Support for the Time-Varying Drift Rate Model of Perceptual Discrimination in Dynamic and Static Noise Using Bayesian Model-Fitting Methodology

Abstract

The drift-diffusion model (DDM) is a common approach to understanding human decision making. It considers decision making as accumulation of evidence about visual stimuli until sufficient evidence is reached to make a decision (decision boundary). Recently, Smith and colleagues proposed an extension of DDM, the time-varying DDM (TV-DDM). Here, the standard simplification that evidence accumulation operates on a fully formed representation of perceptual information is replaced with a perceptual integration stage modulating evidence accumulation. They suggested that this model particularly captures decision making regarding stimuli with dynamic noise. We tested this new model in two studies by using Bayesian parameter estimation and model comparison with marginal likelihoods. The first study replicated Smith and colleagues' findings by utilizing the classical random-dot kinomatogram (RDK) task, which requires judging the motion direction of randomly moving dots (motion discrimination task). In the second study, we used a novel type of stimulus designed to be like RDKs but with randomized hue of stationary dots (color discrimination task). This study also found TV-DDM to be superior, suggesting that perceptual integration is also relevant for static noise possibly where integration over space is required. We also found support for within-trial changes in decision boundaries ("collapsing boundaries"). Interestingly, and in contrast to most studies, the boundaries increased with increasing task difficulty (amount of noise). Future studies will need to test this finding in a formal model.

Keywords: Bayesian cognitive modelling; perceptual decision making; perceptual integration; selective influence.

Figure A1

Cumulative density functions (CDF), average error rate (ER), and conditional accuracy functions (CAF) for the data and both models averaged over participants in the RDK task. The error bar shows the 95% credible interval, indicating the variability in the distributional measures due to the uncertainty of the parameter estimates (posterior distribution).

Figure A2

Cumulative density functions (CDF), average error rate (ER), and conditional accuracy functions (CAF) for the data and both models averaged over participants in the RDP task. The error bar shows the 95% credible interval, indicating the variability in the distributional measures due to the uncertainty of the parameter estimates (posterior distribution).

Figure 1

Example random-dot kinematogram (RDK) stimulus. In the typical RDK task, participants are presented with a field of randomly moving dots and asked to judge the motion direction of the coherently moving (blue) dots. The noise present (i.e., difficulty) is manipulated by varying the percentage of coherently moving dots relative to randomly moving (grey) dots. Here, arrows indicate direction of movement and colors are for illustrative purposes only.

Figure 2

Schematic diagram of the drift-diffusion model. Blue (red) traces represent the noisy evidence accumulation process for correct (incorrect) trials and histograms show the resulting reaction-time distributions. If the process hits the upper (lower) boundary, a correct (error) response is made.

Figure 3

Illustration of the gamma function for a range of parameter settings.

Figure 4

(a) Adjusted HSL color space. Areas marked ‘X’ are areas from which noise dot hues could be sampled, while target colors were true red or true cyan. (b) Example RDPs for each noise level and target color.

Figure 5

Average response time and error rate for the motion discrimination and color discrimination task for each level of noise.

Figure 6

Cumulative density functions (CDF), average error rate (ER), and conditional accuracy functions (CAF) for the data and both models averaged over participants in the RDK task. The 95% credible interval is shown for these results are shown in Appendix A.

Figure 7

Strength and direction of model evidence for the motion discrimination (RDK) and color discrimination (RDP) tasks. Note that since we fit the models to each participant/noise level individually, the columns sum to the total number of participants (N = 46 for motion discrimination and N = 36 for color discrimination).

Figure 8

Average expected a posteriori (EAP) estimates for DDM and TV-DDM. The solid lines indicate a significant effect of noise in both measures, the one-way ANOVA and the posterior overlap indicator. The asterisk indicates a significant effect when considering the one-way ANOVA only. The error bars indicated the 95% credible interval to illustrate the uncertainty of EAP estimates (see method section).

Figure 9

Cumulative density functions (CDF), average error rate (ER), and conditional accuracy functions (CAF) for the data and both models averaged over participants in the RDP task. The 95% credible intervals for these results are shown in Appendix A.