A tribute to Howard Rachlin and his two-parameter discounting model: Reliable and flexible model fitting

Delay discounting reflects the rate at which a reward loses its subjective value as a function of delay to that reward. Many models have been proposed to measure delay discounting, and many comparisons have been made among these models. We highlight the two-parameter delay discounting model popularized by Howard Rachlin by demonstrating two key practical features of the Rachlin model. The first feature is flexibility; the Rachlin model fits empirical discounting data closely. Second, when compared with other available two-parameter discounting models, the Rachlin model has the advantage that unique best estimates for parameters are easy to obtain across a wide variety of potential discounting patterns. We focus this work on this second feature in the context of maximum likelihood, showing the relative ease with which the Rachlin model can be utilized compared with the extreme care that must be used with other models for discounting data, focusing on two illustrative cases that pass checks for data validity. Both of these features are demonstrated via a reanalysis of discounting data the authors have previously used for model selection purposes.