migration.gini.total {migration.indices}

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 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

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