Fig 1.
Illustrations of the drift-diffusion and LCA models and their dynamics.
A) The drift-diffusion model (DDM), implemented as two accumulators with feed-forward inhibition, an upper absorbing boundary and a zero activation reflecting boundary [33]; B) The LCA model with two accumulators, mutual-inhibition, leak and zero-activation reflective boundary [3]; C,D) representative example activation trajectories (with Gaussian noise) for the two models.
Fig 2.
Simulation of typical temporal weighting profiles predicted by the drift-diffusion model (DDM) and leaky-competing accumulators model (LCA).
A) DDM simulations with absorbing bound (red line; parameters: noise = 1; boundary = 2) and reflecting bound (blue line; parameters: noise = 1; boundary = 3) as compared to ideal integration (black line; parameters: noise = 1; response was determined by comparing the value of the accumulator to 0). Both models predict weighs that are flat, monotonically decreasing (a primacy bias; bounded diffusion) or monotonically increasing (a recency bias; reflecting boundaries) temporal weights; B) LCA simulations of temporal weights with inhibition dominance (red line; parameters: noise = 1; inhibition = 0.2; leak = 0) and leak dominance (blue line; parameters: noise = 1; inhibition = 0; leak = 0.1) as compared to ideal integration (black line). Y-axis depicts normalized regression coefficients. Inputs to the models were taken from the experiments; responses of each model were simulated for all trials and were subjected to a logistic regression analysis using the inputs as predictors. We iterated this analysis 1000 times per each model and show here average values of the regression coefficients across these 1000 simulations.
Fig 3.
Stimuli and experimental design.
A) Illustration of the stimuli in Experiment-1: Participants were presented with two disks which fluctuated in brightness, and were requested to choose the overall brighter disk at the end of each trial; B-C) Illustration of a congruent signal-perturbation in the 4th temporal window (blue shaded; B) and an incongruent perturbation in the 5th window (red shaded; C) in 2 sec trials. Solid lines depict brightness level after a perturbation, dashed horizontal lines illustrate the baseline brightness levels for the correct (blue) and incorrect (red) responses. Dashed vertical lines show the temporal windows (4 frames in the 2-sec trials).
Fig 4.
Temporal-integration profiles in Exp. 1, for the different trial durations (1, 2 and 3 seconds).
Y-axis shows the relative influence of the signal-perturbation on accuracy, as compared to baseline (see text);X-axis depicts the 5 temporal-windows each corresponds to 1/5 of a trial); error bars denote 1 within-participant S.E.M [39].
Fig 5.
Temporal weighting profile for the 3-sec perceptual decisions in experiment-2 and 3 (data collapsed).
Error bars denote 1 within-participant S.E.M [39].
Fig 6.
Inter-subjective correlation between temporal-bias and accuracy.
Table 1.
Summary of the model comparison.
Fig 7.
Data and models’ predictions of temporal weight index (left panel) and regression weights (right panel) in 3-sec trials.
A) Observed temporal weights (N = 33; error bars denote 1 within-participant S.E.M; [39]); B) Predictions of the Dynamic LCA (DLCA); C) Predictions of the LCA; D) Predictions of the DDM with cf. Fig 2.
Fig 8.
DLCA’s predicted temporal weights as a function of trial-duration (2-, 3- and 5-sec trials).
The model’s predictions were generated using the best-fitting parameters that were obtained by fitting the DLCA to the decisions observed in the 3-sec trials.
Fig 9.
Observed (left panel) and predicted (right panel) accuracy per trial duration in Exp.1. Error bars denote 1 within-participant S.E.M [39].
Accuracy was calculated based on actual samples; the model's predictions were generated using the best-fitting parameters that were obtained by fitting the DLCA to the 3-sec trials.