Comparing non-parametric methods for ungrouping coarsely aggregated age-specific distributions

Demographers have often access to vital statistics that are less than ideal for the purpose of their research. In many instances demographic data are reported in coarse histograms, where the values given are only the summation of true latent values, thereby making detailed analysis troublesome. One example are abridged life tables, where data are typically summarized in 5-years age classes with an open ended interval starting at the age of 85. With increasing longevity this age structure becomes inappropriate: precious information about nonagenarians and centenarians is covered in the tail area of the age-specific distribution. Therefore it is often useful to estimate age-specific distributions by single-year of age from aggregated data. Flexible non-parametric techniques often used for this purpose are spline interpolation methods (Smith et al., 2004; Wilmoth et al., 2007; Jasilioniene et al., 2015). Recently a novel non-parametric method, based on the composite link model with a penalized likelihood, has been proposed (Rizzi et al., 2015). Here we aim to examine the performance of these different ungrouping methods in an empirical application with particular focus on the open-ended last interval. To do so we compare original NORDCAN data by single-year of age with the estimated distributions resulting from the models. We show that the penalized composite link model outperforms spline interpolation methods in presence of wide open-ended intervals.