model_fertility {mpmsim}

Model fertility with age using set functional forms

Description

This function computes fertility based on the logistic, step, von Bertalanffy, Hadwiger, and normal models. The logistic model assumes that fertility increases sigmoidally with age from maturity until a maximum fertility is reached. The step model assumes that fertility is zero before the age of maturity and then remains constant. The von Bertalanffy model assumes that, after maturity, fertility increases asymptotically with age until a maximum fertility is reached. In this formulation, the model is set up so that fertility is 0 at the 'age of maturity - 1', and increases from that point. The Hadwiger model is rather complex and is intended to model human fertility with a characteristic hump-shaped fertility. For all models, the output ensures that fertility is zero before the age at maturity.

Usage

model_fertility(params, age = NULL, maturity = 0, model = "logistic")

Arguments

params

A numeric vector of parameters for the selected model. The number and meaning of parameters depend on the selected model.

age

A numeric vector representing age.

maturity

A non-negative numeric value indicating the age at maturity. Whatever model is used, the fertility is forced to be 0 below the age of maturity.

model

A character string specifying the model to use. Must be one of "logistic", "step", "vonbertalanffy","normal" or "hadwiger".

Details

The required parameters varies depending on the fertility model. The parameters are provided as a vector and the parameters must be provided in the order mentioned here.

• Logistic: f(x) = A / (1 + exp(-k (x - x_m)))

• Step: f(x)= \begin{cases} A, x \geq m \\ A, x < m \end{cases}

• von Bertalanffy: f(x) = A (1 - exp(-k (x - x_0)))

• Normal: f(x) = A \times \exp\left( -\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^{\!2}\,\right)

• Hadwiger: f(x) = \frac{ab}{c} \left (\frac{c}{x} \right ) ^\frac{3}{2} \exp \left \{ -b^2 \left ( \frac{c}{x}+\frac{x}{c}-2 \right ) \right \}

Value

A numeric vector representing the computed fertility values.

Author(s)

Owen Jones [e-mail]

References

Bertalanffy, L. von (1938) A quantitative theory of organic growth (inquiries on growth laws. II). Human Biology 10:181–213.

Peristera, P. & Kostaki, A. (2007) Modeling fertility in modern populations. Demographic Research. 16. Article 6, 141-194 doi:10.4054/DemRes.2007.16.6

See Also

model_survival() to model age-specific survival using mortality models.

Other trajectories: model_survival()

Examples

# Compute fertility using the step model
model_fertility(age = 0:20, params = c(A = 10), maturity = 2, model = "step")

# Compute fertility using the logistic model
model_fertility(
  age = 0:20, params = c(A = 10, k = 0.5, x_m = 8), maturity =
    0, model = "logistic"
)

# Compute fertility using the von Bertalanffy model
model_fertility(
  age = 0:20, params = c(A = 10, k = .3), maturity = 2, model =
    "vonbertalanffy"
)

# Compute fertility using the normal model
model_fertility(
  age = 0:20, params = c(A = 10, mu = 4, sd = 2), maturity = 0,
  model = "normal"
)

# Compute fertility using the Hadwiger model
model_fertility(
  age = 0:50, params = c(a = 0.91, b = 3.85, c = 29.78),
  maturity = 0, model = "hadwiger"
)