CR}}{G^T}
As this index is standardized, it "facilitate comparisons from one period to the next" of the exchange indices.
Usage
migration.gini.exchange.standardized(
m,
gini.total = migration.gini.total(m, FALSE)
)
Arguments
m |
migration matrix |
gini.total |
optionally pass the pre-computed Total Flows Gini Index to save resources |
Value
A percentage range from 0% to 100% where 0% means that the migration flows are uniform, while a higher value indicates spatial focusing.
References
David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. Demography 34, 251–262
See Also
migration.gini
migration.gini.exchange
Examples
data(migration.hyp)
migration.gini.exchange.standardized(migration.hyp) # 25
migration.gini.exchange.standardized(migration.hyp2) # 22.22222
In-migration Field Gini Index
Description
The In-migration Field Gini Index is a decomposed version of the Columns Gini Index (migration.gini.col
) representing "the contribution of each region's columns to the total index" () (migration.gini.total
):
G^I_j = \frac{\sum_{i \neq j} \sum_{k \neq j,i} | M_{ij} - M_{kj} | }{ 2(n-2) \sum_{i \neq j} M_{ij}}
These Gini indices facilitates the direct comparison of different territories without further standardization.
Usage
migration.gini.in(m, corrected = TRUE)
Arguments
m |
migration matrix |
corrected |
Bell et al. (2002) updated the formula of Plane and Mulligan (1997) to be |
Value
A numeric vector with the range of 0 to 1 where 0 means no spatial focusing and 1 shows maximum focusing.
References
David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. Demography 34, 251–262
M. Bell, M. Blake, P. Boyle, O. Duke-Williams, P. Rees, J. Stillwell and G. Hugo (2002) Cross-National Comparison of Internal Migration. Issues and Measures. Journal of the Royal Statistical Society. Series A (Statistics in Society) 165, 435–464
See Also
migration.gini
migration.gini.out
migration.weighted.gini.in
Examples
data(migration.hyp)
migration.gini.in(migration.hyp) # 0.2000000 0.5000000 0.3333333
migration.gini.in(migration.hyp2) # 0.2000000 0.0000000 0.4285714
migration.gini.in(migration.hyp, FALSE) # 0.1000000 0.2500000 0.1666667
migration.gini.in(migration.hyp2, FALSE) # 0.1000000 0.0000000 0.2142857
Out-migration Field Gini Index
Description
The Out-migration Field Gini Index is a decomposed version of the Rows Gini Index (migration.gini.row
) representing "the contribution of each region's row to the total index" () (migration.gini.total
):
G^O_i = \frac{\sum_{j \neq i} \sum_{l \neq i,j} | M_{ij} - M_{il} | }{ 2(n-2) \sum_{j \neq k} M_{ij}}
These Gini indices facilitates the direct comparison of different territories without further standardization.
Usage
migration.gini.out(m, corrected = TRUE)
Arguments
m |
migration matrix |
corrected |
Bell et al. (2002) updated the formula of Plane and Mulligan (1997) to be |
Value
A numeric vector with the range of 0 to 1 where 0 means no spatial focusing and 1 shows maximum focusing.
References
David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. Demography 34, 251–262
M. Bell, M. Blake, P. Boyle, O. Duke-Williams, P. Rees, J. Stillwell and G. Hugo (2002) Cross-National Comparison of Internal Migration. Issues and Measures. Journal of the Royal Statistical Society. Series A (Statistics in Society) 165, 435–464
See Also
migration.gini
migration.gini.in
migration.weighted.gini.out
Examples
data(migration.hyp)
migration.gini.out(migration.hyp) # 0 0 0
migration.gini.out(migration.hyp2) # 0.000 0.25 0.000
migration.gini.out(migration.hyp, FALSE) # 0 0 0
migration.gini.out(migration.hyp2, FALSE) # 0.000 0.125 0.000
Rows Gini Index
Description
The Rows Gini index concentrates on the "relative extent to which the destination selections of out-migrations are spatially focused":
G^T_R = \frac{\sum_i \sum_{j \neq i} \sum_{h \neq i,j} | M_{ij} - M_{ih} | }{ (2n(n-1)-1) \sum_i \sum_{j \neq i} M_{ij}}
This implementation solves the above formula by computing the dist
matrix for each row.
Usage
migration.gini.row(m)
Arguments
m |
migration matrix |
Value
A number between 0 and 1 where 0 means no spatial focusing and 1 shows maximum focusing.
