Age-period-cohort (APC) analysis is one of the fundamental time-series analyses used in the social sciences. This paper evaluates APC analysis via systematic simulation in term of how well the artificial parameters are recovered. We consider three models of Bayesian regularization using normal prior distributions: the random effects model with reference to multilevel analysis, the ridge regression model equivalent to the intrinsic estimator, and the random walk model referred to as the Bayesian cohort model. The proposed simulation generates artificial data through combinations of the linear components, focusing on the fact that the identification problem affects the linear components of the three effects. Among the 13 cases of artificial data, the random walk model recovered the artificial parameters well in 10 cases, while the random effects model and the ridge regression model did so in 4 cases. The cases in which the models failed to recover the artificial parameters show the estimated linear component of the cohort effects as close to zero. In conclusion, the models of Bayesian regularization in APC analysis have a bias: the index weights have a large influence on the cohort effects and these constraints drive the linear component of the cohort effects close to zero. However, the random walk model mitigates underestimating the linear component of the cohort effects.

翻译：年龄-时期-队列（APC）分析是社会科学中使用的基础时间序列分析方法之一。本文通过系统仿真评估APC分析在恢复人工参数方面的表现。我们考虑三种使用正态先验分布的贝叶斯正则化模型：参照多层次分析的随机效应模型、等同于固有估计量的岭回归模型以及被称为贝叶斯队列模型的随机游走模型。所提出的仿真通过线性成分的组合生成人工数据，重点聚焦识别问题对三种效应的线性成分的影响。在13种人工数据案例中，随机游走模型在10个案例中较好地恢复了人工参数，而随机效应模型和岭回归模型仅在4个案例中实现。模型未能恢复人工参数的案例显示，队列效应的线性成分估计值趋近于零。结论表明，APC分析中的贝叶斯正则化模型存在偏差：索引权重对队列效应具有较大影响，且这些约束迫使队列效应的线性成分趋近于零。然而，随机游走模型缓解了队列效应线性成分被低估的问题。