Package 'migration.indices' reference manual

Title:	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.
Authors:	Lajos Bálint <[email protected]> and Gergely Daróczi <[email protected]>
Maintainer:	Gergely Daróczi <[email protected]>
License:	AGPL-3
Version:	0.3.0
Built:	2025-01-23 02:37:59 UTC
Source:	https://github.com/daroczig/migration.indices

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)
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

Examples

data(migration.hyp)
migration.acv(migration.hyp)    # 0.3333333
migration.acv(migration.hyp2)   # 0.375
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)
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

Examples

data(migration.hyp)
migration.acv.in(migration.hyp)    # 0.3333333
migration.acv.in(migration.hyp2)   # 0.25
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)
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

Examples

data(migration.hyp)
migration.acv.out(migration.hyp)    # 0
migration.acv.out(migration.hyp2)   # 0.125
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)
migration.cmr(m, PAR, k = 100)

Arguments

`m`	migration matrix
`PAR`	population at risk (estimated average population size)
`k`	scaling constant (set to `100` by default to result in percentage)

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)
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)
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)
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)
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

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)
## 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)
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

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)
## 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)
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. http://hdr.undp.org/en/reports/global/hdr2009/papers/HDRP_2009_30.pdf

Examples

data(migration.hyp)
migration.effectiveness(migration.hyp)
data(migration.world)
migration.effectiveness(migration.world)
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")
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. http://privatewww.essex.ac.uk/~ksg/code/srm_enhanced_code_v5.R 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)
## 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)
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

Examples

data(migration.hyp)
migration.gini(migration.hyp)
migration.gini(migration.hyp2)
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)
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

Examples

data(migration.hyp)
migration.gini.col(migration.hyp)  # 0.05555556
migration.gini.col(migration.hyp2) # 0.04166667
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))
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

Examples

data(migration.hyp)
migration.gini.col.standardized(migration.hyp)     # 25
migration.gini.col.standardized(migration.hyp2)    # 22.22222
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)
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

Examples

data(migration.hyp)
migration.gini.exchange(migration.hyp)     # 0.05555556
migration.gini.exchange(migration.hyp2)    # 0.04166667
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))
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

Examples

data(migration.hyp)
migration.gini.exchange.standardized(migration.hyp)  # 25
migration.gini.exchange.standardized(migration.hyp2) # 22.22222
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)
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 $2(n-2)$ instead of $2(n-1)$ because "the number of comparisons should exclude the diagonal cell in each row and column, and the comparison of each cell with itself".

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

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
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)
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 $2(n-2)$ instead of $2(n-1)$ because "the number of comparisons should exclude the diagonal cell in each row and column, and the comparison of each cell with itself".

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

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
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)
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

Examples

data(migration.hyp)
migration.gini.row(migration.hyp)  # 0
migration.gini.row(migration.hyp2) # 0.02083333
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))
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

Examples

data(migration.hyp)
migration.gini.row.standardized(migration.hyp)     # 0
migration.gini.row.standardized(migration.hyp2)    # 11.11111
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)
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 $2{n(n-1)-1}$ instead of $2n(n-1)$ in the denominator to "ensure that the index can assume the upper limit of 1".

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

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
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"))
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)
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)
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. http://hdr.undp.org/en/reports/global/hdr2009/papers/HDRP_2009_30.pdf

Examples

data(migration.world)
migration.rate(migration.world, 6e+9)
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))
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

Examples

data(migration.hyp)
migration.weighted.gini.in(migration.hyp)   # 0.1222222
migration.weighted.gini.in(migration.hyp2)  # 0.05238095
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)
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

Examples

data(migration.hyp)
migration.weighted.gini.mean(migration.hyp)  # 0.06111111
migration.weighted.gini.mean(migration.hyp2) # 0.03660714
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))
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

Examples

data(migration.hyp)
migration.weighted.gini.out(migration.hyp)   # 0
migration.weighted.gini.out(migration.hyp2)  # 0.02083333
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. http://data.worldbank.org/data-catalog/global-bilateral-migration-database

Package 'migration.indices'

Help Index

Aggregated System-wide Coefficient of Variation

Description

Usage

Arguments

Value

References

See Also

Examples

Aggregated In-migration Coefficient of Variation

Description

Usage

Arguments

Value

References

See Also

Examples

Aggregated Out-migration Coefficient of Variation

Description

Usage

Arguments

Value

References

See Also

Examples

Crude Migration Rate

Description

Usage

Arguments

Value

References

Examples

Migration Connectivity Index

Description

Usage

Arguments

Value

References

Examples

In-migration Coefficient of Variation

Description

Usage

Arguments

Value

References

See Also

Examples

Out-migration Coefficient of Variation

Description

Usage

Arguments

Value

References

See Also

Examples

Migration Effectiveness Index

Description

Usage

Arguments

Value

References

Examples

Joint plot for in and out-migration fields

Description

Usage

Arguments

References

Examples

Spatial Gini Indexes

Description

Usage

Arguments

Value

References

See Also

Examples

Columns Gini Index

Description

Usage