The pitfalls of regression to the mean in bivariate timeseries analysis

Abstract

Plastic traits, capable of taking multiple forms, often correlate with one another or with features of the environment when measured over time. These patterns of correlated change are sometimes assumed to reflect adaptive plasticity, such as coevolved 'integrated phenotypes' within individuals, synchronisation between social or mating partners, or responses to environmental gradients. Such plasticity is ecologically and evolutionarily important, so there is considerable interest in understanding how it varies between individuals and groups. However, 'regression to the mean', the statistical tendency for traits to revert to the average value, may create the illusion of strong bivariate correlations in timeseries data, including substantial but meaningless variation between individuals. We demonstrate this using simulated and real data, revealing how regression to the mean can create bias both within and between samples. We then show, however, that its effects can often be eliminated using autoregressive models. We also offer a detailed discussion of how and why regression to the mean arises, introducing the idea that it is both a statistical and ecological phenomenon.