Dynamic visbility time and evidence model (dynaViTE)

The decision is based on a DDM: A Wiener process X, which is bounded between 0 and a, starts at a starting point (za, 0<z<1) and evolves with a diffusion constant s and drift rate v. The mean drift rate depends on the stimulus identity S, which is either -1 or 1, and the discriminability of the stimulus d, precisely E[v]=Sd. The drift rate is normally distributed between trials with standard deviation sv. In addition, the starting point of X (z) varies uniformly around its mean with range sz.

As soon as the process reaches one of the boundaries (time T), a choice R is triggered: T = min{t| X(t)=a or X(t)=0}. R=1, if X(T)=a, and R=-1, if X(T)=0. Therefore, the accuracy can be determined by S==R.

Post-decisional accumulation: After the response is triggered the Wiener process X continues to evolve for a fixed period of time (tau). The final accumulated decision evidence (X(T+tau)-za) is then scaled by the response direction R (such that positive values always indicate support for the decision, when R=-1) to inform confidence. (In the two-stage signal detection theory (2DSD; Pleskac & Busemeyer, 2010), confidence would be based on this variable.)

Parallel accumulation of evidence about difficulty (visibility): There is a second Wiener process, V, which always starts at 0 and evolves with a diffusion constant svis. Its drift rate is normally distributed between trials with a mean equal to the discriminability d and standard deviation sigvis. The process has no bounds and evolves until the decision process is also finished, i.e. the evidence from this process is V(T+tau).

Computation of confidence: Confidence is computed as a weighted sum between the evidence from the decision process and visibility process, divided by some power of the total accumulation time:

conf = ( wR(X(T+tau)-za) + (1-w) V(T+tau) ) / ( (T+tau)^lambda).

Here 0<w<1 is a weight parameter for the decision and visibility evidence and lambda>0 is the penalization parameter for the accumulation time.

Observed response times: Observed response times for the decision (without confidence judgments), are assumed to include an additional non-decision time component TN, which varies uniformly with minimum t0 and range st0, i.e. RT= T + TN. If confidence and decision are reported simultaneously, the observed response time is the sum of decision time, post-decisional accumulation time and non-decision time component, i.e. RT= T+tau+TN.

The discriminability is assumed to be varied experimentally.