Formal comparison of dual-parameter temporal discounting models in controls and pathological gamblers

Temporal or delay discounting refers to the phenomenon that the value of a reward is discounted as a function of time to delivery. A range of models have been proposed that approximate the shape of the discount curve describing the relationship between subjective value and time. Recent evidence suggests that more than one free parameter may be required to accurately model human temporal discounting data. Nonetheless, many temporal discounting studies in psychiatry, psychology and neuroeconomics still apply single-parameter models, despite their oftentimes poor fit to single-subject data. Previous comparisons of temporal discounting models have either not taken model complexity into account, or have overlooked particular models. Here we apply model comparison techniques in a large sample of temporal discounting datasets using several discounting models employed in the past. Among the models examined, an exponential-power model from behavioural economics (CS model, Ebert & Prelec 2007) provided the best fit to human laboratory discounting data. Inter-parameter correlations for the winning model were moderate, whereas they were substantial for other dual-parameter models examined. Analyses of previous group and context effects on temporal discounting with the winning model provided additional theoretical insights. The CS model may be a useful tool in future psychiatry, psychology and neuroscience work on inter-temporal choice.