Correcting for Regression to the Mean in Behavior and Ecology

Abstract

If two successive trait measurements have a less-than-perfect correlation, individuals or populations will, on average, tend to be closer to the mean on the second measurement (the so-called regression effect). Thus, there is a negative correlation between an individual's state at time 1 and the change in state from time 1 to time 2. In addition, whenever groups differ in their initial mean values, the expected change in the mean value from time 1 to time 2 will differ among the groups. For example, birds feeding nestlings lose weight, but initially heavier birds lose more weight than lighter birds, a result expected from the regression effect. In sexual selection, males who remain unmated in the first year are, on average, less attractive than mated males. The regression effect predicts that these males will increase their attractiveness in the second year more than mated males. In well-designed experiments, changes in the experimental and control groups would be compared. In observational studies, however, no such comparison is available, and expected differential effects must be accounted for before they can be attributed to external causes. We describe methods to correct for the regression effect and assess alternative causal explanations.

Catecholaminergic Regulation of Learning Rate in a Dynamic Environment

“…This analysis suggested that the baseline-dependent atomoxetine effect on learning rate was stronger than expected based on regression to the mean for the change-point trials (proportion of permutations below observed correlation = 0.04 and 0.07 for the nonobvious and obvious change-point trials, respectively) but not for the trials on which no change point occurred (proportion of permutations below observed correlation = 0.42; Fig 5C). Second, a baseline-dependent atomoxetine effect that is larger than expected based on regression to the mean should produce higher across-subject variance in learning rate in the placebo session than in the atomoxetine session [57]. We tested this prediction using Pitman’s test of equality of variance in paired samples [58].…”

Avoiding pitfalls in estimating heritability with the common options approach

“…Despite its ubiquity and venerability, RTM is so subtle and counter-intuitive that it continues to be overlooked29. It can be corrected for in post hoc analyses3031, but is considered to be avoidable by proper experimental designs31. Unfortunately, as our simulations suggest, even classically designed experiments are not immune to RTM and may even amplify its effects.…”

Social learning and the demise of costly cooperation in humans

“…We used absolute differences to avoid the problem of regression to the mean, which we return to later [58].…”

“…This is because such a pattern of behaviour is expected even by chance, through a phenomenon known as 'regression to the mean' [58]. If the behaviour of individuals is varying, even randomly, then on average, individuals who initially cooperate at relatively 'high' or 'low' values will subsequently cooperate at values closer to the mean.…”