This commentary clarifies our original commentary (Bell and Jones, 2014c) and illustrates some concerns we have regarding the response article in this issue (Reither et al., 2015). In particular, we argue that (a) linear effects do not have to be produced by exact linear mathematical functions to behave as if they were linear, (b) linear effects by this wider definition are extremely common in real life social processes, and (c) in the presence of these effects, the Hierarchical Age Period Cohort (HAPC) model will often not work. Although Reither et al. do not define what a 'non-linear monotonic trend' is (instead, only stating that it isn't a linear effect) we show that the model often doesn't work in the presence of such effects, by using data generated as a 'non-linear monotonic trend' by Reither et al. themselves. We then question their discussion of fixed and random effects before finishing with a discussion of how we argue that theory should be used, in the context of the obesity epidemic.
Keywords: Age-period-cohort models; Cohort effects; Collinearity; Model identification; Multilevel modelling; Obesity.
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