DMC: 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)

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:

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)

Author

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

Run this code

# 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))

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