Mixed models, linear dependency, and identification in age-period-cohort models

Area of Science:

• Demography
• Statistics
• Epidemiology

Background:

• Age-period-cohort (APC) models are crucial for analyzing demographic and epidemiological data.
• Traditional APC models using fixed effects encounter identification problems due to linear dependencies among age, period, and cohort variables.
• Existing solutions involve imposing constraints, which can lead to arbitrary and variable results.

Purpose of the Study:

• To investigate the identification problem in age-period-cohort models.
• To explore alternative identification strategies beyond traditional constraint-based methods.
• To demonstrate the identification of APC models when incorporating random effects.

Main Methods:

• Examination of linear and categorical parameterizations in APC models.
• Analysis of identification in traditional fixed-effect regression models.
• Introduction and analysis of APC models with random effects (mixed models).
• Comparison of results based on different constraint choices versus random effect specifications.

Main Results:

• Standard fixed-effect APC models are unidentifiable without constraints due to linear dependencies.
• Imposing specific constraints can yield substantially different estimates.
• APC models with random effects are statistically identified without additional constraints.
• The designation of effects as fixed or random significantly influences the estimation of age, period, and cohort effects.

Conclusions:

• Statistical model identification offers a robust approach to resolving APC model identification issues.
• The use of random effects in APC models provides inherent identification.
• Researchers must carefully consider the implications of fixed versus random effect choices for accurate APC analysis.