References
David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. Demography 34, 251–262
See Also
migration.gini.col
migration.gini.row.standardized
Examples
data(migration.hyp)
migration.gini.row(migration.hyp) # 0
migration.gini.row(migration.hyp2) # 0.02083333
Standardized Rows Gini Index
Description
The standardized version of the Rows Gini Index (migration.gini.row
) by dividing that with the Total Flows Gini Index (migration.gini.total
):
G^{T*}_R = 100\frac{G^T_R}{G^T}
As this index is standardized, it "facilitate comparisons from one period to the next of the rows" indices.
Usage
migration.gini.row.standardized(m, gini.total = migration.gini.total(m, FALSE))
Arguments
m |
migration matrix |
gini.total |
optionally pass the pre-computed Total Flows Gini Index to save computational resources |
Value
A percentage range from 0% to 100% where 0% means that the migration flows are uniform, while a higher value indicates spatial focusing.
References
David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. Demography 34, 251–262
See Also
migration.gini.row
migration.gini.col.standardized
Examples
data(migration.hyp)
migration.gini.row.standardized(migration.hyp) # 0
migration.gini.row.standardized(migration.hyp2) # 11.11111
Total Flows Gini Index
Description
The Total Gini Index shows the overall concentration of migration with a simple number computed by comparing each cell of the migration matrix with every other cell except for the diagonal:
G^T = \frac{\sum_i \sum_{j \neq i} \sum_k \sum_{l \neq k} | M_{ij} - M_{kl} | }{ (2n(n-1)-1) \sum_i \sum_{j \neq i} M_{ij}}
This implementation solves the above formula by a simple loop for performance issues to compare all values to the others at one go, although smaller migration matrices could also be addressed by a much faster dist
method. Please see the sources for more details.
Usage
migration.gini.total(m, corrected = TRUE)
Arguments
m |
migration matrix |
corrected |
Bell et al. (2002) updated the formula of Plane and Mulligan (1997) to have |
Value
A number between 0 and 1 where 0 means no spatial focusing and 1 shows that all migrants are found in one single flow.
References
David A. Plane and Gordon F. Mulligan (1997) Measuring Spatial Focusing in a Migration System. Demography 34, 251–262
M. Bell, M. Blake, P. Boyle, O. Duke-Williams, P. Rees, J. Stillwell and G. Hugo (2002) Cross-National Comparison of Internal Migration. Issues and Measures. Journal of the Royal Statistical Society. Series A (Statistics in Society) 165, 435–464
See Also
migration.gini.col
migration.gini.row
migration.gini.exchange
migration.gini.in
migration.gini.out
Examples
data(migration.hyp)
migration.gini.total(migration.hyp) # 0.2666667
migration.gini.total(migration.hyp2) # 0.225
migration.gini.total(migration.hyp, FALSE) # 0.2222222
migration.gini.total(migration.hyp2, FALSE) # 0.1875
Hypotetical Migration Matrix
Description
A small (3x3) hypotetical migration matrix.
Format
migration matrix
References
David A. Plane and Gordon F. Mulligan (1997): Measuring Spatial Focusing in a Migration System. Demography 34, pp. 253
Andrei Rogers and Stuart Sweeney (1998) Measuring the Spatial Focus of Migration Patterns. The Professional Geographer 50, 232–242
Migration indices
Description
This package provides various indices, like Crude Migration Rate, different Gini indices or the Coefficient of Variation among others, to show the (un)equality of migration.
Migration Inequality Index
Description
Measures the distance from an expected distribution:
I_{MI} = \frac{ \sum_i \sum_{j \neq i} | M_{ij} - M_{ij}' | }{2}
Usage
migration.inequality(m, expected = c("equal", "weighted"))
Arguments
m |
migration matrix |
expected |
type of expected distribution |
Value
A number between 0 and 1 where 1 shows greater inequality.
References
M. Bell, M. Blake, P. Boyle, O. Duke-Williams, P. Rees, J. Stillwell and G. Hugo (2002) Cross-National Comparison of Internal Migration. Issues and Measures. Journal of the Royal Statistical Society. Series A (Statistics in Society) 165, 435–464
Examples
data(migration.hyp)
migration.inequality(migration.hyp)
migration.inequality(migration.hyp, expected = 'weighted')
data(migration.world)
migration.inequality(migration.world)
Aggregate net migration rate
Description
ANMR = 100\frac{ \sum_i |D_i - O_i| }{ \sum_i P_i }
where D_i
is the total inflows to zone i
and O_i
is the total outflows from zone i
.
