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

Area of Science:

• Behavioral economics
• Decision science
• Psychology

Background:

• Delay discounting quantifies preference for immediate rewards.
• Current point-based Area Under Curve (AUC) methods have limitations in accurately measuring discounting behavior.
• Existing methods struggle with data that is challenging to model.

Purpose of the Study:

• To introduce and evaluate a novel model-based Area Under Curve (AUC) metric for analyzing delay discounting data.
• To compare the proposed model-based AUC with traditional point-based AUC methods.
• To assess the utility of numerical integration in delay discounting analysis.

Main Methods:

• Developed a model-based AUC metric integrating approximate Bayesian model selection and numerical integration.
• Compared the novel AUC metric against established point-based AUC methods (Myerson et al., 2001; Borges et al., 2016).
• Utilized computer simulations and analysis of a published dataset for validation.

Main Results:

• The model-based AUC demonstrated more consistent and statistically robust measurements compared to point-based AUC alone.
• Numerical integration enabled AUC calculation even when the Effective Delay 50 (ED50) measure was not computable.
• The approach facilitated discounting model selection in challenging data conditions.

Conclusions:

• Model-based AUC, particularly with numerical integration, provides a superior method for analyzing delay discounting.
• This novel approach enhances the interpretation of delay discounting and improves model selection capabilities.
• Limitations of point-based AUC are highlighted, suggesting the model-based method as a preferred alternative.