Delay Discounting k is Not a Unitless Metric

Discounting analysis has offered countless insights into behavioral health outcomes and continues to draw transdisciplinary attention as a reliable descriptor of decision-making. This paper highlights an analytical issue that may be underappreciated, namely, that the delay discounting parameter (i.e., k) carries units which are not reported in the vast majority of studies, leading potentially to errors in cross-study or test-retest comparisons. Delay discounting analyses conventionally use nonlinear modeling to arrive at a discounting rate that describes subject-level tolerance of temporal reward constraints. This brief report explores the relation between delay discounting k, delay value (i.e., D), and psychophysical scalar (i.e., s) logically and via data manipulation. We reanalyze three extant delay discounting datasets across a variety of discounting assessment methods using systematically different regression delay values. Results support the notion that k retains the reciprocal of time as a unit, where k is modified as D-1 or D-s, pending model mathematical configuration. Researchers should report units on discounting parameters and take care of this potential confound when selecting an appropriate descriptive model and comparing discounting rates across contexts.