rc13: Rogers-Castro Thirteen Parameter Migration Schedule.

In gjabel/agesched: Demographic Age Schedules

Description

Provides a scaled thirteen 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_{3} \exp [ α_{3}(x-μ_{3})- \exp [ λ_{3}(x-μ_{3}) ] ] + a_{4} \exp[λ_{4}x] + c

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

Usage

rc13(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,
  a3 = 0, alpha3 = 0, mu3 = 0, lambda3 = 0, a4 = 0, lambda4 = 0,
  c = 0.03, scaled = TRUE)

Arguments

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.
a3	Numeric value for height of post-labour force curve.
alpha3	Numeric value for descent of post-labour force curve.
mu3	Numeric value for peak location of post-labour force curve.
lambda3	Numeric value for ascent of post-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.

Value

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, a3, a4, c), locations (mu2, mu3) and slopes (alpha1, alpha2, lambda2, alpha3, lambda3, 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-labour force and post-retirement slopes.

Author(s)

Guy J. Abel

References

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

Rogers, A. (1982). Parametrized Multistate Population Dynamics. IIASA Working Paper WP-82-125

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

See Also

rogerscastro7, rogerscastro9, rogerscastro11

Examples

#single year
f0 <- rc13(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,
           a3 = 0.01, alpha3 = 0.1, mu3 = 70, lambda3 = 0.1,
           a4 = 0.005, lambda4 = 0.005,
           c = 0.03)
plot(f0, type = "l")

#five year
f1 <- rc13(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,
           a3 = 0.01, alpha3 = 0.2, mu3 = 75, lambda3 = 0.1,
           a4 = 0.01, lambda4 = 0.005,
           c = 0.05)
plot(f1, type = "l")
sum(f1)

gjabel/agesched documentation built on May 17, 2019, 6:01 a.m.