Fertility models for ASFR approximation

Usage

fert.approx(fx, age, model, boot = F, start = NULL)

Arguments

fx: Numeric vector of age specific fertility rates.
age: Numeric vector of ages.
model: Character. Model name to be estimated. Now "Hadwiger" and "Gamma" are supported.
boot: Logical. Should bootstrapped 95% confidence intervals for ASFR approximation be calculated. Default is FALSE for no bootstrap.
start: Numeric vector with user-specific values of parameters for optimization. Default is NULL (choose automatically)

Value

list with estimated model (parameters, R-squred, variance-covariance matrix of parameters) and dataframe with predicted ASFR.

Details

This function runs least squares optimization of the selected fertility function using Port algorithm with 2000 maximum iterations and 1e-07 as tolerance parameter.

Hadwiger model

The model is as follows: $$f(age) = \frac{ab}{c} \frac{c}{age}^{3/2} exp[-b^2(\frac{c}{age}+\frac{age}{c}-2)]$$

Gamma model

The model is as follows: $$f(age) = \frac{R}{\Gamma(b)c^b}(age-d)^{b-1} exp[-(\frac{age-d}{c})]$$

Brass model

The model is as follows: $$f(age) = \frac{R}{\Gamma(b)c^b}(age-d)^{b-1} exp[-(\frac{age-d}{c})]$$

References

Peristera, P., & Kostaki, A. (2007). Modeling fertility in modern populations. Demographic Research, 16, 141-194.

Examples


# fert.approx(fx = ASFR, age = 15:55, model = "Hadwiger", boot = FALSE)