Modelling and decomposing vital rates: a non-parametric approach

Demographic events have characteristic age-specific patterns of occurrence. Finding model schedules to summarize the age-pattern of demographic rates has a long tradition, however, parametric models are predominantly used. Many demographic rates shows complex shape in their overall age-pattern. However such pattern can be attributed to different distinct components.

While some of the components can be described by a parametric model, such as the Gompertz hazard for adult mortality, many others cannot. Additional complication arises if data are provided in age groups, which is still the case in many official statistics and historical data.

In the article we propose a model that allows to specify rates across a wide range of ages as the sum of several components, which are modelled on the log scale and are assumed to be smooth, but do not have to follow a particular parametric form. A penalized composite link model is used to decompose complex trajectories into smooth additive components.

Parametric and non-parametric forms can be used. Data can be given in age-groups which can eventually be of variable lengths. Furthermore, monotonicity or shape constraints on the components can be incorporated and the model can cope with two-dimensional settings in which age-patterns change over time.