Bayesian informative priors with Yang and Land’s hierarchical age–period–cohort model

Abstract

Previous work (Bell and Jones, Demogr Res 2013a; Bell and Jones, Soc Sci Med 2013c; Luo and Hodges, Under review 2013) has shown that, when there are trends in either the period or cohort residuals of Yang and Land’s Hierarchical age–period–cohort (APC) model (Yang and Land, Sociol Methodol 36:75–97 2006; Yang and Land, APC analysis: new models, methods, and empirical applications. CRC Press, Boca Raton 2013), the model can incorrectly estimate those trends, because of the well-known APC identification problem. Here we consider modelling possibilities when the age effect is known, allowing any period or cohort trends to be estimated. In particular, we suggest the application of informative priors, in a Bayesian framework, to the age trend, and we use a variety of simulated but realistic datasets to explicate this. Similarly, an informative prior could be applied to an estimated period or cohort trend, allowing the other two APC trends to be estimated. We show that a very strong informative prior is required for this purpose. As such, models of this kind can be fitted but are only useful when very strong evidence of the age trend (for example physiological evidence regarding health) is available. Alternatively, a variety of strong priors can be tested and the most plausible solution argued for on the basis of theory.