migest (version 1.3)

ipf3: Iterative Proportional Fitting Routine for the Indirect Estimation of Origin-Destination-Migrant Type Migration Flow Tables with Known Origin and Destination Margins.

Description

The ipf3 function finds the maximum likelihood estimates for fitted values in the log-linear model: $$\log y_{ijk} = \log \alpha_{i} + \log \beta_{j} + \log \lambda_{k} + \log \gamma_{ik} + \log \kappa_{jk} + \log m_{ijk}$$ where $m_{ijk}$ is a set of prior estimates for $y_{ijk}$ and is no more complex than the matrices being fitted.

Usage

ipf3(rtot = NULL, ctot = NULL, m = NULL, tol = 1e-05, maxit = 500, iter = TRUE)

Arguments

rtot

Matrix of origin totals (by migrant characteristic) to constrain indirect estimates to. Row of matrix corresponds to origin and column of table corresponds to migrant type/characteristic.

ctot

Matrix of destination totals (by migrant characteristic) to constrain indirect estimates to. Row of matrix corresponds to destination and column of table corresponds to migrant type/characteristic.

m

Array of auxiliary data. By default set to 1 for all origin-destination-migrant type combinations.

tol

Tolerance level for parameter estimation.

maxit

Maximum number of iterations for parameter estimation.

iter

Print the parameter estimates at each iteration. By default FALSE.

Value

• 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

Details

Iterative Proportional Fitting routine set up in a similar manner to Agresti (2002, p.343). The arguments rtot and ctot take the row-table and column-table specific known 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) to equal those provided in the row and column totals.

References

Abel, G. J. (2013). Estimating Global Migration Flow Tables Using Place of Birth. Demographic Research 28, (18) 505-546 Agresti, A. (2002). Categorical Data Analysis 2nd edition. Wiley.

See Also

ipf3.qi, ipf2

Examples

## create row-table and column-table specific known margins.
dn <- LETTERS[1:4]
P1 <- matrix(c(1000, 100, 10, 0, 55, 555, 50, 5, 80, 40, 800, 40, 20, 25, 20, 200), 4, 4, 
        dimnames = list(pob = dn, por = dn), byrow = TRUE)
P2 <- matrix(c(950, 100, 60, 0, 80, 505, 75, 5, 90, 30, 800, 40, 40, 45, 0, 180), 4, 4, 
        dimnames = list(pob = dn, por = dn), byrow = TRUE)
# display with row and col totals
addmargins(P1)
addmargins(P2)

# run ipf
y <- ipf3(rtot = t(P1), ctot = P2)
# display with row, col and table totals
round(addmargins(y$mu), 1)
# origin-destination flow table
round(fm(y$mu), 1)

## with alternative offset term
dis <- array(c(1, 2, 3, 4, 2, 1, 5, 6, 3, 4, 1, 7, 4, 6, 7, 1), c(4, 4, 4))
y <- ipf3(rtot = t(P1), ctot = P2, m = dis)
# display with row, col and table totals
round(addmargins(y$mu), 1)
# origin-destination flow table
round(fm(y$mu), 1)