Usage
migration.rate(m, PAR)
Arguments
m |
migration matrix |
PAR |
population at risk |
References
Martin Bell and Salut Muhidin (2009) Cross-National Comparisons of Internal Migration. Research Paper. UNDP. https://hdr.undp.org/content/cross-national-comparisons-internal-migration
Examples
data(migration.world)
migration.rate(migration.world, 6e+9)
Migration-weighted In-migration Gini Index
Description
The Migration-weighted In-migration Gini Index is a weighted version of the In-migration Field Gini Index (migration.gini.in
) "according to the zone of destination's share of total migration and the mean of the weighted values is computed as":
MWG^I = \frac{ \sum_j G^I_j \frac{\sum_j M_{ij}}{\sum_{ij} M_{ij}}}{n}
Usage
migration.weighted.gini.in(m, mgi = migration.gini.in(m))
Arguments
m |
migration matrix |
mgi |
optionally passed (precomputed) Migration In-migration Gini Index |
References
M. Bell, M. Blake, P. Boyle, O. Duke-Williams, P. Rees, J. Stillwell and G. Hugo (2002) Cross-National Comparison of Internal Migration. Issues and Measures. Journal of the Royal Statistical Society. Series A (Statistics in Society) 165, 435–464
See Also
migration.gini
migration.gini.in
migration.weighted.gini.out
migration.weighted.gini.mean
Examples
data(migration.hyp)
migration.weighted.gini.in(migration.hyp) # 0.1222222
migration.weighted.gini.in(migration.hyp2) # 0.05238095
Migration-weighted Mean Gini Index
Description
The Migration-weighted Mean Gini Index is simply the average of the Migration-weighted In-migration (migration.weighted.gini.in
) and the Migration-weighted Out-migration (migration.weighted.gini.out
) Gini Indices:
MWG^A = \frac{MWG^O + MWG^I}{2}
Usage
migration.weighted.gini.mean(m, mwgi, mwgo)
Arguments
m |
migration matrix |
mwgi |
optionally passed (precomputed) Migration-weighted In-migration Gini Index |
mwgo |
optionally passed (precomputed) Migration-weighted Out-migration Gini Index |
Value
This combined index results in a number between 0 and 1 where 0 means no spatial focusing and 1 shows maximum focusing.
References
M. Bell, M. Blake, P. Boyle, O. Duke-Williams, P. Rees, J. Stillwell and G. Hugo (2002) Cross-National Comparison of Internal Migration. Issues and Measures. Journal of the Royal Statistical Society. Series A (Statistics in Society) 165, 435–464
See Also
migration.weighted.gini.in
migration.weighted.gini.out
Examples
data(migration.hyp)
migration.weighted.gini.mean(migration.hyp) # 0.06111111
migration.weighted.gini.mean(migration.hyp2) # 0.03660714
Migration-weighted Out-migration Gini Index
Description
The Migration-weighted Out-migration Gini Index is a weighted version of the Out-migration Field Gini Index (migration.gini.out
) "according to the zone of destination's share of total migration and the mean of the weighted values is computed as":
MWG^O = \frac{ \sum_i G^O_i \frac{\sum_j M_{ij}}{\sum_{ij} M_{ij}}}{n}
Usage
migration.weighted.gini.out(m, mgo = migration.gini.out(m))
Arguments
m |
migration matrix |
mgo |
optionally passed (precomputed) Migration In-migration Gini Index |
References
M. Bell, M. Blake, P. Boyle, O. Duke-Williams, P. Rees, J. Stillwell and G. Hugo (2002) Cross-National Comparison of Internal Migration. Issues and Measures. Journal of the Royal Statistical Society. Series A (Statistics in Society) 165, 435–464
See Also
migration.weighted.gini.in
migration.weighted.gini.mean
migration.gini
migration.gini.out
migration.weighted.gini.in
migration.weighted.gini.mean
Examples
data(migration.hyp)
migration.weighted.gini.out(migration.hyp) # 0
migration.weighted.gini.out(migration.hyp2) # 0.02083333
Global Bilateral Migration Database (2000)
Description
Global (country-to-country) matrix of bilateral migrant stocks in 2000 with 226 economies involved.
Format
migration matrix
References
World Bank (2010): Global Bilateral Migration Database.