lca: Model mortality or fertility data using Lee-Carter approach

Description

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
)

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.

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.

Author

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

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.

Examples

Run this code

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)
}

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