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Lee-Carter model

leecart.Rd

Lee-Carter model

Usage

leecart(
  data,
  n = 10,
  alpha = 0.05,
  model = "RWwD",
  ax_method = "classic",
  bx_method = "classic",
  boot = FALSE,
  bn = 1000,
  ktadj = "none",
  ...
)

Arguments

data

Dataframe in the long format with the following columns: age, year, mx (age specific mortality rates). For some types of ktadj argument N (population at age x) and Dx (number of deaths at age x) columns should also be presented.

n

Numeric. Forecasted horizon

alpha

Numeric. The level of uncertainty. By default, alpha = 0.05 for 95% CI.

model

Character. Model type for kt forecasting. Can be "RWwD" for random walk with drift (by default, for original Lee-Carter model) or "ARIMA" for ARIMA model which parameters are chosen automatically by forecast::auto.arima().

ax_method

Character. Method for ax calculation. Can be "classic" from original Lee-Carter model (by default), "last" or "last_smooth". See details.

bx_method

Character. Method for bx calculation. Can be "classic" from original Lee-Carter model (by default) and "rotate" for rotating bx (Li et al., 2013).

boot

Logical. Should bootstrap estimates for uncertainty be used? FALSE by default.

bn

Numeric. Used if boot = TRUE, number of bootstrap samples. By default, bn = 1000.

ktadj

Character. Type of kt adjustment. It can be set to 'none' (defaukt, no adjustment), 'Dmin', 'e0min', 'poisson' or 'edaggermin' (see Details). Note that 'Dmin' and 'poisson' require data on the age-specific number of deaths (Dx column in the data) and the age-specific population (N column in the data).

...

Optional. Additional arguments for LT() function.

Value

Dataframe with the projected mx and ex for t+n periods with mean, low95 and high 95 values

Details

The model argument specifies the forecasting method.

  • model ="RWwD" – classic random walk option

  • model = "ARIMA" for selecting a more complex time series model

The ax_method argument allows to control how a_x is calculated.

  • ax_method = "classic" – classic option with the average of the logarithm of mortality rates (but there is so-called "jump-off bias").

  • ax_method = "last" uses the logarithm of mortality for the last available year (as proposed in Lee & Miller, 2001).

  • ax_method = "last_smooth" uses data for the last year with smoothing (see Ševčíková et al., 2016, p. 288).

The bx_method argument allows to control how b_x is calculated.

  • bx_method = "classic" for the original method.

  • bx_method = "rotate" for the rotational variant (see Li et al., 2013).

The ktadj argument allows to control how k_t is calculated.

  • ktadj = "none" for no adjustment.

  • ktadj = "Dmin" for minimizing the deviance of predicted/actual annual deaths (as proposed in the original Lee-Carter paper). This method requires data on the age-specific number of deaths (Dx column in the data) and the age-specific population (N column in the data).

  • ktadj = "e0min" for minimizing the deviance of predicted/actual life expectancy (as proposed in Lee & Miller, 2001).

  • ktadj = "poisson" for minimizing the deviance from a Poisson model, where the dependent variable is the age-specific annual number of deaths (as proposed in Booth et al., 2002). This method requires data on the age-specific number of deaths (Dx column in the data) and the age-specific population (N column in the data).

  • ktadj = "edaggermin" for minimizing the deviance of predicted/actual edagger (see edagger()) as proposed in Rabbi & Mazzuco, 2021.

References

Booth, H., Maindonald, J., & Smith, L. (2002). Applying Lee-Carter under conditions of variable mortality decline. Population studies, 56(3), 325-336. https://doi.org/10.1080/00324720215935

Lee, R. D., & Carter, L. R. (1992). Modeling and forecasting US mortality. Journal of the American Statistical Association, 87(419), 659–671. https://doi.org/10.1080/01621459.1992.10475265

Lee, R., & Miller, T. (2001). Evaluating the performance of the lee-carter method for forecasting mortality. Demography, 38(4), 537–549. https://doi.org/10.1353/dem.2001.0036

Li, N., Lee, R., & Gerland, P. (2013). Extending the Lee-Carter Method to Model the Rotation of Age Patterns of Mortality Decline for Long-Term Projections. Demography, 50(6), 2037–2051. https://doi.org/10.1007/s13524-013-0232-2

Rabbi, A. M. F., & Mazzuco, S. (2021). Mortality forecasting with the lee–carter method: Adjusting for smoothing and lifespan disparity. European Journal of Population, 37(1), 97-120. https://doi.org/10.1007/s10680-020-09559-9

Ševčíková, H., Li, N., Kantorová, V., Gerland, P., & Raftery, A. E. (2016). Age-Specific Mortality and Fertility Rates for Probabilistic Population Projections. In R. Schoen (Ed.), Dynamic Demographic Analysis (Vol. 39, pp. 285–310). Springer International Publishing. https://doi.org/10.1007/978-3-319-26603-9_15