Modeling Mortality of Related Populations via Parameter Shrinkage

Parameter shrinkage is known to reduce fitting and prediction errors in linear models. When the variables are dummies for age, period, etc. shrinkage is more commonly applied to differences between adjacent parameters, perhaps by fitting cubic splines or piecewise-linear curves (linear splines) across the parameters. A common problem in mortality is modeling related populations where some commonality is desired. We do this by shrinking slope changes of linear splines for the largest population, then shrinking differences from those slope changes for the other populations. There are frequentist and Bayesian approaches to shrinkage, and they have a good deal of similarity. Here we use a unified approach that compromises a bit with both of these paradigms. It uses Bayesian tools without some of the historical Bayesian concepts, and pushes the random-effects framework slightly to accommodate. Modeling Swedish and Danish male mortality data is used as an illustration.