m7 {StMoMo}

Create an M7 type extension of the Cairns-Blake-Dowd mortality model

Description

Utility function to initialise a StMoMo object representing the M7 extension of the Cairns-Blake-Dowd mortality model introduced in Cairns et al (2009).

Usage

m7(link = c("logit", "log"))

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. Note that the default is the logit link.

Details

The created model is either a logit-Binomial or a log-Poisson version of the M7 model which has predictor structure

\eta_{xt} = \kappa_t^{(1)} + (x-\bar{x})\kappa_t^{(2)} + ((x-\bar{x})^2 - \hat{\sigma}^2_x)\kappa_t^{(2)} + \gamma_{t-x},

where \bar{x} is the average age in the data and \hat{\sigma}^2_x is the average value of (x-\bar{x})^2.

Identifiability of the model is accomplished by applying parameters constraints

\sum_c\gamma_c = 0, \sum_c c\gamma_c = 0, \sum_c c^2\gamma_c = 0

which ensure that the cohort effect fluctuates around zero and has no linear or quadratic trend. These constraints are applied using the strategy discussed in Appendix A of Haberman and Renshaw (2011).

Value

An object of class "StMoMo".

References

Cairns, A. J. G., Blake, D., Dowd, K., Coughlan, G. D., Epstein, D., Ong, A., & Balevich, I. (2009). A quantitative comparison of stochastic mortality models using data from England and Wales and the United States. North American Actuarial Journal, 13(1), 1-35.

Haberman, S., & Renshaw, A. (2011). A comparative study of parametric mortality projection models. Insurance: Mathematics and Economics, 48(1), 35-55.

See Also

StMoMo, central2initial, cbd, m6, m8

Examples

M7 <- m7()
wxt <- genWeightMat(55:89,  EWMaleData$years, clip = 3)
M7fit <- fit(M7, data = central2initial(EWMaleData), ages.fit = 55:89)
plot(M7fit, parametricbx = FALSE)