demofit (version 0.1.4)

APCS: Age-period-cohort model

Description

Fits and forecasts mortality rates using age-period-cohort model.

Usage

APCS(
  x,
  M,
  curve = c("gompertz", "makeham", "oppermann", "thiele", "wittsteinbumsted", "perks",
    "weibull", "vandermaen", "beard", "heligmanpollard", "rogersplanck", "siler",
    "martinelle", "thatcher", "gompertz2", "makeham2", "oppermann2", "thiele2",
    "wittsteinbumsted2", "perks2", "weibull2", "vandermaen2", "beard2",
    "heligmanpollard2", "rogersplanck2", "siler2", "martinelle2", "thatcher2"),
  h = 10,
  jumpoff = 1
)

Value

An object of class APCS with associated S3 methods coef, forecast (which = 1 for smoothed (default); which = 2 for raw), plot, residuals, and simulate (nsim for setting number of simulations; seed for initialising random number generator).

Arguments

x

vector of ages.

M

matrix of mortality rates (rows as years and columns as ages).

curve

name of mortality curve for smoothing forecasted mortality rates (including gompertz, makeham, oppermann, thiele, wittsteinbumsted, perks, weibull, vandermaen, beard, heligmanpollard, rogersplanck, siler, martinelle, thatcher, gompertz2, makeham2, oppermann2, thiele2, wittsteinbumsted2, perks2, weibull2, vandermaen2, beard2, heligmanpollard2, rogersplanck2, siler2, martinelle2, thatcher2, where first 14 curves' parameters are unconstrained and last 14 curves' parameters are generally restricted to be positive).

h

forecast horizon (default = 10).

jumpoff

if 1, forecasts are based on estimated parameters only; if 2, forecasts are anchored to observed mortality rates in final year (default = 1).

Details

The age-period-cohort (APC) model is specified as

\(ln(m_{x,t}) = \alpha_x + \kappa_t + \gamma_{t-x} + \epsilon_{x,t}\).

The model is estimated by Newton updating scheme and is forecasted by ARIMA applied to \(\kappa_t\) and \(\gamma_c\). Constraints include sum of \(\kappa_t\) is zero and and sum of \(\gamma_c\) is zero. It can be applied to whole age range.

References

Bray, I. (2002). Application of Markov chain Monte Carlo methods to projecting cancer incidence and mortality. Journal of the Royal Statistical Society Series C, 51(2), 151-164.

Examples

x <- 60:89
a <- c(-4.8499,-4.7676,-4.6719,-4.5722,-4.4847,-4.3841,-4.2813,-4.1863,-4.0861,-3.9962,
-3.8885,-3.7896,-3.6853,-3.5737,-3.4728,-3.3718,-3.2586,-3.1474,-3.0371,-2.9206,
-2.7998,-2.6845,-2.5653,-2.4581,-2.3367,-2.2159,-2.1017,-1.9941,-1.8821, -1.7697)
b <- rep(1/30,30)
k <- c(12.11,10.69,11.18,9.64,9.35,8.21,6.89,5.74,4.56,3.6,
3.27,2.04,1.11,-0.44,-1.05,-1.03,-1.84,-2.9,-4.03,-4.12,
-5.18,-5.64,-6,-6.51,-6.91,-6.9,-8.32,-8.53,-9.69,-9.31)
set.seed(123)
M <- exp(outer(k,b)+matrix(a,nrow=30,ncol=30,byrow=TRUE)+rnorm(900,0,0.035))
fit <- APCS(x=x,M=M,curve="makeham",h=30,jumpoff=2)
coef(fit)
forecast::forecast(fit)
plot(fit)
residuals(fit)