Generate a grid of response-time values and the corresponding PDF values.
For more details on the model see, for example, dSSP.
dSSP_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 \(z = b_l + w*(b_u - b_l)\).
Width of the attentional spotlight (\(sd_{a0}\)). Initial standard deviation of the attentional process.
Linear rate of spotlight decrease (\(r_d\)). Spotlight width \(sd_a(t) = sd_{a0} - r_d*t\).
Congruency parameter (\(c\)). In congruent condition \(c = 1\), in incongruent condition \(c = -1\), and in neutral condition \(c = 0\).
Lower bound of target’s attentional allocation (\(lb_{target}\)). Typically fixed to -0.5.
Upper bound of target’s attentional allocation (\(ub_{target}\)). Typically fixed to 0.5.
Upper bound of inner units attentional allocation (\(ub_{inner}\)). Typically fixed to 1.5.
Perceptual input strength of target (\(p_{target}\)).
Perceptual input strength of inner units (\(p_{inner}\)).
Perceptual input strength of outer units (\(p_{outer}\)).
Noise scale (\(\sigma\)). Model noise scale parameter.
Decision thresholds (\(b\)). Sets the location of each decision threshold. The upper threshold \(b_u\) is above 0 and the lower threshold \(b_l\) is below 0 such that \(b_u = -b_l = b\). The threshold separation \(a = 2b\).
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
White, C. N., Ratcliff, R., & Starns, J. J. (2011). Diffusion models of the flanker task: Discrete versus gradual attentional selection. Cognitive Psychology, 63(4), 210–238.