rc9: Rogers-Castro Nine Parameter Migration Schedule.
In gjabel/agesched: Demographic Age Schedules

Description Usage Arguments Value Author(s) References See Also Examples

Provides a scaled nine parameter Rogers-Castro schedule,

m(x) = a_{1} \exp[-α_{1}x] + a_{2} \exp [ α_{2}(x-μ_{2})- \exp [ λ_{2}(x-μ_{2}) ] ] + a_{4} \exp[λ_{4}x] + c

for a given set of parameter values and sequence of ages.

1
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3

rc9(tot_mig = 1, x = seq(from = 0, to = 100, by = 1), a1 = 0.02,
  alpha1 = 0.1, a2 = 0.06, mu2 = 20, alpha2 = 0.1, lambda2 = 0.4,
  a4 = 0, lambda4 = 0, c = 0.03, scaled = TRUE)

`tot_mig`	Total migration of the returned age schedule.
`x`	Vector for the sequence of ages.
`a1`	Numeric value for height pre-labour force curve.
`alpha1`	Numeric value for descent of pre-labour force curve.
`a2`	Numeric value for height of labour force curve.
`mu2`	Numeric value for peak location of labour force curve.
`alpha2`	Numeric value for descent of labour force curve.
`lambda2`	Numeric value for ascent of labour force curve.
`a4`	Numeric value for height of post-retirement curve.
`lambda4`	Numeric value for ascent of post-retirement curve.
`c`	Numeric value for basic height of all migration curves.
`scaled`	Boolean value to return age specific migration that scale to sum to `tot_mig` or not. Default `TRUE`.

Returns the m(x) values from the Rogers-Castro schedule of age specific migration. The age range for the calculation can take any sequence of positive numbers, such as ages in single or 5-year intervals. The function is primarily intended for use in decomposing an aggregate migration total or rate into an age-specific values. Set scaled = FALSE if you wish to simply generate an migration age schedule that is not scaled to the aggregate level given by tot_mig.

The parameters relate to the heights (a1, a2, a4, c), locations (mu2) and slopes (alpha1, alpha2, lambda2, lambda4).

The default values of the parameters match the fundamental parameters of a simplified basic standard schedule migration schedule given in Rogers and Castro (1981). See examples below for non-zero parameters for the post-retirement slope.

Guy J. Abel

Rogers, A. and Castro. L. J. (1981). Model Migration Schedules. IIASA Research Report 81 RR-81-30

Rogers, A., Little, J. and Raymer J. (2010). The Indirect Estimation of Migration. Springer Series on Demographic Methods and Population Analysis 26

rc7, rc11, rc13

#single year
f0 <- rc9(tot_mig = 100, x = seq(0, 100, 1),
          a1 = 0.02, alpha1 = 0.1,
          a2 = 0.06, mu2 = 20, alpha2 = 0.1, lambda2 = 0.4,
          a4 = 0.005, lambda4 = 0.005,
          c = 0.03)
plot(f0, type = "l")

#five year
f1 <- rc9(tot_mig = 0.05, x = seq(0, 100, 5),
          a1 = 0.02, alpha1 = 0.1,
          a2 = 0.06, mu2 = 25, alpha2 = 0.1, lambda2 = 0.4,
          a4 = 0.01, lambda4 = 0.005,
          c = 0.05)
plot(f1, type = "l")
sum(f1)