cm_net_tot {migest}

Conditional maximization routine for the indirect estimation of origin-destination-type migration flow tables with known net migration and grand totals.

Description

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

\log y_{ij} = \log \alpha_{i} + \log \alpha_{i}^{-1} + \log m_{ij}

Usage

cm_net_tot(
  net_tot = NULL,
  tot = NULL,
  m = NULL,
  tol = 1e-06,
  maxit = 500,
  verbose = TRUE,
  alpha0 = rep(1, length(net_tot)),
  lambda0 = 1,
  alpha_constrained = TRUE
)

Arguments

net_tot

Vector of net migration totals to constrain the sum of the imputed cell row and columns. Elements must sum to zero.

tot

Numeric value of grand total to constrain sum of all imputed cells.

m

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

alpha0

Vector of initial estimates for alpha

lambda0

Numeric value of initial estimates for lambda

alpha_constrained

Logical value to indicate if the first alpha should be constrain to unity. By default TRUE

Value

Conditional maximisation routine set up using the partial likelihood derivatives. The argument net_tot takes the known net migration totals. The user must ensure that the net migration totals sum globally to zero.

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

Author(s)

Guy J. Abel, Peter W. F. Smith

Examples

m <- matrix(data = 1:16, nrow = 4)
# m[lower.tri(m)] <- t(m)[lower.tri(m)]
addmargins(m)
sum_net(m)

y <- cm_net_tot(net_tot = c(30, 40, -15, -55), tot = 200, m = m)
addmargins(y$n)
sum_net(y$n)

m <- matrix(data = c(0, 100, 30, 70, 50, 0, 45, 5, 60, 35, 0, 40, 20, 25, 20, 0),
            nrow = 4, ncol = 4, byrow = TRUE,
            dimnames = list(orig = LETTERS[1:4], dest = LETTERS[1:4]))
addmargins(m)
sum_net(m)

y <- cm_net_tot(net_tot = c(-100, 125, -75, 50), tot = 600, m = m)
addmargins(y$n)
sum_net(y$n)