Fig 1.
The DDM assumes that evidence accumulates, from the starting point (S0), through random diffusion in combination with drift at a constant rate r until a boundary (i.e., threshold, θ) is reached (illustrated in blue). The Linear Approach to Threshold with Ergodic Rate (LATER) model (illustrated in red) makes the same assumptions, except that there is no random diffusion, but instead the rate r varies across trials (so as to explain trial-to-trial variability in RTs). In addition, a non-decision time (NDT) τ is added to the boundary crossing time on each trial, to capture time spent on everything else than the perceptual decision (e.g., the time to prepare and execute a selected motor response).
Fig 2.
Illustration of the search display and the positional inter-trial transitions. The circles were not part of the actual stimulus, but are only shown to illustrate how the items were positioned on a circle. On each trial, four out of eight possible locations were occupied by the search items, allowing the items to form either a square or a diamond arrangement.
Fig 3.
Mean response times for repeated/non-repeated color, target notch ‘orientation’ (the response- critical feature), and for the different positional transitions: target at previous target position (TT), target at previously neutral (i.e., empty) position (TN), and target at previous distractor position (TD). Error bars show the 95% confidence intervals. RCF: response-critical feature.
Fig 4.
Illustration of the hierarchical modeling framework.
Each hierarchical model consists of an evidence accumulation model (either the drift-diffusion model or the LATER model) and either no updating or one updating rule for each parameter of the evidence accumulation model (starting point S0, evidence accumulation rate r, and non-decision time τ). Each updating rule belongs to one of the four categories shown in the middle layer of the figure, and is applied to one of the three inter-trial updating variables shown in the blue box on the right side of the figure: the response-critical feature (RCF), the target-defining color, or the target position. For some of the updating rules based on the RCF or color, there are three different versions of the rule, differing in their degree of position-specificity (top level of the hierarchy). These rules could be fully position-independent (PI), fully position-dependent (PD), with a gradient-like dependence on the change of position (PG), or starting out fully position-dependent but then spreading (PS). See the main text for detailed descriptions.
Fig 5.
Model comparison for color-based updating.
Mean relative AIC for all different color-based updating rules when using the best updating rules for response-critical feature (RCF) and position. The dashed vertical line separates rules that update based on color alone (left) and rules that also take the target position into account (right). The different background colors mark rules that update either the rate (orange) or the non-decision time (green). Error bars represent the standard error of the mean over participants and sessions. PI: position-independent; PD: full position-dependent; PG: a gradient-like dependence on the change of position; NDT: Non-decision time.
Fig 6.
Model comparison for position-based updating.
Mean relative AIC for all different position-based updating rules when using the best updating rules for response-critical feature (RCF) and color. The different background colors mark rules that update either the rate (orange) or the non-decision time (green). Error bars represent the standard error of the mean over participants and sessions. DI: distractor inhibition; NDT: Non-decision time.
Fig 7.
Model comparison for response feature-based updating.
Mean relative AIC for all different RCF-based updating rules when using the best updating rules for color and position. The dashed vertical line separates rules that update based on the RCF alone (left) and rules that also take the target position into account (right). The different background colors mark rules that update either the starting point (blue), the rate (orange) or the non-decision time (green). Error bars represent the standard error of the mean over participants and sessions. PI: position-independent; PD: fully position-dependent; PG: a gradient-like dependence on the change of position; NDT: Non-decision time; S0: Starting point.
Fig 8.
Example of color-based updating.
Example of the weight changes to the different colors predicted by the weighted-rate updating rule for the first eight trials of a typical participant (A), and the associated changes in the evidence accumulation rate on the same eight trials (B). The letters “T” and “D” denote the target color and, respectively, the distractor color on each trial. The dashed line marks the baseline evidence accumulation rate. The evidence accumulation rate on each trial was the baseline rate scaled by the weight associated with the target position on that trial.
Fig 9.
Temporal profile of the color-based inter-trial effects.
Mean normalized RT for repeated vs. switched target color on (current) trial n compared to (preceding) trial n-1 (lag 1), n-2 (lag 2) up to n-8 (lag 8). Normalized RTs were first averaged across the two sessions for each participant; the resulting (individual mean normalized) RTs were then used to compute the overall means and confidence intervals, across participants. Filled circles depict the behavioral data, lines the model predictions. Error bars represent 95% confidence intervals.
Fig 10.
Example of position-based updating.
Example of the weight changes to the different positions predicted by the “weighted rate with distractor inhibition” updating rule for the first eight trials of a typical participant (A), and the associated changes in the evidence accumulation rate on the same eight trials (B). The letters “T” and “D” denote the target position and, respectively, the positions of the three distractors on each trial. The dashed line marks the baseline evidence accumulation rate. The evidence accumulation rate on each trial was the baseline rate scaled by the weight associated with the target position on that trial.
Fig 11.
Temporal profile of the position based inter-trial effects.
Mean normalized RT for different positional inter-trial conditions, target in previous target condition (TT), target in previous distractor position (TD), target in previously neutral (unoccupied) position (TN), compared to trial n-1 (lag 1), n-2 (lag 2) up to n-8 (lag 8). Normalized RTs were first averaged across the two sessions for each participant; the resulting (individual mean normalized) RTs were then used to compute the overall means and confidence intervals, across participants. Filled circles show the behavioral data, while lines show model predictions. Error bars represent 95% confidence intervals.
Fig 12.
Example of response-based updating.
Example of the starting point changes associated with the different positions predicted by the gradient-like dependence on the change of position (i.e., “PG Bayesian S0” updating rule) for the first eight trials of a typical participant (A), and the starting point for the target position on the same eight trials (B). The position of the triangles represent the target position on each trial, and the shape of the triangle indicates the response-critical feature (RCF, i.e., whether the notch was on the top or bottom of the target item).
Fig 13.
Temporal profile of the response feature-based inter-trial effects.
Mean normalized RT for repetition vs. switch of the response defining target feature (notch on top or bottom of the diamond shape), compared to trial n-1 (lag 1), n-2 (lag 2) up to n-8 (lag 8) for the different positional inter-trial conditions, target in previous target condition (TT), target in previous distractor position (TD), target in previously neutral (unoccupied) position (TN). Normalized RTs were first averaged across the two sessions for each participant; the resulting (individual mean normalized) RTs were then used to compute the overall means and confidence intervals, across participants. Filled circles show the behavioral data, while lines show model predictions. Error bars represent 95% confidence intervals. RCF: response-critical feature.
Table 1.
Average log-likelihood, across participants and sessions, for the best model and the no-update model, evaluated on the training set as well as on the test set, and the difference between the test and training set log-likelihood (right column).
The bottom column shows the difference in log-likelihood between the best model and the no-update model.