Multilevel models for age–period–cohort analysis

Multilevel models (aka mixed models, random effects models, hierarchical linear models) have been used widely when considering age, period and cohort (APC) effects. In some cases, this is presented as a solution to the identification problem, for example the Hierarchical APC model. This chapter shows why this is not the case, using both simulations and real-data examples, illustrating why mixed models produce the results that they do, and showing that those results are often not in line with the underling reality. Whilst mixed models may allow APC models to be identified, they do so by making strong assumptions that are implicit in the model design and data structure. The chapter goes on to show ways in which mixed models can be used, not as a solution to the identification problem, but as a way of framing APC models that makes the assumptions of those models explicit. This is illustrated using examples of mental health in the UK at the turn of the 20th/21st century, and changes in mortality across the 20th century.