Decision-making components and times revealed by the single-trial electroencephalogram
- University of Groningen, Netherlands
- Utrecht University, Netherlands
Figures
Figure 1
Contrast manipulation used in the experiment.
Top shows two example stimuli illustrating minimum (left) and maximum (right) contrast values. The bottom panel shows the prediction for the Piéron, the Fechner, and the linear laws for all contrast levels () used in the study for a fixed set of parameters. The y-axis refers to the time predicted by each law given a contrast value (x-axis) and the chosen set of parameters. , , and are respectively the estimated participant-specific intercept, slope, and exponent for the three laws. The Fechner diffusion model additionally includes nondecision and decision threshold parameters (see ‘Materials and methods’).
Figure 2
Behavioral results partially support Fechner’s law.
Left: mean RT (dot) for each contrast level and averaged predictions of the individual fits (line) with accuracy (top) and speed (bottom) instructions. Right: mean proportion of correct responses averaged over trials and participant for each contrast level (triangles) along the average predicted proportions for the Fechner diffusion models (line) in accuracy (top) and speed (bottom).
Figure 3
Hidden multivariate pattern (HMP) estimation reveals five sequential cognitive events.
Top: trial and participant-averaged cumulative event occurrence probabilities (gray lines) for the five detected hidden multivariate events. Overlaid is the average representation of the time location (vertical lines) and electrode contribution of the five identified events based on their trial-by-trial maximum probability. Bottom: t-values from one-sample t-tests on the by-participant differences for each symmetric electrode pair for each event. White dots indicate electrode pairs that deviate significantly from 0 after a Bonferroni correction with a base alpha level of 0.05 (corrected p-value = 0.00071), black dots denote nonsignificant electrode pairs.
Figure 4
Inter-event interval as a function of experimental factors.
(A) The panels represent the average duration between events for each contrast level, averaged across participants and trials (stimulus and response respectively as first and last events) for accuracy (top) and speed instructions (bottom). The lines represent the fits for the linear (black), Piéron (green), and Fechner (yellow) models. Winning model lines are represented as thicker than the other for each panel. (B) Same as in (A) but with similar intervals summed together to form encoding (Ev.1-Ev2+Ev.2-Ev.3) and decision (Ev.3-Ev4+Ev.4-Ev.5) times. (C) Observed proportion of correct responses (triangles) compared to the prediction (lines) from the Fechner diffusion model fit to the decision interval in (B).
Figure 5
Electrophysiological analysis of the time leading to each event.
(A) Stimulus-centered event-related potentials (ERPs) obtained by averaging three electrodes in occipital, parietal, and frontal areas across trials and participants for 10 binned contrast levels in both speed–accuracy instructions. Vertical lines indicate the average peak time of each hidden multivariate pattern (HMP) event (later = darker). To statistically test for an effect of contrast, we performed a nonparametric cluster-level paired t-test for high (> 50%) vs. low (< 50%) contrasts on the participant-averaged waveforms. Significant clusters are marked as black dots at the corresponding times in each panel. (B) Illustration of the event match computation. A single-trial match time series (right-most panel) is obtained by taking the dot product between the single-trial electrode time series and the weights of an events’ average topography. (C) HMP detected events time courses obtained by using the average topographies (top panel) as a spatial filter for the stimulus onset to 100 ms after the single-trial event peak time. For each speed–accuracy instruction, the data is presented at the single-trial level (surface plot), with trials sorted by the single trial most likely peak time of the event, and averaged across trials for 10 contrast bins after aligning to the most likely peak time of the event (waveform plot). On the surface plot, a z-scoring was performed after applying a Gaussian window over 50 trials and with a standard deviation of 20. Black lines represent the peak(s) of previous or following events, relative to the event used as spatial filter, obtained from a rolling mean over 50 trials.
Box 1—figure 1
Both the intercepts and slopes of the linear models predict the proportion of correct responses with correlation coefficients ranging from 0.38 to 0.61 (all p-values < 0.001).
Appendix 1—figure 1
Simulating a ramp or a half-sine and expecting a half-sine.
(A) Representation of the averaged times and topographies for the three events detected by HMP on the downsampled real data. (B) Trial and participant-averaged topography (top panels) and time courses (bottom panels) of the electrodes matched to the third HMP event for the ramp simulation (left panels) vs. the half-sine simulation (right panels). As in the main text, the trials were first centered on the peak of the third event before computing the average ERP for the different contrast values binned into 10 bins.
