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.

翻译：年龄-时期-队列（APC）模型在人口学和流行病学中具有特殊重要性，用于分析基于三种不同因素的面板数据：生物学因素（年龄）、技术因素（时期）和文化因素（队列）。APC模型的核心目标是区分时期效应和队列效应对现象的解释作用。本文旨在开发一个能够建模广泛人口与流行病现象、并改进现有统计方法的贝叶斯年龄-时期-队列框架。该APC框架需应对三大挑战：（1）所有APC模型均存在的识别问题，通常通过施加效应约束处理；（2）在模型定义中纳入专家知识；（3）计算问题的高效求解。通过允许完全参数不确定性、采用稳健先验以及高效的计算实现，贝叶斯方法成功应对了这些挑战。贝叶斯模型还产生支持直觉性实施和理论知识的可解释结果。我们的原创方法包括：（i）对尺度参数采用缩放Beta2先验分布；（ii）施加不同的时期和队列约束并进行比较；（iii）易于适配事件的可扩展实现；（iv）多种模型比较准则，以合理解释APC效应。我们考察了波多黎各生育率的急剧下降——这一案例因变化的加速而难以建模，且具有重要人口学启示，挑战了最低低生育率国家中时期效应主导地位的假设，强调队列（文化）惯性作用。本文提出的方法适用范围广泛，例如可应用于肥胖或吸烟行为研究。