SDPM: Sequential Dual Process Model

In ream: Density, Distribution, and Sampling Functions for Evidence Accumulation Models

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)

Arguments

rt	vector of response times
resp	vector of responses ("upper" and "lower")
phi	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). 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}). Stimulus strength (\mu). Stimulus strength of process 2 (\mu_2). Noise scale (\sigma). Model scaling parameter. Effective noise scale of continuous approximation (\sigma_{eff}). See ream publication for full description. 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. 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}. 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.
x_res	spatial/evidence resolution
t_res	time resolution
n	number of samples
dt	step size of time. We recommend 0.00001 (1e-5)

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).

Author(s)

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)

ream documentation built on Oct. 7, 2024, 1:20 a.m.