Tables
Table 1
Square root of the mean prediction error (milliseconds) from the leave-one-out procedure for the models applied to the intervals between each event (Ev.) including stimulus onset (S.) and response (R.).
Bold indicates the best model per interval. The in parentheses refers to the fit of the predicted vs. observed mean durations. Prop. corr. refers to the for the proportion of correct responses observed vs. the proportion predicted by the fit of the Fechner diffusion model to each interval.
| RT | S.-Ev.1 | Ev.1 - Ev.2 | Ev.2 - Ev.3 | Ev.3 - Ev.4 | Ev.4 - Ev.5 | Ev.5 - R. | Encoding | Decision | |
|---|---|---|---|---|---|---|---|---|---|
| Accuracy | |||||||||
| Linear | 44.37 (0.81) | 1.64 (0.13) | 5.08 (0.17) | 5.78 (0.13) | 42.91 (0.81) | 7.27 (0.37) | 0.68 (0.08) | 7.26 (0.15) | 45.52 (0.81) |
| Píeron | 89.93 (0.07) | 1.77 (–0.01) | 4.81 (0.27) | 5.63 (0.17) | 86.91 (0.07) | 8.85 (0.05) | 0.70 (0.01) | 6.60 (0.30) | 92.15 (0.08) |
| Fechner | 41.24 (0.85) | 1.80 (0.00) | 5.55 (0.01) | 6.38 (–0.07) | 39.20 (0.85) | 7.12 (0.40) | 0.73 (0.00) | 8.05 (–0.07) | 40.10 (0.86) |
| Prop. corr. | (0.84) | (–5.75) | (–7.90) | (–6.68) | (0.83) | (–1.76) | (–6.63) | (–7.76) | (0.83) |
| Speed | |||||||||
| Linear | 18.02 (0.39) | 1.81 (0.14) | 4.19 (0.33) | 5.51 (0.22) | 16.37 (0.49) | 5.51 (0.33) | 0.66 (0.11) | 8.18 (0.34) | 18.23 (0.53) |
| Píeron | 23.22 (0.00) | 1.79 (0.14) | 3.76 (0.47) | 4.83 (0.38) | 21.99 (0.07) | 6.44 (0.09) | 0.69 (0.04) | 6.64 (0.57) | 25.37 (0.07) |
| Fechner | 19.91 (0.27) | 1.90 (0.04) | 4.90 (0.06) | 6.06 (0.05) | 16.89 (0.45) | 5.12 (0.43) | 0.66 (0.12) | 9.27 (0.12) | 18.16 (0.52) |
| Prop. corr. | (0.03) | (–3.58) | (–3.61) | (–4.12) | (0.17) | (0.19) | (–2.49) | (–4.73) | (0.66) |
Table 2
Summary of the linear mixed models coefficients with the mean and the 95% credible intervals from the posterior distributions for the linear mixed models on intervals for each event (Ev.) including stimulus onset (S.) and response (R.).
| Interval | Intercept | Contrast | SAT | Contrast × SAT |
|---|---|---|---|---|
| S.-Ev.1 | 34.69 (33.25, 36.15) | -0.90 (–2.49, 0.60) | 0.61 (–0.64, 1.73) | 2.36 (0.41, 4.55) |
| Ev.1–Ev.2 | 71.66 (67.57, 75.62) | –7.49 (–11.38, –3.86) | 5.65 (3.32, 8.06) | 0.67 (–3.98, 5.39) |
| Ev.2–Ev.3 | 93.97 (88.72, 99.61) | –8.10 (–12.87, -2.64) | 7.80 (3.80, 11.82) | 3.68 (–2.57, 10.35) |
| Ev.3–Ev.4 | 260.10 (225.28, 292.15) | 46.07 (9.27, 86.43) | 175.28 (121.63, 233.48) | 249.76 (154.58, 344.71) |
| Ev.4–Ev.5 | 82.48 (76.53, 88.85) | 11.88 (6.16, 17.51) | 16.85 (11.93, 22.27) | 6.21 (–1.35, 13.13) |
| Ev.5–R. | 13.31 (12.77, 13.84) | 0.36 (-0.19, 0.89) | 1.34 (0.91, 1.79) | –0.32 (–1.12, 0.52) |
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Decision-making components and times revealed by the single-trial electroencephalogram
eLife 14:RP108049.
https://doi.org/10.7554/eLife.108049.3
