cm_net_tot: 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: $\log y_{i j} = \log α_{i} + \log α_{i}^{- 1} + \log m_{i j}$

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
)

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

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

Author

Guy J. Abel, Peter W. F. Smith

Examples

Run this code

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)