brass_mort: Brass's Relational Model of Mortility
In gjabel/agesched: Demographic Age Schedules

Description Usage Arguments Details Value Author(s) Examples

Brass' relational model of mortility makes use of a standard model mortility schedule, based on $L_x^s$ that is linearised using

Y_s(x) = \frac{1}{2} \ln ≤ft( \frac{a l_0 - L_x^s}{L_x^s} \right)

where l_0 is the population of the cohort at age zero.

1 2	brass_mort(model = NULL, x = seq(from = 0, to = 100, by = 1), alpha = 0, beta = 1, l0 = 1e+05)

`model`	Vector of a 'model' age specific person years lived schedule $L_x$. Will be used to derive the standardised transformed age schedule, \Y_s(x) above.
`x`	Vector for the sequence of ages.
`alpha`	Numeric value for intercept adjustment to the standardised transformed age schedule
`beta`	Numeric value for slope adjustment to the standardised transformed age schedule

The modified transformed schedule is formed by adjusting the demographer's logit above using

Y(x) = α + β Y_s(x)

where β changes the slope and α the intercept of the linearised $L_x$

The modified transformed schedule is converted back into $L_x$ by applying the anti-function used to linearise the standard schedule.

Returns vector of $L_x$ from the relational model schedule. The function is primarily intended for creating synthetic survivorships for projection models.

The alpha and beta parameters relate a modified schedule to the schedule provided by the model argument.

Guy J. Abel

#single year
df0 <- subset(austria, Year == 2014)
f0 <- df0$Lx_f
f1 <- brass_mort(model = f0, x = df0$Age, alpha = 0.8, beta = 1)
plot(f0, type = "l")
lines(f1, col = "red")
e0 <- sum(Lx)/l0
e0