Learn more from your data with asymptotic regression

All measures of behaviour have a temporal context, and the context often takes a similar form: monotonically decreasing or increasing towards an asymptote. Whether these behavioural dynamics are the object of study or a nuisance variable, their inclusion in models of data makes conclusions more complete, robust and well-specified, and can contribute to theory development. Here we demonstrate that asymptotic regression is a relatively simple tool that can be applied to repeated-measures data to estimate three parameters: starting point, rate of change, and asymptote. Each of these parameters has a meaningful interpretation in terms of ecological validity, learning and performance limits, respectively. They can also be used to help decide how many trials to include in an experiment, and as a principled approach to reducing noise in data. We demonstrate the broad utility of asymptotic regression for modeling the effect of the passage of time within a single trial, and for changes over trials of an experiment, using four simple examples from existing data. An important limit of asymptotic regression is that it cannot be applied to data that is stationary or changes non-monotonically. But for data that has performance changes that progress steadily towards an asymptote, as many behavioural measures do, it is a simple and powerful tool for describing those changes.