ream (version 1.0-5)

SDDM: Simple Drift Diffusion Model

Description

Density (PDF), distribution function (CDF), and random sampler for the simple drift diffusion model (SDDM) without across-trial variabilities.

Usage

dSDDM(rt, resp, phi, x_res = "default", t_res = "default")
pSDDM(rt, resp, phi, x_res = "default", t_res = "default")
rSDDM(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. Stimulus strength (\(\mu\)). Strength of the stimulus and used to set the drift rate. For the SDDM, \(v(x,t) = \mu\).

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

5. 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 \(a = 2b\).

6. 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 \(f_i(t)\).

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

8. 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

Ratcliff, R. (1978). A theory of memory retrieval. Psychological Review, 85(2), 59-108.

Ratcliff, R., & McKoon, G. (2008). The Diffusion Decision Model: Theory and Data for Two-Choice Decision Tasks. Neural Computation, 20(4), 873-922.

Examples

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

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

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