# m7: Create an M7 type extension of the Cairns-Blake-Dowd... In StMoMo: Stochastic Mortality Modelling

## 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

 1 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

η_{xt} = κ_t^{(1)} + (x-\bar{x})κ_t^{(2)} + ((x-\bar{x})^2 - \hat{σ}^2_x)κ_t^{(2)} + γ_{t-x},

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

Identifiability of the model is accomplished by applying parameters constraints

∑_cγ_c = 0, ∑_c cγ_c = 0, ∑_c c^2γ_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.

StMoMo, central2initial, cbd, m6, m8
 1 2 3 4 M7 <- m7() wxt <- genWeightMat(55:89, EWMaleData\$years, clip = 3) M7fit <- fit(M7, data = central2initial(EWMaleData), ages.fit = 55:89) plot(M7fit, parametricbx = FALSE)