Table 2.
Mathematical modeling characteristics of the 16 included studies.
| References | Dependent variable | Mathematical models | Level of analysis |
|---|---|---|---|
| Bickel et al. (2016) | k-values | Equation 1 | Aggregate |
| Bidewell et al. (2006) | Average amount of money sacrificed for early retirement | NA | Aggregate |
| Dixon et al. (2018) | IP & AUC | Equations 1, 2 | Individual & Aggregate |
| Duan et al. (2017)-ex2 | k-values | Equation 1 | Aggregate |
| Hernández-Toledano et al. (2025) | k-values & AUC* | Equation 1 | Aggregate |
| Hesketh (2000)-ex2 | k-values & Average of percentage match point by delay | Equations 1, 3 | Aggregate |
| Joshi and Fast (2013)-ex1 | k-values | Equation 1 | Aggregate |
| Lahav et al. (2011) | Annual subjective discount rate | NA | Aggregate |
| Logue and Anderson (2001) | k-values & IP | Equation 1 | Aggregate |
| Losina et al. (2017) | k-values | Equation 1 | Aggregate |
| Mellis et al. (2018a) | k-values | Equation 1 | Aggregate |
| Mellis et al. (2018b) | k-values | Equation 1 | Aggregate |
| Saunders and Fogarty (2001) | Point of change | NA | Individual & Aggregate |
| Shavit et al. (2013) | Annual subjective discount rate | NA | Aggregate |
| Weißmüller (2022) | k-values & h-values | Equation 1 | Aggregate |
| Xu and Yin (2020) | IP & Area above the curve | NA | Aggregate |
Equation 1: Hyperbolic (Mazur, 1987). Equation 2: Hyperboloid (Myerson and Green, 1995). Equation 3 Exponential (Samuelson, 1937). NA, no applicable; IP, indifference points; AUC, area under the curve. Studies in bold reported fit indicators for the mathematical models used. *AUC calculated with Killeen's method 2023.