Iterative proportional fitting routine for the indirect estimation of origin-destination-type migration flow tables with known origin and destination margins and block diagonal elements.
Source:R/ipf2_block.R
ipf2_block.RdThe ipf2.b function finds the maximum likelihood estimates for fitted values in the log-linear model:
$$ \log y_{pq} = \log \alpha_{p} + \log \beta_{q} + \log \lambda_{ij}I(p \in i, q \in j) + \log m_{pq} $$
where \(m_{pq}\) is a prior estimate for \(y_{pq}\) and is no more complex than the matrices being fitted. The \(\lambda_{ij}I(p \in i, q \in j)\) term ensures a saturated fit on the block the \((i,j)\) block.
Usage
ipf2_block(
row_tot = NULL,
col_tot = NULL,
block_tot = NULL,
block = NULL,
m = NULL,
tol = 1e-05,
maxit = 500,
verbose = TRUE,
...
)Arguments
- row_tot
Vector of origin totals to constrain the sum of the imputed cell rows.
- col_tot
Vector of destination totals to constrain the sum of the imputed cell columns.
- block_tot
Matrix of block totals to constrain the sum of the imputed cell blocks.
- block
Matrix of block structure corresponding to
block_tot.- m
Matrix of auxiliary data. By default set to 1 for all origin-destination combinations.
- tol
Numeric value for the tolerance level used in the parameter estimation.
- maxit
Numeric value for the maximum number of iterations used in the parameter estimation.
- verbose
Logical value to indicate the print the parameter estimates at each iteration. By default
FALSE.- ...
Additional arguments passes to
block_matrix.
Value
Iterative Proportional Fitting routine set up using the partial likelihood derivatives. The arguments row_tot and col_tot take the row-table and column-table specific known margins. The block_tot take the totals over the blocks in the matrix defined with b. Diagonal values can be added by the user, but care must be taken to ensure resulting diagonals are feasible given the set of margins.
The user must ensure that the row and column totals in each table sum to the same value. Care must also be taken to allow the dimension of the auxiliary matrix (m) equal those provided in the row and column totals.
Returns a list object with
- mu
Array of indirect estimates of origin-destination matrices by migrant characteristic
- it
Iteration count
- tol
Tolerance level at final iteration
Examples
y <- ipf2_block(row_tot= c(30,20,30,10,20,5,0,10,5,5,5,10),
col_tot = c(45,10,10,5,5,10,50,5,10,0,0,0),
block_tot = matrix(data = c(0,0 ,50,0, 35,0,25,0, 10,10,0,0, 10,10,0,0),
nrow = 4, byrow = TRUE),
block = block_matrix(x = 1:16, b = c(2,3,4,3)))
#> 1 38
#> 2 3.552714e-15
addmargins(y$mu)
#> A1 A2 B1 B2 B3 C1 C2 C3
#> A1 0.000000 0.0000000 0.00 0.000 0.000 4.0000000 20.000000 2.0000000
#> A2 0.000000 0.0000000 0.00 0.000 0.000 2.6666667 13.333333 1.3333333
#> B1 14.318182 3.1818182 0.00 0.000 0.000 1.6666667 8.333333 0.8333333
#> B2 4.772727 1.0606061 0.00 0.000 0.000 0.5555556 2.777778 0.2777778
#> B3 9.545455 2.1212121 0.00 0.000 0.000 1.1111111 5.555556 0.5555556
#> C1 2.045455 0.4545455 1.25 0.625 0.625 0.0000000 0.000000 0.0000000
#> C2 0.000000 0.0000000 0.00 0.000 0.000 0.0000000 0.000000 0.0000000
#> C3 4.090909 0.9090909 2.50 1.250 1.250 0.0000000 0.000000 0.0000000
#> C4 2.045455 0.4545455 1.25 0.625 0.625 0.0000000 0.000000 0.0000000
#> D1 2.045455 0.4545455 1.25 0.625 0.625 0.0000000 0.000000 0.0000000
#> D2 2.045455 0.4545455 1.25 0.625 0.625 0.0000000 0.000000 0.0000000
#> D3 4.090909 0.9090909 2.50 1.250 1.250 0.0000000 0.000000 0.0000000
#> Sum 45.000000 10.0000000 10.00 5.000 5.000 10.0000000 50.000000 5.0000000
#> C4 D1 D2 D3 Sum
#> A1 4.0000000 0 0 0 30
#> A2 2.6666667 0 0 0 20
#> B1 1.6666667 0 0 0 30
#> B2 0.5555556 0 0 0 10
#> B3 1.1111111 0 0 0 20
#> C1 0.0000000 0 0 0 5
#> C2 0.0000000 0 0 0 0
#> C3 0.0000000 0 0 0 10
#> C4 0.0000000 0 0 0 5
#> D1 0.0000000 0 0 0 5
#> D2 0.0000000 0 0 0 5
#> D3 0.0000000 0 0 0 10
#> Sum 10.0000000 0 0 0 150