rh: Create a Renshaw and Haberman (Lee-Carter with cohorts)...
In StMoMo: Stochastic Mortality Modelling

Description Usage Arguments Details Value References See Also Examples

Utility function to initialise a StMoMo object representing a Renshaw and Haberman (Lee-Carter with cohorts) mortality model introduced in Renshaw and Haberman (2006).

1 2	rh(link = c("log", "logit"), cohortAgeFun = c("1", "NP"), approxConst = FALSE)

`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.
`cohortAgeFun`	defines the cohort age modulating parameter β_x^{(0)}. It can take values: `"NP"` for a non-parametric age term or `"1"` for β_x^{(0)}=1 (the default).
`approxConst`	defines if the approximate identifiability constraint of Hunt and Villegas (2015) is applied or not. If `TRUE`, the output object is of class `rh` and subsequent model fitting is performed with `fit.rh`. If `FALSE`, the output object is of class `StMoMo` and subsequent model fitting is performed with `fit.StMoMo`.

The created model is either a log-Poisson or a logit-Binomial version of the Renshaw and Haberman model which has predictor structure

η_{xt} = α_x + β^{(1)}_xκ_t + β^{(0)} γ_{t-x}.

η_{xt} = α_x + β^{(1)}_xκ_t + γ_{t-x}.

depending on the value of argument cohortAgeFun.

To ensure identifiability the following constraints are imposed

∑_tκ_t = 0, ∑_xβ^{(1)}_x = 1, ∑_cγ_c = 0

plus

∑_xβ^{(0)}_x = 1

if cohortAgeFun = "NP"

In addition, if approxConst=TRUE then the approximate identifiability constraint

∑_c (c-\bar{c})γ_c = 0

is applied to improve the stability and robustness of the model (see Hunt and Villegas (2015)).

By default β^{(0)}_x = 1 as this model has shown to be more stable (see Haberman and Renshaw (2011) and Hunt and Villegas (2015)).

An object of class "StMoMo" or "rh".

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.

fit.rh, StMoMo, lc, apc

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)