ream (version 1.0-5)

LIMF: Leaky Integration Model With Flip

Description

LIM with time varying drift rate. Specifically, the stimulus strength changes from \(\mu_1\) to \(\mu_2\) at time \(t_0\). Identified by (Evans et al., 2020; Trueblood et al., 2021) as a way to improve recovery of the leakage rate. Drift rate becomes \(v(x,t) = \mu_1 - L*x\) if \(t < t_0\) and \(v(x,t) = \mu_2 - L*x\) if \(t >= t_0.\)

Usage

dLIMF(rt, resp, phi, x_res = "default", t_res = "default")
pLIMF(rt, resp, phi, x_res = "default", t_res = "default")
rLIMF(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 1 (\(\mu_1\)). Strength of the stimulus prior to \(t_0\).

4. Stimulus strength 2 (\(\mu_2\)). Strength of the stimulus after \(t_0\).

5. Log10-leakage (\(log_{10}(L)\)). Rate of leaky integration.

6. Flip-time (\(t_0\)). Time when stimulus strength changes.

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

8. 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 \(a = 2b\).

9. 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 \(f_i(t)\).

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

11. 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

Evans, N. J., Trueblood, J. S., & Holmes, W. R. (2019). A parameter recovery assessment of time-variant models of decision-making. Behavior Research Methods, 52(1), 193-206.

Trueblood, J. S., Heathcote, A., Evans, N. J., & Holmes, W. R. (2021). Urgency, leakage, and the relative nature of information processing in decision-making. Psychological Review, 128(1), 160-186.

Examples

# Probability density function
dLIMF(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, 1.0, 0.5, 0.0, 0.0, 1.0))

# Cumulative distribution function
pLIMF(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, 1.0, 0.5, 0.0, 0.0, 1.0))

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