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Abstract
Recently a large number of new mortality models have been proposed to analyze historic mortality rates and project them into the future. Many of these suffer from being over-parametrized or have terms added in an ad hoc manner that cannot be justified in terms of demographic significance. In addition, poor specification of a model can lead to period effects in the data being wrongly attributed to cohort effects, which results in the model making implausible projections. We present a general procedure for constructing mortality models using a combination of a toolkit of functions and expert judgment. By following the general procedure, it is possible to identify sequentially every significant demographic feature in the data and give it a parametric structural form. We demonstrate using U.K. mortality data that the general procedure produces a relatively parsimonious model that nevertheless has a good fit to the data.
Notes
This structural form and demographic significance of the terms in it are discussed in depth in Hunt and Blake (Citation2013c).
Introduced in Cairns et al. (Citation2006b) and defined as “a method of reasoning used to establish a causal association (or relationship) between two factors that is consistent with existing medical knowledge.”
Defined in Hunt and Blake (Citation2013c) as one taking a specific functional form that is defined by an algebraic formula.
Defined in Hunt and Blake (Citation2013c) as one fitted without imposing any a priori structure across ages.
Defined as max(log-likelihood)−0.5×no. free parameters×ln(no. data points).
Number of data points less number of free parameters.
This function can be thought of as a very simple linear spline with a single knot, similar to those used as basis functions in Aro and Pennanen (Citation2011). More complex splines could also be considered as part of the toolkit of age functions.
We have tested whether the use of an indicator function at age 18 or a narrow, triangular “spike” function centred on this age would improve the goodness of fit. However, when using the BIC, which penalizes for excessive parametrization, the use of these functions did not improve the fit of the model. The use of an indicator function also leads to mortality rates at age 18 being fitted perfectly, which does not accord with our desire for parsimony and may lead to discontinuous mortality rates that are not biologically reasonable.
This issue is discussed in Hunt and Blake (Citation2013b).
We will compare the relative performance of alternative mortality models in Section 6.
More recently, stratified (see D’Amato et al. Citation2011) and block-bootstrapping (see Liu and Braun Citation2010) procedures have been used, as have those based on geostatistical techniques that look at the correlation structure across residuals (see Debón et al. Citation2008, Citation2010).
This age/period term was chosen as the most specific age function fitted and therefore probably the most susceptible to uncertainty under this analysis.
Corresponding graphs for the age functions and other period functions, not shown here, also show considerable robustness.
