ream (version 1.0-5)

SDPM: Sequential Dual Process Model

Description

The Sequential Dual Process Model (SDPM) is similar in principle to the DSTP, but instead of simultaneous accumulators, it contains sequential accumulator s. Its drift rate is given by \(v(x,t) = w(t)*\mu\) where \(w(t)\) is 0 if the second process hasn't crossed a threshold yet and 1 if it has. The noise scale has a similar structure \(D(x,t) = w(t)*\sigma\).

Usage

dSDPM(rt, resp, phi, x_res = "default", t_res = "default")
pSDPM(rt, resp, phi, x_res = "default", t_res = "default")
rSDPM(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. Relative start of the target selection process (\(w_{ts}\)). Sets the start point of accumulation for the target selection process as a ratio of the two decision thresholds. Related to the absolute start \(z_{ts}\) point via equation \(z_{ts} = b_{lts} + w_ts*(b_{uts} – b_{lts})\).

4. Stimulus strength (\(\mu\)).

5. Stimulus strength of process 2 (\(\mu_2\)).

6. Noise scale (\(\sigma\)). Model scaling parameter.

7. Effective noise scale of continuous approximation (\(\sigma_{eff}\)). See ream publication for full description.

8. 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 \(a = 2b\).

9. Target selection decision thresholds (\(b_{ts}\)). Sets the location of each decision threshold for the target selection process. The upper threshold \(b_{uts}\) is above 0 and the lower threshold \(b_{lts}\) is below 0 such that \(b_{uts} = -b_{lts} = b_{ts}\). The threshold separation \(a_{ts} = 2b_{ts}\).

10. 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 \(f_i(t)\).

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

12. 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

Hübner, R., Steinhauser, M., & Lehle, C. (2010). A dual-stage two-phase model of selective attention. Psychological Review, 117(3), 759-784.

Examples

# Probability density function
dSDPM(rt = c(1.2, 0.6, 0.4), resp = c("upper", "lower", "lower"),
      phi = c(0.3, 1.0, 0.5, 1.0, 1.0, 1.0, 1.0, 0.75, 0.75, 0.0, 0.0, 1.0))

# Cumulative distribution function
pSDPM(rt = c(1.2, 0.6, 0.4), resp = c("upper", "lower", "lower"),
      phi = c(0.3, 1.0, 0.5, 1.0, 1.0, 1.0, 1.0, 0.75, 0.75, 0.0, 0.0, 1.0))

# Random sampling
rSDPM(n = 100, phi = c(0.3, 1.0, 0.5, 1.0, 1.0, 1.0, 1.0, 0.75, 0.75, 0.0, 0.0, 1.0),
      dt = 0.001)