Smoothing for age-period-cohort models: a comparison between splines and random process

TL;DR

This paper compares smoothing techniques in age-period-cohort models, highlighting their theoretical connections, similarities in predictions, and potential advantages of Bayesian methods for out-of-sample forecasting.

Contribution

It clarifies the theoretical link between penalised splines and random processes in APC models, with practical examples illustrating their similarities and differences.

Findings

Both methods produce similar in-sample predictions.

Bayesian random process approach may improve out-of-sample predictions.

Theoretical connection between frequentist and Bayesian smoothing methods is established.

Abstract

Age-Period-Cohort (APC) models are well used in the context of modelling health and demographic data to produce smooth estimates of each time trend. When smoothing in the context of APC models, there are two main schools, frequentist using penalised smoothing splines, and Bayesian using random processes with little crossover between them. In this article, we clearly lay out the theoretical link between the two schools, provide examples using simulated and real data to highlight similarities and difference, and help a general APC user understand potentially inaccessible theory from functional analysis. As intuition suggests, both approaches lead to comparable and almost identical in-sample predictions, but random processes within a Bayesian approach might be beneficial for out-of-sample prediction as the sources of uncertainty are captured in a more complete way.