The line of solutions and understanding age–period–cohort models

In this chapter the author presents the line of solutions and some of its associated properties, and employs these to tie together the various approaches used in the chapters of this book. The previous chapters involve many different approaches to examining age–period–cohort multiple classification (APCMC) data. Some of these approaches use the traditional fixed effect APCMC regression models while others move beyond ordinary least squares (OLS) and generalized linear model (GLM) regression to use mixed models, characteristic models and Bayesian models. One chapter even uses a purely graphical approach. For the OLS and GLM models, the line of solutions is exact in terms of describing all of the best fitting solutions and provides certain estimable functions and relationships among trends for the age, period, and cohort effects. For mixed, characteristic and Bayesian models the line of solutions and its associated properties provide only approximations. But in all cases it is helpful in understanding how these approaches to APCMC solutions work and in evaluating their strengths and weaknesses.