Fertility models for ASFR approximation

Usage

fert.approx(fx, age, model, start = NULL, se = F, alpha = 0.05, bn = 1000)

Arguments

fx: Numeric vector of age specific fertility rates.
age: Numeric vector of ages.
model: Character. Model name to be estimated. Now "Hadwiger", "Gamma", "Brass" and "Beta" are supported.
start: Numeric vector with user-specific values of parameters for optimization. Default is NULL (choose automatically)
se: Logical. Should bootstrapped variance for ASFR approximation be calculated. Default is FALSE for no bootstrap.
alpha: Numeric. Used if se = TRUE, the level of uncertainty. By default, alpha = 0.05 for 95% CI.
bn: Numeric. Used if se = TRUE, number of bootstrap samples. By default, bn = 1000.

Value

list with estimated model (parameters, variance-covariance matrix, percentiles of parameters) and dataframe with predicted and observed ASFR as well as SE and percentile of predictions

Details

This function runs least squares optimization of the selected fertility function with 1e-06 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", se = FALSE)