rh {StMoMo} | R Documentation |
Create a Renshaw and Haberman (Lee-Carter with cohorts) mortality model
Description
Utility function to initialise a StMoMo
object representing a
Renshaw and Haberman (Lee-Carter with cohorts) mortality model introduced
in Renshaw and Haberman (2006).
Usage
rh(link = c("log", "logit"), cohortAgeFun = c("1", "NP"),
approxConst = FALSE)
Arguments
link |
defines the link function and random component associated with
the mortality model. |
cohortAgeFun |
defines the cohort age modulating parameter
|
approxConst |
defines if the approximate identifiability constraint of
Hunt and Villegas (2015) is applied or not. If |
Details
The created model is either a log-Poisson or a logit-Binomial version of the Renshaw and Haberman model which has predictor structure
\eta_{xt} = \alpha_x + \beta^{(1)}_x\kappa_t + \beta^{(0)} \gamma_{t-x}.
or
\eta_{xt} = \alpha_x + \beta^{(1)}_x\kappa_t + \gamma_{t-x}.
depending on the value of argument cohortAgeFun
.
To ensure identifiability the following constraints are imposed
\sum_t\kappa_t = 0, \sum_x\beta^{(1)}_x = 1, \sum_c\gamma_c = 0
plus
\sum_x\beta^{(0)}_x = 1
if cohortAgeFun = "NP"
In addition, if approxConst=TRUE
then the approximate
identifiability constraint
\sum_c (c-\bar{c})\gamma_c = 0
is applied to improve the stability and robustness of the model (see Hunt and Villegas (2015)).
By default \beta^{(0)}_x = 1
as this model has shown to be more
stable (see Haberman and Renshaw (2011) and Hunt and Villegas (2015)).
Value
An object of class "StMoMo"
or "rh"
.
References
Haberman, S., & Renshaw, A. (2011). A comparative study of parametric mortality projection models. Insurance: Mathematics and Economics, 48(1), 35-55.
Hunt, A., & Villegas, A. M. (2015). Robustness and convergence in the Lee-Carter model with cohorts. Insurance: Mathematics and Economics, 64, 186-202.
Renshaw, A. E., & Haberman, S. (2006). A cohort-based extension to the Lee-Carter model for mortality reduction factors. Insurance: Mathematics and Economics, 38(3), 556-570.
See Also
Examples
LCfit <- fit(lc(), data = EWMaleData, ages.fit = 55:89)
wxt <- genWeightMat(55:89, EWMaleData$years, clip = 3)
RHfit <- fit(rh(), data = EWMaleData, ages.fit = 55:89, wxt = wxt,
start.ax = LCfit$ax, start.bx = LCfit$bx, start.kt = LCfit$kt)
plot(RHfit)
#Impose approximate constraint as in Hunt and Villegas (2015)
## Not run:
RHapprox <- rh(approxConst = TRUE)
RHapproxfit <- fit(RHapprox, data = EWMaleData, ages.fit = 55:89,
wxt = wxt)
plot(RHapproxfit)
## End(Not run)