Methodological insights in Bayesian Age-Period-Cohort analysis: an application to the case of Puerto Rico's fertility decline
Age-Period-Cohort (APC) models are of special importance in Demography and Epidemiology for analyzing panel data according to three different factors: biological (age), technological (period) and cultural (cohort). The main goal of APC modeling is to separate the explanation of both period and cohort effects to the phenomenon. The objective of this paper is to develop a Bayesian Age-Period-Cohort framework that can model a wide range of demographic and epidemiological phenomena and improve upon existing statistical methodologies. The APC framework consists of addressing three main challenges: (1) the identification problem of all APC models, usually managed by imposing constraints on effect groups, (2) considering expert knowledge in the model definition, and (3) efficient solution of computational issues. By allowing full parameter uncertainty, use of robust priors, and an efficient computational implementation, a Bayesian methodology manages these concerns. Bayesian models also produce results that allow intuitive implementation and support theoretical knowledge. Our original methodology consists of the use of (i) a Scaled Beta2 prior distribution for the scale parameters, (ii) imposing different period and cohort constraints and comparing them,(iii) user-friendly implementation that can be easily adapted to the event, and (iv) various model comparison criteria that leads to reasonable interpretation of APC effects. We examine the dramatic collapse of fertility in Puerto Rico, an application that is difficult to model due to the accelerated changes and has interesting demographic implications that challenge the predominance of period effects in lowest-low fertility countries, emphasizing the cohort (cultural) momentum. The scope of the methodology introduced here is wide, including applications to obesity or smoking studies, for example.