Figure 1.
(a) Delayed reward offers corresponded with one of five different levels of discounted value. Each level of discounted value corresponded to one of five probabilities of choosing the delayed reward: 0.1, 0.3, 0.5, 0.7 or 0.9. (b) Every delay could be combined with any of five different amounts to yield a different discounted value and probability of choosing the delayed reward. (c) Delay and amount information was presented sequentially. Delays were presented first for 1000 ms. Amounts were presented second, replacing the presentation of the delay and remaining on the screen for a maximum of 4000 ms. After every trial, a fixation cross was presented on the center of the screen for a randomly chosen inter-trial-interval in the order of hundreds of milliseconds during the EEG experiment and several seconds during the fMRI experiment.
Figure 2.
Illustrative diagram of the Linear Ballistic Accumulator model for intertemporal choice, where each response option is represented as a separate accumulator.
Following the presentation of a stimulus and some non-decision time , information accumulates ballistically for each alternative. A decision is made that coincides with the accumulator that reaches the threshold
first. The model assumes trial-to-trial variation in both starting point and drift rate.
Table 1.
Mean Bayesian predictive information criterion fit statistics for each model variant we tested (standard deviations of the BPIC values computed across chains appear in parentheses).
Figure 3.
A comparison of model fits to empirical data.
The top row shows the aggregated posterior predictive distribution (densities) overlaid on the aggregated empirical data (histograms). The response time distribution for the immediate reward is plotted on the left (i.e., with a negative axis; red), whereas the delayed reward is plotted on the right (green). The choice probability can be inferred by comparing the relative heights of the two distributions. The bottom row shows the same distributions as overlapping density functions with corresponding colors. The model fits are shown as black densities. The median response times for the empirical data are shown as the dashed vertical lines with corresponding colors.
Figure 4.
Relationships between model parameters, choice probability, and RT statistics.
The left panel shows the estimated group level non-decision time parameter for each value condition. The middle and right panels show the maximum a posteriori (MAP) estimate for each subject's non-decision time parameter against their minimum and median response time, respectively.
Figure 5.
Relationships between model parameters, choice probability, and discounted value.
The left panel shows the estimated group level drift rate for each value condition. The middle panel shows the maximum a posteriori (MAP) estimate for each subject's drift rate against observed choice probabilities for the delayed reward (). The right panel shows the MAP estimate as a function of subject-specific discounted values for the delayed reward (
).