Estimable functions in age-period-cohort models: a unified approach

Age-period-cohort (APC) models have an intriguing appeal because each of these factors may be independently associated with age-period-specific rates (or other values). Unfortunately, one can not uniquely estimate the effects that generated the outcome data because these effects are linearly dependent. It is possible, however, to estimate certain linear combinations of these effects that are themselves unique estimates of the data generating parameters. The author demonstrates that all of the least square solutions for the APC model lie on a line in multidimensional solution space. This characteristic of the solutions to the APC model allows for a unified approach to the derivation of estimable functions, which is then used to derive the most prominent estimable functions in the APC literature and can be used to discover new ones.