Generate a grid of response-time values and the corresponding PDF values.
For more details on the model see, for example, dRTM.
dRTM_grid(rt_max = 10, phi, x_res = "default", t_res = "default")list of RTs and corresponding defective PDFs at lower and upper threshold
maximal response time <- max(rt)
parameter vector in the following order:
Non-decision time (\(t_{nd}\)). Time for non-decision processes such as stimulus encoding and response execution. Total decision time t is the sum of the decision and non-decision times.
Relative start (\(w\)). Sets the start point of accumulation as a ratio of the two decision thresholds. Related to the absolute start z point via equation \(z = b_l + w*(b_u - b_l)\).
Stimulus strength (\(\mu\)). Strength of the stimulus and used to set the drift rate. For changing threshold models \(v(x,t) = \mu\).
Noise scale (\(\sigma\)). Model noise scale parameter.
Initial decision threshold location (\(b_0\)). Sets the location of each decision threshold at time \(t = 0\).
Amount of decision threshold collapse (\(\kappa\)).
Semi-saturation constant (\(t_{0.5}\)). The semi-saturation constant is the value of time at which the boundaries have collapsed by half \(\kappa\).
Contamination (\(g\)). Sets the strength of the contamination process. Contamination process is a uniform distribution \(f_c(t)\) where \(f_c(t) = 1/(g_u-g_l)\) if \(g_l <= t <= g_u\) and \(f_c(t) = 0\) if \(t < g_l\) or \(t > g_u\). It is combined with PDF \(f_i(t)\) to give the final combined distribution \(f_{i,c}(t) = g*f_c(t) + (1-g)*f_i(t)\), which is then output by the program. If \(g = 0\), it just outputs \(f_i(t)\).
Lower bound of contamination distribution (\(g_l\)). See parameter \(g\).
Upper bound of contamination distribution (\(g_u\)). See parameter \(g\).
spatial/evidence resolution
time resolution
Raphael Hartmann & Matthew Murrow
Churchland, A. K., Kiani, R., & Shadlen, M. N. (2008). Decision-making with multiple alternatives. Nature Neuroscience, 11(6), 693-702.
Hanks, T. D., Mazurek, M. E., Kiani, R., Hopp, E., & Shadlen, M. N. (2011). Elapsed Decision Time Affects the Weighting of Prior Probability in a Perceptual Decision Task. The Journal of Neuroscience, 31(17), 6339-6352.
Voskuilen, C., Ratcliff, R., & Smith, P. L. (2016). Comparing fixed and collapsing boundary versions of the diffusion model. Journal of Mathematical Psychology, 73, 59-79.