Modelling fertility rates by age, time, and birth order from coarsely grouped data: a penalized composite link model approach

Diego Ayma Anza, Universidad Carlos III de Madrid
Carlo G. Camarda, Institut National d'Études Démographiques (INED)

In practice, fertility and population data can be only available in age classes and calendar year classes, which may have different levels of aggregation. Moreover, these coarse data can be recorded along a third dimension, making their analysis more challenging. Data aggregation process may, however, hinder the visualization of the underlying distribution that follows the data. In this paper, we propose the use of the penalized composite link model to estimate the latent trend behind these coarsely grouped data. This model only assumes that the underlying distribution is smooth, making it suitable for other applications in which disaggregation is required. We illustrate our proposal using a Canadian fertility dataset, which is recorded by age of the mother, calendar year, and birth order.