migration.indices (version 0.3.1)

migration.gini.in: 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 \(2(n-2)\) 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

See Also

migration.gini migration.gini.out migration.weighted.gini.in

Examples

# NOT RUN {
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
# }