Contrast manipulation used in the experiment

Top shows two example stimuli illustrating minimum (left) and maximum (right) contrast values. Bottom panel shows the prediction for the Piéron, the Fechner and the linear laws for all contrast levels (C) used in the study for a fixed set of parameters. α, β and V are respectively the estimated participant specific intercept, slope and exponent for the three laws. The Fechner diffusion law additionally includes non-decision and decision threshold parameters (see methods).

Square root of the mean prediction error (milliseconds) from the leave-one-out procedure for each interval and model for both instructions (bold indicates the best model).

The R2 (italic) refers to the fit of the predicted vs. observed mean durations.

behavioral results partially support Fechner’s law

Left: Mean RT (dot) and average fit (line) over trials and participants for each contrast level used in the study 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).

HMP estimation reveals three sequential cognitive events

Top: model components with the inter-event interval distributions estimated for all participants (left) and the weights of each electrode towards each event (right).

Bottom: Trial and participant averaged cumulative event occurrence probabilities for the three detected hidden multivariate events. Overlaid is the average representation of the time location (vertical lines) and electrode contribution of the three identified events based on their by-trial maximum probability.

Summary of the linear mixed models coefficients with the maximum a posteriori and the 95% credible intervals in parentheses for the linear mixed models on intervals (top) and electrode match (bottom) for each event (Ev.).

Inter-event interval as a function of experimental factors

The four first panels represent the trial and participant averaged duration between events (stimulus and response respectively as first and last events). The lines represent the fits for the linear (black), Piéron (green) and Fechner (yellow) models. Winning model line is represented as thicker than the other for each panel. The right most panel shows the observed proportion of correct responses (triangles) compared to the prediction (lines) from the Fechner diffusion model fit to each inter-event duration (color saturation indicates order of the interval).

Single trial surface plot of the decision related event

A) Topographical map of the last event, based on the electrode activity at the by-trial most likely time of the event, averaged over trials and participants. B) Spatial filtering using the last event obtained by the dot product between electrode weights of the last event in A) with the single-trial activity of each electrode at all time points resulting in the match between the event topography and the signal (see example timeseries for the first trial of the first participant). C) Surface plot of the match for all trials for speed and accuracy instructions. Zscoring was performed after applying a Gaussian window over 50 trials and with a standard deviation of 20.

Electrophysiological analysis of the time leading to each event

For each HMP detected event we used the average topographies (top panel) as a spatial filter for the samples from the by-trial event peak time down to the average time of the previous event (vertical lines). For each speed and accuracy instructions, all trials were averaged across 10 bins of contrast values. To statistically test for an effect of contrast we performed a non-parametric cluster-level paired t-test for high (> 50%) vs. low (< 50%) contrasts. Significant clusters are marked as dots in the lower part of each panel.

Simulating ramp and expecting a half-sine

Top: Representation of the averaged times and topographies for the three events detected by HMP on the simulated accumulation data. Bottom: Trial and participant averaged time-course of the electrodes matched to the third HMP event. 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. Dots indicate significant differences between high (> 50%) and low (< 50%) contrast values.