migration.gini.out: 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

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

Run this code

# NOT RUN {
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
# }

Run the code above in your browser using DataCamp Workspace