Some simulations of age-period-cohort analysis applying Bayesian regularization: Conditions for using random walk...

Area of Science:

• Statistics
• Epidemiology
• Time-Series Analysis

Background:

• Age-period-cohort (APC) analysis is a fundamental time-series model with an inherent identification problem, making it difficult to separate linear components of age, period, and cohort effects.
• Existing constraints to solve this problem remain controversial, with multilevel analysis often yielding near-zero linear cohort effects.
• Previous research has not adequately compared Nakamura's Bayesian cohort model with the intrinsic estimator.

Purpose of the Study:

• To compare three Bayesian regularization models for Age-period-cohort (APC) analysis: a random effects model (multilevel analysis), a ridge regression model (intrinsic estimator), and a random walk model (Bayesian cohort model).
• To investigate the performance of these models in estimating linear components by utilizing nonlinear components and priors.
• To suggest conditions for optimal use of the random walk model based on simulation results.

Main Methods:

• The study employed Bayesian regularization with normal priors, focusing on three models: random effects, ridge regression, and random walk.
• Simulations were conducted with varying settings for linear and nonlinear components to assess model performance.
• Simulation 1 manipulated nonlinear component magnitudes, Simulation 2 varied component changes, and Simulation 3 considered scenarios where only linear components were unlikely.

Main Results:

• Simulation 1 indicated the random walk model mitigated underestimation of linear cohort effects, unlike the other two models, particularly when nonlinear components were small.
• In Simulation 2, none of the models successfully recovered artificial parameters when both linear and nonlinear components changed randomly.
• Simulation 3 demonstrated that the random walk model exhibited less bias compared to the other models when considering the Bayesian regularization assumption.

Conclusions:

• There is no universally optimal Age-period-cohort (APC) analysis model; the choice depends on the data generating process.
• The random walk model shows relative advantages in scenarios where purely linear components are improbable.
• Bayesian regularization offers a viable approach to estimate linear components in APC analysis by incorporating nonlinear effects and priors.