Clarifying hierarchical age-period-cohort models: A rejoinder to Bell and Jones.

Previously, Reither et al. (2015) demonstrated that hierarchical age-period-cohort (HAPC) models perform well when basic assumptions are satisfied. To contest this finding, Bell and Jones (2015) invent a data generating process (DGP) that borrows age, period and cohort effects from different equations in Reither et al. (2015). When HAPC models applied to data simulated from this DGP fail to recover the patterning of APC effects, B&J reiterate their view that these models provide "misleading evidence dressed up as science." Despite such strong words, B&J show no curiosity about their own simulated data--and therefore once again misapply HAPC models to data that violate important assumptions. In this response, we illustrate how a careful analyst could have used simple descriptive plots and model selection statistics to verify that (a) period effects are not present in these data, and (b) age and cohort effects are conflated. By accounting for the characteristics of B&J's artificial data structure, we successfully recover the "true" DGP through an appropriately specified model. We conclude that B&Js main contribution to science is to remind analysts that APC models will fail in the presence of exact algebraic effects (i.e., effects with no random/stochastic components), and when collinear temporal dimensions are included without taking special care in the modeling process. The expanded list of coauthors on this commentary represents an emerging consensus among APC scholars that B&J's essential strategy--testing HAPC models with data simulated from contrived DGPs that violate important assumptions--is not a productive way to advance the discussion about innovative APC methods in epidemiology and the social sciences.