Model mortality or fertility data using Lee-Carter approach

Lee-Carter model of mortality or fertility rates. lca produces a standard Lee-Carter model by default, although many other options are available. bms is a wrapper for lca and returns a model based on the Booth-Maindonald-Smith methodology.

Usage

lca(
  data,
  series = names(data$rate)[1],
  years = data$year,
  ages = data$age,
  max.age = 100,
  adjust = c("dt", "dxt", "e0", "none"),
  chooseperiod = FALSE,
  minperiod = 20,
  breakmethod = c("bai", "bms"),
  scale = FALSE,
  restype = c("logrates", "rates", "deaths"),
  interpolate = FALSE
)

bms(
  data,
  series = names(data$rate)[1],
  years = data$year,
  ages = data$age,
  max.age = 100,
  minperiod = 20,
  breakmethod = c("bms", "bai"),
  scale = FALSE,
  restype = c("logrates", "rates", "deaths"),
  interpolate = FALSE
)

Arguments

data: demogdata object of type “mortality” or “fertility”. Output from read.demogdata.
series: name of series within data containing mortality or fertility values (1x1)
years: years to include in fit. Default: all available years.
ages: ages to include in fit. Default: all available ages up to max.age.
max.age: upper age to include in fit. Ages beyond this are collapsed into the upper age group.
adjust: method to use for adjustment of coefficients $k_t kt$. Possibilities are “dxt” (BMS method), “dt” (Lee-Carter method), “e0” (method based on life expectancy) and “none”. Defaults are “dxt” for bms() and “dt” for lca().
chooseperiod: If TRUE, it will choose the best fitting period.
minperiod: Minimum number of years to include in fitting period if chooseperiod=TRUE.
breakmethod: method to use for identifying breakpoints if chooseperiod=TRUE. Possibilities are “bai” (Bai's method computed using breakpoints in the strucchange package) and “bms” (method based on mean deviance ratios described in BMS).
scale: If TRUE, it will rescale bx and kt so that kt has drift parameter = 1.
restype: method to use for calculating residuals. Possibilities are “logrates”, “rates” and “deaths”.
interpolate: If TRUE, it will estimate any zero mortality or fertility rates using the same age group from nearby years.

Value

Object of class “lca” with the following components:

label: Name of region
age: Ages from data object.
year: Years from data object.
<series>: Matrix of mortality or fertility data as contained in data. It takes the name given by the series argument.
ax: Average deathrates across fitting period
bx: First principal component in Lee-Carter model
kt: Coefficient of first principal component
residuals: Functional time series of residuals.
fitted: Functional time series containing estimated mortality or fertility rates from model
varprop: Proportion of variance explained by model.
y: The data stored as a functional time series object.
mdev: Mean deviance of total and base lack of fit, as described in Booth, Maindonald and Smith.

Details

All mortality or fertility data are assumed to be in matrices of mortality or fertility rates within data$rate. Each row is one age group (assumed to be single years). Each column is one year. The function produces a model for the series mortality or fertility rate matrix within data$rate. Forecasts from this model can be obtained using forecast.lca.

References

Booth, H., Maindonald, J., and Smith, L. (2002) Applying Lee-Carter under conditions of variable mortality decline. Population Studies, 56, 325-336.

Lee, R.D., and Carter, L.R. (1992) Modeling and forecasting US mortality. Journal of the American Statistical Association, 87, 659-671.

Author

Heather Booth, Leonie Tickle, John Maindonald and Rob J Hyndman.

Examples

if (FALSE) {
france.LC1 <- lca(fr.mort, adjust="e0")
plot(france.LC1)
par(mfrow=c(1,2))
plot(fr.mort,years=1953:2002,ylim=c(-11,1))
plot(forecast(france.LC1,jumpchoice="actual"),ylim=c(-11,1))

france.bms <- bms(fr.mort, breakmethod="bai")
fcast.bms <- forecast(france.bms)
par(mfrow=c(1,1))
plot(fcast.bms$kt)
}