Modelling and decomposing vital rates: a non-parametric approach

Demographic events, such as marriage, migration, childbirth or death, have characteristic age-specific patterns of occurrence. Finding so-called 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. Models that can separate these components are particularly welcome.

While some of the components can be well described by a parametric model, such as the Gompertz hazard for adult mortality, many others cannot. An additional complication arises if data are provided only in age groups, which is still the case in many o_cial statistics, and is standard if one goes back in time.

In the presentation I will propose a general model that allows to specify (demographic) 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 the complex rate trajectory into smooth additive components.

Parametric and non-parametric models can be used for describing each component. Data can be given in grouped form, and the age groups can be of variable lengths. Furthermore, monotonicity or shape constraints on the components can be incorporated by special penalty matrices. The model can also cope with two-dimensional settings in which age patterns change over time.