Discounting model selection with area‐based measures: A case for numerical integration
Use the new model-based AUC to keep your delay-discounting data clean even when ED50 is missing.
01Research in Context
What this study did
Gilroy et al. built a new way to measure delay discounting. They used computer math called numerical integration instead of old point-counting.
They tested the new tool on fake data sets and on real studies that were already published. The goal was to see if the new area-under-curve (AUC) gave cleaner answers when the old ED50 value could not be found.
What they found
The model-based AUC beat the old point-based AUC every time. It stayed steady even when data were messy or had missing points.
When they re-ran past papers, the new numbers told the same story but with less noise. That means fewer Type-I errors for you.
How this fits with other research
Jarus et al. (2015) used a two-step method to pull apart time and risk. Gilroy keeps the same idea but swaps in the stronger AUC, so you can now handle tricky data in one step.
Yeh et al. (2025) took the new AUC idea and stretched it to choices that mix delay and risk. Their single equation hit R² = .99, showing the tool works outside pure delay tasks.
Cairney et al. (2011) warned that kappa breaks when base rates are extreme. Gilroy gives the same kind of fix—trade the old statistic for a tougher one when the data fight back.
Why it matters
If you run delay-discounting probes with kids or adults who skip questions or give wild numbers, switch to the model-based AUC. You will keep more data, cut false positives, and make cleaner graphs for treatment teams or funding reports. One free script does the math; no new software needed.
Want CEUs on This Topic?
The ABA Clubhouse has 60+ free CEUs — live every Wednesday. Ethics, supervision & clinical topics.
Join Free →Download the Gilroy R code, re-run last month’s discounting file, and compare the new AUC column to your old one.
02At a glance
03Original abstract
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.
Journal of the Experimental Analysis of Behavior, 2018 · doi:10.1002/jeab.318