Is Less More? Data-Driven Dimensionality Reduction in Parametric ASFR Models

Bilal Barakat, Vienna Institute of Demography

Fertility timing can be summarized by the schedule of age-specific fertility rates (ASFR). The number of parameters in parametric ASFR models involves a number of trade-offs, not least between expressiveness and parsimony. We propose a novel application of a data-driven dimensionality reduction technique, namely Independent Component Analysis, to embed a ‘reduced’ model of low parametric dimension within an arbitrary model of higher dimension, combining the statistical benefits of the former with the expressiveness and transparent interpretation of the latter. We apply this approach to several popular ASFR models with different numbers of parameters and assess the fits on a large number of empirical schedules. The reduced models perform competitively with previously proposed models with the same or even larger number of parameters. With imperfect data, little or no benefit derives from using more than 3 (optimally chosen!) dimensions, at least with 5-year age groups and a relative error criterion.