Estimates migrant transitions flows between two sequential migrant stock tables using approached based on rates.

ffs_rates(m1 = NULL, m2 = NULL, M = NULL, method = "dennett")

## Arguments

m1

Matrix of migrant stock totals at time t. Rows in the matrix correspond to place of birth and columns to place of residence at time t

m2

Matrix of migrant stock totals at time t+1. Rows in the matrix correspond to place of birth and columns to place of residence at time t+1.

M

Numeric value for the global sum of migration flows, used for dennett approach.

method

Method to estimate flows. Can take values dennett or rogers-von-rabenau. See details section for more information. Uses dennett as default.

## Value

Estimates migrant transitions flows based on migration rates.

When method = "dennett" migration are derived from the matrix supplied to m1. Dennett uses bilateral migrant stocks at beginning of period. Rates then multiplied by global migration flows supplied in M.

When method = "rogers-von-rabenau" a matrix of growth rates are derived from the changes in initial populations stock m1 to obtain m2; $$P^{t+1} = g P^{t}$$

and then multiplied by the corresponding populations at risk in m1. Can result in negative flows.

ffs_demo, ffs_rates

Guy J. Abel

## Examples

s1 <- matrix(data = c(100, 10, 10, 0, 20, 55, 25, 10, 10, 40, 140, 65, 20, 25, 20, 200),
nrow = 4, ncol = 4, byrow = TRUE)
s2 <- matrix(data = c(75, 25, 5, 15, 20, 45, 30, 15, 30, 40, 150, 35, 10, 50, 5, 200),
nrow = 4, ncol = 4, byrow = TRUE)
r <- LETTERS[1:4]
dimnames(s1) <- dimnames(s2) <- list(pob = r, por = r)
s1; s2
#>    por
#> pob   A  B   C   D
#>   A 100 10  10   0
#>   B  20 55  25  10
#>   C  10 40 140  65
#>   D  20 25  20 200
#>    por
#> pob  A  B   C   D
#>   A 75 25   5  15
#>   B 20 45  30  15
#>   C 30 40 150  35
#>   D 10 50   5 200

# calculate total migration flows for dennett approach
n <- colSums(s2) - colSums(s1)

ffs_rates(m1 = s1, M =  sum(abs(n)), method = "dennett" )
#>     dest
#> orig        A        B        C         D
#>    A 0.000000 2.352941 2.352941  0.000000
#>    B 4.705882 0.000000 5.882353  2.352941
#>    C 2.352941 9.411765 0.000000 15.294118
#>    D 4.705882 5.882353 4.705882  0.000000
ffs_rates(m1 = s1, m2 = s2, method = "rogers-von-rabenau" )
#>     dest
#> orig          A         B         C         D
#>    A   0.000000 26.584620 -10.22741  24.16653
#>    B   3.474032  0.000000  11.71799  20.12425
#>    C  34.097610 -0.125662   0.00000 -51.85130
#>    D -12.047899 38.857311 -24.36993   0.00000