Aggregate versus Individual Change

Maren Rebke, Max Planck Institute for Demographic Research and Imperial College London
Zhen Zhang, Max Planck Institute for Demographic Research

Heterogeneity within a population can produce dynamics at the population level that are very different from the dynamics within homogeneous subgroups or dynamics at the individual level. Therefore, conclusions about individual characteristics can very often not directly be drawn from observations made on the aggregate population level (Vaupel and Yashin 1985, Am. Stat., 39, 176-185). We present a straightforward and simple approach to decompose the observed change at the aggregate population level into parts with clear meaning, namely the individual change and the change due to selective mortality. Our approach not only provides information about whether there are individual and compositional changes, but also makes it possible to quantify how much of the change observed on the population level is due to a compositional change and how much is due to an actual change in the individuals. The approach can be extended to account for new individuals entering the study.