ream (version 1.0-5)

SSP: Shrinking Spotlight Model

Description

The SSP is an evidence accumulation model developed to study cognition in conflict tasks like the Eriksen flanker task. It is based on theories of visual attention and assumes that attention acts like a shrinking spotlight which is gradually narrowed on the target. It maintains all SDDM parameters outside of the drift rate. A full description of the model is in the REAM publication.

Usage

dSSP(rt, resp, phi, x_res = "default", t_res = "default")
pSSP(rt, resp, phi, x_res = "default", t_res = "default")
rSSP(n, phi, dt = 1e-05)

Value

For the density a list of PDF values, log-PDF values, and the sum of the log-PDFs, for the distribution function a list of of CDF values, log-CDF values, and the sum of the log-CDFs, and for the random sampler a list of response times (rt) and response thresholds (resp).

Arguments

rt

vector of response times

resp

vector of responses ("upper" and "lower")

phi

parameter vector in the following order:

1. 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.

2. 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 \(z = b_l + w*(b_u - b_l)\).

3. Width of the attentional spotlight (\(sd_{a0}\)). Initial standard deviation of the attentional process.

4. Linear rate of spotlight decrease (\(r_d\)). Spotlight width \(sd_a(t) = sd_{a0} - r_d*t\).

5. Congruency parameter (\(c\)). In congruent condition \(c = 1\), in incongruent condition \(c = -1\), and in neutral condition \(c = 0\).

6. Lower bound of target’s attentional allocation (\(lb_{target}\)). Typically fixed to -0.5.

7. Upper bound of target’s attentional allocation (\(ub_{target}\)). Typically fixed to 0.5.

8. Upper bound of inner units attentional allocation (\(ub_{inner}\)). Typically fixed to 1.5.

9. Perceptual input strength of target (\(p_{target}\)).

10. Perceptual input strength of inner units (\(p_{inner}\)).

11. Perceptual input strength of outer units (\(p_{outer}\)).

12. Noise scale (\(\sigma\)). Model noise scale parameter.

13. 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 \(a = 2b\).

14. 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 \(f_i(t)\).

15. Lower bound of contamination distribution (\(g_l\)). See parameter \(g\).

16. Upper bound of contamination distribution (\(g_u\)). See parameter \(g\).

x_res

spatial/evidence resolution

t_res

time resolution

n

number of samples

dt

step size of time. We recommend 0.00001 (1e-5)

Author

Raphael Hartmann & Matthew Murrow

References

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.

Examples

# Probability density function
dSSP(rt = c(1.2, 0.6, 0.4), resp = c("upper", "lower", "lower"),
     phi = c(0.3, 0.5, 1.0, 7.5, -1.0, -0.5, 0.5, 1.5, 3.75, 3.75, 3.75, 1.0,
             0.75, 0.0, 0.0, 1.0))

# Cumulative distribution function
pSSP(rt = c(1.2, 0.6, 0.4), resp = c("upper", "lower", "lower"),
     phi = c(0.3, 0.5, 1.0, 7.5, -1.0, -0.5, 0.5, 1.5, 3.75, 3.75, 3.75, 1.0,
             0.75, 0.0, 0.0, 1.0))

# Random sampling
rSSP(n = 100, phi = c(0.3, 0.5, 1.0, 7.5, -1.0, -0.5, 0.5, 1.5, 3.75, 3.75, 3.75,
                      1.0, 0.75, 0.0, 0.0, 1.0))