Time estimation variability in delay discounting: Model comparison and considerations

Delay discounting describes an organism's sensitivity to delayed consequences. The advent of hyperboloid discounting models introduced the s discounting parameter, a fitted metric that reduces residual variance when working with human subjects. Mathematically, discounting s allows for a nonlinear relation between consequence (A) and delay (D) and could be conceptually accounted for as a psychophysical scalar that describes subjective differences in the rate of time passage. This study offers a proof-of-concept examination of hyperboloid s in relation to participant time-based experiences. A crowdsourced sample of adults (N = 211) completed tasks measuring time estimation (i.e., reporting how much time passed during a distractor task) and temporal distance estimation (i.e., reporting how temporally distant a delay feels). Participants generally underestimated durations in the time estimation task, where income and completion of a preceding day-framed discounting task (versus date-framed), but not Myerson and Green's s (b = -0.19), and modestly Rachlin's s (b = 0.82), exhibited a statistically significant relation with time estimation accuracy. Similarly, participant age and delay framing, but not hyperboloid s, exhibited a statistically significant relation with temporal distance estimation discrepancies. Broadly, data suggest that s may not be accounting for differences in time estimation as measured in this sample. At most, the modest effect observed for Rachlin's s suggests limited conceptual value, meriting further consideration of the metric's account of subject-level differences.