Article Figures & Data
Figures
- Figure 1.
A, Food options presented to the participants before starting the DD task. Example of (B) money and (C) food DD task trials. During fMRI, participants had to choose between a smaller but immediate or a larger but delayed reward. In each trial, participants first saw a fixation cross in the center of the screen (2–8 s, in 1 s steps). The following presentation of the two reward options was ceased when participants pressed the button, resulting in a variable duration of the decision-making phase. The chosen option remained on the screen for 1 s before the next trial started (feedback phase). “In 1. Monat” means in one month; “Sofort” means now.
- Figure 2.
Plot of the posterior distribution of the hyperpriors k_Mu (Table 3) for the exponential discounting model with scaling in the food condition. The y-axis tracks the relative count of the parameter estimates, and the x-axis the estimated parameter value. The assumed normal distribution is not cutoff at the right side, which would have affected our sampling.
- Figure 3.
Model comparison for food and money discounting. In the plots on the left, red circles indicate WAIC scores (scaled as the negative log-likelihood), and the red line indicates standard deviations. The tables on the right list model-wise absolute WAIC scores.
- Figure 4.
Estimates for the difference in k (kfood − kmoney) between conditions. The 95% HDI is in the range [−0.1, 0] with a mean difference of −0.01259, indicating steeper discounting of food rewards.
- Figure 5.
Condition-specific brain activity. Money as compared with food discounting revealed significantly [i.e., p(FDR) < 0.05] enhanced activity in the right putamen, (i.e., dorsal striatum), right dorsolateral prefrontal cortex, and left hippocampus. For food as compared with money discounting, we found enhanced activity only in the left temporoparietal junction. For x, y, and z coordinates, cluster size (amount of activated voxels), and T-scores, please refer to Table 4.
- Figure 6.
Exemplary plot for two participants, a typical impulsive one with high k values (top row) and a less impulsive one with low k values (bottom row), showing the estimated indifference points (orange), the 95% HDI range of estimated parameters for the two-parameter exponential discounting model (green), and the one-parameter version (blue). The y-axis shows the estimated SVs for 40 units of food (2 plots on the left side) and money (right side). The x-axis shows the delay in days. The plots show that, even with varying levels of discounting, the two-parameter model better aligns with the estimated indifference points than the one-parameter model.
Tables
- Table 1.
Listed are the five SV discounting models: exponential and hyperbolic discounting, either with or without second scaling
Exponential discounting Hyperbolic discounting No time scaling Time scaling SV is the subjective value, A is the amount of options, k is the discounting factor that multiplies the value of reward, D is the time delay, and k is the degree of discounting. The scaling parameter s in the lower exponential discounting equation describes scaling of individual differences in delay and k (Loewenstein and Prelec, 1992; Rachlin, 1989; Green and Myerson, 2004; McKerchar et al., 2009; Peters et al., 2012). For hyperbolic discounting, scaling either affects just the time delay or it additionally considers k. Note that when s = 1, there is no time scaling, or in other words, the model with time scaling equals the model without scaling. When s is <1, the SV is more sensitive to changes at shorter delays and less sensitive to changes at longer delays (Frederick et al., 2002).
- Table 2.
Heuristic choice models (Wulff and van den Bos, 2018): The ITCH model contains four free parameters:
ITCH DRIFT TRADE Factor 1 Factor 2 Factor 3 Factor 4 SV(DEL)-SV(Immediate) = Factor 1 + Factor 2 + Factor 3 + Factor 4 Factor 1 + Factor 2 + Factor 3 + Factor 4 Factor 2 − Factor 4 For the DRIFT model,
SV parameter Mu range (uniform) SD range (uniform) Starting point (Mu, SD) K (normal) [E−10 |E−2] [10−2|3] E−2.5 |1 s (0|4] [0.01|3] 1|1 Heuristic models [−1,1] (0,1] 0.5|0.5 [−1,1] (0,1] 0.5|0.5 [−1,1] (0,1] 0.5|0.5 [−1,1] (0,1] 0.5|0.5 [−1,1] (0,1] 0.5|0.5 [−1,1] (0,1] 0.5|0.5 [−1,1] (0,1] 0.5|0.5 [−1,1] (0,1] 0.5|0.5 Inv-Logit Error (0,0.2] (0,0.2] 0.1|0.1 All parameters were normally distributed. Their mean (Mu) and standard deviation (SD) were uniformly distributed. Listed are the ranges of uniform distributions. Following standard range notation, round brackets indicate that the distribution does not include the given value and squared brackets indicate that the value is within the range, for example, [0, 1] would indicate a normal distribution with values larger than 0 that can include 1.
- Table 4.
Regions with significant higher activity for money as compared with food and vice versa
Name x y z k(cluster size) T Money > Food Hippocampus −36 −22 −18 296 4.21 dlPFC −32 34 36 912 4.06 Putamen 32 2 2 2,216 3.69 Food > Money TPJ −32 −30 12 256 3.91 The table lists regions’ topographic assignment, coordinates in MNI space, cluster size (i.e., amount of activated voxels), and the T values. dlPFC, dorsolateral prefronal cortex; TPJ, temporoparietal junction.
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