Multialternative drift-diffusion model predicts the relationship between visual fixations and choice in value-based decisions

Abstract

How do we make decisions when confronted with several alternatives (e.g., on a supermarket shelf)? Previous work has shown that accumulator models, such as the drift-diffusion model, can provide accurate descriptions of the psychometric data for binary value-based choices, and that the choice process is guided by visual attention. However, the computational processes used to make choices in more complicated situations involving three or more options are unknown. We propose a model of trinary value-based choice that generalizes what is known about binary choice, and test it using an eye-tracking experiment. We find that the model provides a quantitatively accurate description of the relationship between choice, reaction time, and visual fixation data using the same parameters that were estimated in previous work on binary choice. Our findings suggest that the brain uses similar computational processes to make binary and trinary choices.

Fig. 1.

(A) Task. Subjects were forced to fixate at the center of the screen for 2 s before the trial commenced, and were then presented with images of three food items and given as much time as needed to make a choice. After a selection was made, a yellow box highlighted the chosen item for 1 s. Fixations were recorded at 50 Hz. (B) Model. An RDV is computed for each item based on the evidence accumulated for that item compared with the highest accumulated evidence for the other items. The average rate of evidence accumulation is higher for an item when it is fixated on than when it is not. In addition to the average accumulation rate, there is also noise drawn from a Gaussian distribution. When one of the RDVs hits its barrier at +1, then that item is chosen. In this particular simulation of the model we assumed r^left = 3, r^center = 5, and r^right = 7, and it was simulated with an exaggerated signal-to-noise ratio (larger d and smaller σ) for illustrative purposes.

Fig. 2.

Basic psychometrics. (A) Psychometric choice curve for the left item relative to the average rating of the other two items. (B) Psychometric choice curve for the left item relative to the worst-rated item. (C) Reaction time and (D) number of fixations as a function of the difference in liking ratings between the maximum rated item and the average of the other two items. In all panels, the axes were cut short whenever less than half of the subjects had any observations at those values. The red dashed lines indicate the simulated model. Bars denote SEs.

Fig. 3.

Model prediction and choice biases. (A) Probability that the last fixation is to the chosen item as a function of the difference in liking ratings between the last seen item and the average of the other two items. (B) Difference in time spent looking at the unchosen items compared with the chosen item, before the last fixation, as a function of the duration of that last fixation. (C) Probability that left is chosen as a function of the excess amount of time that the left item was fixated on during the trial and (D) the same but for a model with θ = 1 in which there is no fixation bias. (E) Probability that the first-seen item is chosen as a function of the duration of that first fixation. The values are rounded to the nearest 200 ms, so the bars correspond to 0–100 ms, 100–300 ms, 300–500 ms, and 500–700 ms. (F) Fixation duration by type. Middle fixations are any fixations that are not the first, second, or last fixations of the trial. Bars denote SEs. The red dashed lines indicate the simulated model. P values are based on paired two-sided t tests.

Fig. 4.

Fixation properties. (A) Fraction of fixations to items with the maximum, middle, and minimum ratings as a function of fixation number from the beginning of the trial, and (B) from the end of the trial (0 indicates the final fixation). (C) Fraction of fixations to the left, center, and right items as a function of fixation number from the beginning of the trial and (D) from the end of the trial (0 indicates the final fixation). (E) Histogram of the number of fixations that subjects made within a trial. Bars denote SEs. Tests are based on paired two-sided t tests against 33.33% for the two extremes in each panel (maximum and minimum, or left and right). *P = 0.05; **P = 0.0042 (Bonferroni corrected for the 12 tests in each panel), and ***P = 0.001 (Bonferroni corrected for all 48 tests in the figure).