Modelling non‐linear age‐period‐cohort effects and covariates, with an application to English obesity 2001–2014

We develop an age-period-cohort model for repeated cross-section data with individual covariates, which identifies the non-linear effects of age, period and cohort. This is done for both continuous and binary dependent variables. The age, period and cohort effects in the model are represented by a parametrization with freely varying parameters that separates the identified non-linear effects and the unidentifiable linear effects. We develop a test of the parametrization against a more general 'time-saturated' model. The method is applied to analyse the obesity epidemic in England using survey data. The main non-linear effects we find in English obesity data are age-related among women and cohort-related among men.