Discounting model selection with area-based measures: A case for numerical integration

A novel method for analyzing delay discounting data is proposed. This newer metric, a model-based Area Under Curve (AUC) combining approximate Bayesian model selection and numerical integration, was compared to the point-based AUC methods developed by Myerson, Green, and Warusawitharana (2001) and extended by Borges, Kuang, Milhorn, and Yi (2016). Using data from computer simulation and a published study, comparisons of these methods indicated that a model-based form of AUC offered a more consistent and statistically robust measurement of area than provided by using point-based methods alone. Beyond providing a form of AUC directly from a discounting model, numerical integration methods permitted a general calculation in cases when the Effective Delay 50 (ED50) measure could not be calculated. This allowed discounting model selection to proceed in conditions where data are traditionally more challenging to model and measure, a situation where point-based AUC methods are often enlisted. Results from simulation and existing data indicated that numerical integration methods extended both the area-based interpretation of delay discounting as well as the discounting model selection approach. Limitations of point-based AUC as a first-line analysis of discounting and additional extensions of discounting model selection were also discussed.