Given a set of ages and parameters, calculate the migration age schedule based on the Rogers and Castro formula. Choose between a 7,9,11 or 13 parameter model.
numeric. A vector of ages for migration rates to be calculated.
numeric. A named list of parameters. See below for details.
In the full 13 parameter model, the migration rate at age x, \(m(x)\) is defined as $$m(x) = a1*exp(-1*alpha1*x) + a2*exp(-1*alpha2*(x - mu2) - exp(-1*lambda2*(x - mu2))) + a3*exp(-1*alpha3*(x - mu3) - exp(-1*lambda3*(x - mu3))) + a4*exp(lambda4*x) + c$$
The first, second, third and fourth pieces of the equation represent pre-working age, working age, retirement and post-retirement age patterns, respectively. Models with less parameters gradually remove terms at the older ages. Parameters in each family are:
pre-working age: a1, alpha1
working age: a2, alpha2, mu2, lambda2
retirement: a3, alpha3, mu3, lambda3
post retirement: a4, lambda4
For a specific family to be included, values for all parameters in that family must be specified.
Rogers A, Castro LJ (1981). Model migration schedules. RR-81-030.