An analysis of discounting model selection methods: Assessing the generalization of discounting models

Bailey et al. (2025) ran computer simulations to test which statistic best picks the true discounting model.

They compared AIC, BIC, and leave-one-out cross-validation (LOOCV) under many fake data sets.

Each fake set came from a known model, so the team could see how often each statistic chose the right one.

AIC, BIC, and LOOCV all found the real model most of the time.

LOOCV paired with multilevel modeling gave the lowest cross-validation error when the Rachlin hyperboloid was in play.

If you fit discounting curves, LOOCV with multilevel is the safest pick.

Bigby et al. (2009) asked the same question for IOA algorithms: which one gets you closest to the truth? Their answer was “it depends,” because no algorithm won every time. Bailey’s team got a clearer win for LOOCV, showing model choice can be more straightforward than IOA choice.

Kubina et al. (2022) also looked at analyst tools, but for graphs instead of equations. They found ratio graphs beat linear ones for speed and agreement. Bailey’s paper extends that theme—better tools give faster, cleaner decisions—now for model fit instead of visual trend.

Chang et al. (2024) and Zhi et al. (2023) compared acquisition criteria in single-case designs. Like Bailey, they ran systematic replications to refine measurement rules. All three studies push the same bottom line: small changes in how we score data can save time without hurting accuracy.

If you plot delay-discounting curves for adults or kids, you need to pick between the hyperboloid, exponential, or other forms. Use LOOCV with multilevel modeling and you are less likely to pick the wrong curve. That means cleaner data stories and better treatment decisions when reward timing matters.