DMC: Diffusion Model for Conflict Tasks

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

Diffusion Model for Conflict Tasks

Description

The DMC is a two-process evidence accumulation model for the study of conflict tasks. It sums together a controlled and an automatic process to generate a single accumulator for generating the likelihood function. This accumulator has the same parameters as the SDDM with the exception of the drift rate, given by

v(x,t) = s*A*exp(-t/\tau)*[e*t/(\tau*(\alpha-1))]^{\alpha-1}*[(\alpha-1)/t - 1/\tau] + \mu_c.

Usage

dDMC(rt, resp, phi, x_res = "default", t_res = "default")

pDMC(rt, resp, phi, x_res = "default", t_res = "default")

rDMC(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). Coherence parameter (s). Sets stimulus coherence. If s = 1, coherent condition; if s = 0, neutral condition; if s = -1, incoherent condition. Automatic process amplitude (A). Max value of automatic process. Scale parameter (\tau). Contributes to time automatic process. Time to max t_{max} = (\alpha – 1)*\tau. Shape parameter (\alpha). Indicates the shape of the automatic process. Must have value more than 1 (\alpha > 1). Drift rate of the controlled process (\mu_c). 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.
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

Ulrich, R., Schröter, H., Leuthold, H., & Birngruber, T. (2015). Automatic and controlled stimulus processing in conflict tasks: Superimposed diffusion processes and delta functions. Cognitive psychology, 78, 148-174.

Examples

# Probability density function
dDMC(rt = c(1.2, 0.6, 0.4), resp = c("upper", "lower", "lower"),
     phi = c(0.3, 0.5, -1.0, 0.2, 0.05, 2.5, 3.0, 1.0, 0.5, 0.0, 0.0, 1.0))

# Cumulative distribution function
pDMC(rt = c(1.2, 0.6, 0.4), resp = c("upper", "lower", "lower"),
     phi = c(0.3, 0.5, -1.0, 0.2, 0.05, 2.5, 3.0, 1.0, 0.5, 0.0, 0.0, 1.0))

# Random sampling
rDMC(n = 100, phi = c(0.3, 0.5, -1.0, 0.2, 0.05, 2.5, 3.0, 1.0, 0.5, 0.0, 0.0, 1.0))

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