# 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{∑_{i \neq j} ∑_{k \neq j,i} | M_{ij} - M_{kj} | }{ 2(n-2) ∑_{i \neq j} M_{ij}}

These Gini indices facilitates the direct comparison of different territories without further standardization.

### Usage

 1  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

migration.gini migration.gini.out migration.weighted.gini.in
 1 2 3 4 5 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