Addressing the interdependency of k and s parameters in hyperboloid discounting models using modified regression procedures and half-life calculations

Document Type

Thesis

College

College of Arts and Sciences

Department

Psychology

Degree

M.S. Applied Behavior Analysis

Date Completed

2021

First Committee Member

Bourret, Jason

Second Committee Member

Henley, Amy

Third Committee Member

Pinkston, Jonathan

Abstract

"Two-parameter hyperboloid models provide better fits for delay discounting data than the single-parameter hyperbolic model, but the free parameters of the hyperboloid models, k and s, are independent, making within or between-subject comparisons challenging. In order to make comparisons using these parameters, either the s parameter values must be held constant so that the k parameters can be compared, or the half-life value must be calculated using the two parameters. We examined two methods for holding the s parameter constant and compared the resulting k parameters to area under the curve (AUC) data. We also used, model parameters to calculate half-life values and those were also compared to AUC. The results of these comparisons showed that problems due to interdependency in k and s estimation can be resolved by either holding s constant across comparisons or using half-life values rather than k as measures of discounting rate. We found that half-life data are more closely correlated with AUC data than k data determined using a common s parameter. The implications support the use of half-life measures from hyperboloid discounting models to make comparisons of delay discounting across individuals or commodities."

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