Hadwiger: Hadwiger's model fertility and its fitting

Description

Implementing Hadwiger's model of age-specific fertility rates and fitting the model to actual ASFR.

Usage

Hadwiger(a=3.4, b=2.5, c=22.2)
 fitHad(initialpar=c(3.4, 2.5, 22.2), data, Method="Nelder-Mead", ...)

Arguments

The parameter a of the Hadwiger model, ASFR(x) = a*b/c*(c/x)^1.5*exp(-b^2*(c/x+x/c-2)) for age x from 15 to 54.

The parameter b of the Hadwiger model, ASFR(x) = a*b/c*(c/x)^1.5*exp(-b^2*(c/x+x/c-2)) for age x from 15 to 54.

The parameter c of the Hadwiger model, ASFR(x) = a*b/c*(c/x)^1.5*exp(-b^2*(c/x+x/c-2)) for age x from 15 to 54.

initialpar

Initial value for the parameters to be estimated. If not given, c(3.4, 2.5, 22.2) is used.

data

Actual vector of ASFR (which must be given for from ages from 15 to 54 for each age) to be used to obtain the best-fit parameters of the Hadwiger's model.

Method

The method to be used in optim() function. Default is "Nelder-Mead".

...

Other options to be passed to optim().

Value

Hadwiger() returns model ASFR for ages from 15 to 54. fitHad() returns the numeric vector of fitted parameters a, b and c, RMSE for those values, and the flag of convergence.

References

Chandola T, Coleman DA, Horns RW (1999) Recent European fertility patterns: fitting curves to 'distorted' distributions. Population Studies, 53(3): 317-329.

http://www.jstor.org/stable/2584702

Examples

Run this code

# NOT RUN {
 res <- fitHad(,Jfert$ASFR2000)
 FLAG <- res[5]
 while (FLAG>0) {
   res <- fitHad(res[1:3], Jfert$ASFR2000)
   FLAG <- res[5]
 }
 print(res)
# }