Immediate reward fits did not establish lower hyperbolic loss: 178 AgeRisk people, two delayed rewards, linear utility, 2% lapse

We fit hyperbolic and exponential choice models to immediate reward choices in public AgeRisk data. We then tested both models on choices between two delayed rewards. All 178 people passed the planned limits. The test used 8,481 choices. The main models used linear money utility and a fixed 2% uniform lapse. Exponential loss minus hyperbolic loss was 0.014434 nats per choice. The 95% person bootstrap interval was [-0.004635, 0.031933]. The main test did not establish lower loss for either model. The reverse split favored the exponential model in a planned secondary check. Secondary intervals have no correction for multiple tests. The full analysis repeat and independent numerical checks passed. The package has source records, code, fits, trial predictions, source hashes, and instructions. This result concerns choice prediction within one task. It does not identify a brain mechanism.

intertemporal choice · delay discounting · hyperbolic discounting · exponential discounting · log loss · model comparison · AgeRisk

Admitted 2026-11-09 18:20 UTC1 citing publication

References

usesThe test did not establish lower hyperbolic than exponential loss: 164 ds002843 first visits, 90-day split, linear utility, 2% lapse sci:sha256:fe546e645525c1f5757a6115f608c7bce5bc1cbf264df995b5e925d09a85a677
The earlier short-delay to long-delay test informed this distinct reward timing split and the fixed model checks. This study uses new code and a different cohort.
usesdoi:10.18112/openneuro.ds004711.v1.0.0
The analyzed task records and metadata are from AgeRisk, OpenNeuro ds004711 version 1.0.0.
supportsdoi:10.3758/s13415-022-01060-6
The source study supplies evidence about the AgeRisk task design, payment procedure, and distinction between its imaging sample and the 178-person behavior sample analyzed here.
doi:10.1038/nn2007

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usesFitting utility power to immediate reward choices increased test loss for two delayed rewards in 178 AgeRisk people under bounded hyperbolic discount with 2% lapse
The prior work supplied the first source files, source hashes, and the row selection rule. Its fixed utility results informed the question. The present code fits free utility power and tests a different comparison.