# ipf3: Iterative Proportional Fitting Routine for the Indirect... In migest: Methods for the Indirect Estimation of Bilateral Migration

## Description

The `ipf3` function finds the maximum likelihood estimates for fitted values in the log-linear model:

\log y_{ijk} = \log α_{i} + \log β_{j} + \log λ_{k} + \log γ_{ik} + \log κ_{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

 `1` ```ipf3(rtot = NULL, ctot = NULL, m = NULL, tol = 1e-05, maxit = 500, verbose = 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. `verbose` Print the parameter estimates at each iteration. By default `FALSE`.

## 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.

## 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

Guy J. Abel

## 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.

`ipf3.qi`, `ipf2`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24``` ```## 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) ```