Formal Comparison of Dual-Parameter Temporal Discounting Models in Controls and Pathological Gamblers

Jan Peters,Stephan Franz Miedl,Christian Büchel,Giuseppe Di Pellegrino

doi:10.1371/journal.pone.0047225

Jan Peters, Stephan Franz Miedl + Show 2 more

Open Access

https://doi.org/10.1371/journal.pone.0047225

Copy DOI

Abstract

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.

Highlights

Delay or temporal discounting refers to the phenomenon that humans and many animals discount reward value over time [1]
We applied several model comparison procedures: 1) comparison of R2 based on model fits to group-aggregate and single-subject indifference points [10], 2) examination of group aggregate [41] and mean individual DAIC scores 3) a randomeffects Bayesian model comparison [56,65]
The first approach was included primarily to improve accessibility of this report for researchers more familiar with more classical model selection procedures, and because this procedure is still widely applied in the psychological literature on temporal discounting [10,15,20]

Summary

Introduction

Delay or temporal discounting refers to the phenomenon that humans and many animals discount reward value over time [1]. According to the exponential model (Table 1, Eq 2), a waiting period of 1 week from today should be treated the same way as a waiting period of 1 week in a year’s time In contrast to this prediction of ‘‘normative’’ exponential discounting, and in line with hyperbolic discounting, humans often violate this assumption, an effect that has been termed ‘‘dynamic inconsistency’’ [19], the ‘‘common difference effect’’ [11], or ‘‘non-stationarity’’. In line with this effect, it is well replicated that the hyperbolic model fits temporal discounting data better than the exponential model [1,10,14,16,20,21,22,23]

Methods

Results

Conclusion