UGMF: Urgency Gating Model With Flip

Description

UGM with time varying drift rate. Specifically, the stimulus strength changes from $E_{01}$ to $E_{02}$ at time $t_0$. Identified by (Trueblood et al., 2021) as a way to improve recovery of the leakage rate and urgency. Drift rate becomes $$v(x,t) = E_{01}*(1 + k*t) + (k/(1+k*t) - L)*x \ \text{ if } \ t < t_0$$ and $$v(x,t) = E_{02}*(1 + k*t) + (k/(1+k*t) - L)*x \ \text{ if } \ t >= t_0.$$

Usage

dUGMF(rt, resp, phi, x_res = "default", t_res = "default")
pUGMF(rt, resp, phi, x_res = "default", t_res = "default")
rUGMF(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 $z = b_l + w*(b_u - b_l)$.
Stimulus strength before the flip ($E_{01}$).
Stimulus strength after the flip ($E_{02}$).
Log10-leakage ($log_{10}(L)$). Rate of leaky integration.
Log10-urgency ($log_{10}(k)$). Decision urgency. If $k$ is small, the choice is dominated by leakage and approximates a LIM. If $k$ is large, it is an urgency dominated decision.
Flip-time ($t_0$). Time when stimulus strength changes.
Noise scale ($\sigma$). Model scaling 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

Cisek, P., Puskas, G. A., & El-Murr, S. (2009). Decisions in changing conditions: the urgency-gating model. Journal of Neuroscience, 29(37), 11560-11571.

Trueblood, J. S., Heathcote, A., Evans, N. J., & Holmes, W. R. (2021). Urgency, leakage, and the relative nature of information processing in decision-making.

Examples

Run this code

# Probability density function
dUGMF(rt = c(1.2, 0.6, 0.4), resp = c("upper", "lower", "lower"),
      phi = c(0.3, 0.5, 1.0, 0.9, 0.5, 0.5, 0.5, 1.0, 1.5, 0.0, 0.0, 1.0))

# Cumulative distribution function
pUGMF(rt = c(1.2, 0.6, 0.4), resp = c("upper", "lower", "lower"),
      phi = c(0.3, 0.5, 1.0, 0.9, 0.5, 0.5, 0.5, 1.0, 1.5, 0.0, 0.0, 1.0))

# Random sampling
rUGMF(n = 100, phi = c(0.3, 0.5, 1.0, 0.9, 0.5, 0.5, 0.5, 1.0, 1.5, 0.0, 0.0, 1.0))

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