brass_fert: Brass's Relational Gompertz Model of Fertility
In gjabel/agesched: Demographic Age Schedules

Description Usage Arguments Details Value Author(s) See Also Examples

Brass' relational Gompertz model of fertility makes use of a standard fertility schedule that is linearised using

Y_s(x) = -ln [ -ln( F_s(x) ) ]

where \Y_s(x) is the standardised transformed age schedule and F_s(x) is the culmative fertility function of the standardised model schedule, scaled to sum to 1.

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brass_fert(tfr = NULL, x = seq(from = 0, to = 100, by = 1), model = NULL,
  alpha = 0, beta = 1, start_fertage = 15, width_fertage = 35,
  model_ages = "auto")

`tfr`	Numeric value for total fertitliy rate of the returned age schedule.
`x`	Vector for the sequence of ages.
`model`	Vector of a 'model' age specific fertility rates. Will be used to derive the standardised transformed age schedule, \Y_s(x) above.
`alpha`	Numeric value for intercept adjustment to the standardised transformed age schedule
`beta`	Numeric value for slope adjustment to the standardised transformed age schedule
`start_fertage`	Numeric value for the start of the fertility age range.
`width_fertage`	Numeric value for the width of the fertility age range.
`model_age`	String value to indicate if model is for fertility age range only or all ages.

The modified transformed age schedule is formed by adjusting the standardised transformed age schedule into an alternative other straight line

Y_m(x) = α + β Y_s(x)

where β changes the slope and α the intercept.

The modified transformed age schedule is converted back into a fertility schedule by applying the anti-function used to linearise the standard schedule.

Returns the f(x) values from a relational model schedule of age specific fertility. 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 a total fertility rate into an age-specific values.

The alpha and beta parameters relate a modified schedule to the schedule provided by the model argument. The arguments for the start and width of the fertility age range (start_fertage, width_fertage) are used to select where the model distribution is applied over the range of ages given in x. Ensure that these match those of the model age schedule.

If the model schedule covers both fertility and non-fertility age ranges, set model_age to all to ignore the values passed to start_fertage, start_fertage, x. The auto option attempts to guess, based on the length of the vetor passed to model and the age groups used in x.

Guy J. Abel

gage romainuk hadwiger

#single year
f0 <- subset(austria, Year == 2014)$Fx
plot(f0, type = "l")
sum(f0)
f1 <- brass_fert(tfr = 2.1, model = f0, alpha = 0.1, beta = 1.1)
sum(f1)
plot(f1, type = "l")
lines(f0, col = "red")

#five year
f1 <- brass_fert(tfr = 3, x = seq(from = 0, to = 100, by = 5), model = un1956$high, alpha = -0.1, beta = 0.9)
plot(f1, type = "l")