On fitting generalized linear and non-linear models of mortality

Abstract

Many common models of mortality can be expressed compactly in the language of either generalized linear models or generalized non-linear models. The R language provides a description of these models which parallels the usual algebraic definitions but has the advantage of a transparent and flexible model specification. We compare eight model structures for mortality. For each structure, we consider (a) the Poisson models for the force of mortality with both log and logit link functions and (b) the binomial models for the rate of mortality with logit and complementary log–log link functions. Part of this work shows how to extend the usual smooth two-dimensional P-spline model for the force of mortality with Poisson error and log link to the other smooth two-dimensional P-spline models with Poisson and binomial errors defined in (a) and (b). Our comments are based on the results of fitting these models to data from six countries: Australia, France, Japan, Sweden, UK and USA. We also discuss the possibility of forecasting with these models; in particular, the introduction of cohort terms generally leads to an improvement in overall fit, but can also make forecasting with these models problematic.

Keywords:

• constraints
• forecasting
• generalized linear models
• identifiability
• mortality
• R language

Acknowledgements

I am grateful to Stephen Richards for comments on earlier drafts of this paper and to Maria Durban and the Spanish Ministry of Science and Innovation (project MTM2011-28285-C02-02) for financial support.