Matsumoto Yuta
Quality Assurance Office Institutional Research, Hosei University, Chiyoda-ku, Tokyo, Japan.
PLoS One. 2025 Aug 8;20(8):e0329223. doi: 10.1371/journal.pone.0329223. eCollection 2025.
Age-period-cohort (APC) analysis, one of the fundamental time-series models, has an identification problem of the inability to separate linear components of the three effects. However, constraints to solve the problem are still controversial because multilevel analysis used in many studies results in the linear component of cohort effects being close to zero. In addition, previous studies do not compare the Bayesian cohort model proposed by Nakamura with the well-known intrinsic estimator. This paper focuses on three models of Bayesian regularization using priors of normal distributions. A random effects model refers to multilevel analysis, a ridge regression model is equivalent to the intrinsic estimator, and a random walk model refers to the Bayesian cohort model. Here, applying Bayesian regularization in APC analysis is to estimate linear components by using nonlinear components and priors. We aim to suggest conditions for using the random walk model by comparing the three models through some simulations with settings for the linear and nonlinear components. Simulation 1 emphasizes an impact of the indexes by making absolute values of the nonlinear components small. Simulation 2 randomly generates the amounts of change in the linear and nonlinear components. Simulation 3 randomly generates artificial parameters with only linear components are less likely to appear, to consider the Bayesian regularization assumption. As a result, Simulation 1 shows the random walk model, unlike the other two models, mitigates underestimating the linear component of cohort effects. On the other hand, in Simulation 2, none of the models can recover the artificial parameters. Finally, Simulation 3 shows the random walk model has less bias than the other models. Therefore, there is no one-size-fits-all APC analysis. However, this paper suggests the random walk model performs relatively well in data generating processes, where only linear components are unlikely to appear.
年龄-时期-队列（APC）分析是基本的时间序列模型之一，存在无法分离三种效应线性成分的识别问题。然而，解决该问题的约束条件仍存在争议，因为许多研究中使用的多水平分析导致队列效应的线性成分接近零。此外，以往研究未将中村提出的贝叶斯队列模型与著名的内在估计器进行比较。本文聚焦于使用正态分布先验的三种贝叶斯正则化模型。随机效应模型指多水平分析，岭回归模型等同于内在估计器，随机游走模型指贝叶斯队列模型。在此，在APC分析中应用贝叶斯正则化是通过使用非线性成分和先验来估计线性成分。我们旨在通过对线性和非线性成分设置进行一些模拟来比较这三种模型，从而提出使用随机游走模型的条件。模拟1通过使非线性成分的绝对值变小来强调指标的影响。模拟2随机生成线性和非线性成分的变化量。模拟3随机生成仅线性成分不太可能出现的人工参数，以考虑贝叶斯正则化假设。结果，模拟1表明，与其他两个模型不同，随机游走模型减轻了对队列效应线性成分的低估。另一方面，在模拟2中，没有一个模型能够恢复人工参数。最后，模拟3表明随机游走模型的偏差比其他模型小。因此，不存在适用于所有情况的APC分析。然而，本文表明随机游走模型在仅线性成分不太可能出现的数据生成过程中表现相对较好。
