Learn More From Your Data With Asymptotic Regression

Abstract

All measures of behavior have a temporal context. Changes in behavior over time often take a similar form: monotonically decreasing or increasing toward an asymptote. Whether these behavioral 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, behavioral dynamics, 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 two existing data sets and a set of new visual search data. An important limit of asymptotic regression is that it cannot be applied to data that are stationary or change nonmonotonically. But for data that have performance changes that progress steadily toward an asymptote, as many behavioral measures do, it is a simple and powerful tool for describing those changes.