Moore-Penrose Generalized-Inverse Solution to APC Modeling for Historical Epidemiology and Global Health

Age-period-cohort (APC) modeling provides a powerful method for global health research in resource-limited countries and regions with limited data. This method enables researchers to investigate medical and health conditions and influential factors, potentially up to 100+ year in the past with data collected in recent decades. Although widely used in research to examine mortality of various diseases, suicide and quality of life, an APC model is mathematically nonidentifiable. This is because the conlinearity among the three time-related predictors (age, period, and birth cohort). Various methods are reported to deal with this identifiability issue, particularly the intrinsic estimator (IE) that has been most accepted. IE method has been developed through much effort, including mathematical proof, simulations and empirical testing. In this chapter, we introduce the application of Moor-Penrose generalized inverse matrix method (MP) in handling the nonidentifiable issue. Relative to the IE method, the MP method is straight-forward to understand and easy to implement. We also show that mathematically MP method is equivalent to IE method.