Bayesian Ridge Estimation of Age-Period-Cohort Models
Age-Period-Cohort (APC) analysis offers a framework to study trends in the three temporal dimensions underlying age by period tables. However, the perfect linear relationship among age, period, and cohort leads to a well-known identification issue due perfect colinearity from the identity Cohort = Period − Age. A number of methods have been proposed to deal with this identification issue, e.g., the intrinsic estimator (IE), which may be viewed as a limiting form of ridge regression. Bayesian regression offers an alternative approach to modeling tabular age, period, cohort data. This study views the ridge estimator from a Bayesian perspective by introducing prior distributions for the ridge parameters, which permits these parameters to be estimated jointly with the substantive parameters rather than being assigned (and fixed) a-priori. Results show that a Bayesian ridge model with a common prior for the ridge parameter yields estimated age, period, and cohort effects similar to those based on the intrinsic estimator and to those based on a conventional ridge estimator with a shrinkage penalty obtained from cross-validation. The performance of Bayesian models with distinctive priors for the ridge parameters of age, period, and cohort effects is, however, affected by the choice of prior distributions. Further investigation of the influence of the choice of prior distributions is therefore warranted.
KeywordsAge Period and cohort analysis Ridge regression Bayesian analysis
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