lc {StMoMo}

Create a Lee-Carter model

Description

Utility function to initialise a StMoMo object representing a Lee-Carter model.

Usage

lc(link = c("log", "logit"), const = c("sum", "last", "first"))

Arguments

link

defines the link function and random component associated with the mortality model. "log" would assume that deaths follow a Poisson distribution and use a log link while "logit" would assume that deaths follow a Binomial distribution and a logit link.

const

defines the constraint to impose to the period index of the model to ensure identifiability. The alternatives are "sum"(default), "last" and "first" which apply constraints \sum_t\kappa_t = 0, \kappa_n = 0 and \kappa_1 = 0, respectively.

Details

The created model is either a log-Poisson (see Brouhns et al (2002)) or a logit-Binomial version of the Lee-Carter model which has predictor structure

\eta_{xt} = \alpha_x + \beta_x\kappa_t.

To ensure identifiability one of the following constraints is imposed

\sum_t\kappa_t = 0,\,\kappa_1 = 0,\, \kappa_n = 0

depending on the value of const, and

\sum_x\beta_x = 1.

Value

An object of class "StMoMo".

References

Brouhns, N., Denuit, M., & Vermunt, J. K. (2002). A Poisson log-bilinear regression approach to the construction of projected lifetables. Insurance: Mathematics and Economics, 31(3), 373-393.

Lee, R. D., & Carter, L. R. (1992). Modeling and forecasting U.S. mortality. Journal of the American Statistical Association, 87(419), 659-671.

See Also

StMoMo

Examples

#sum(kt) = 0 and log link
LC1 <- lc()
LCfit1<-fit(LC1, data = EWMaleData, ages.fit = 55:89)
plot(LCfit1)

#kt[1] = 0 and log link
LC2 <- lc(const = "first")
LCfit2<-fit(LC2, data = EWMaleData, ages.fit = 55:89)
plot(LCfit2)

#kt[n] = 0 and logit link
LC3 <- lc("logit", "last")
LCfit3<-fit(LC3, data = EWMaleData, ages.fit = 55:89)
plot(LCfit3)