LIMF: Leaky Integration Model With Flip

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

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)

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 1 (\mu_1). Strength of the stimulus prior to t_0. Stimulus strength 2 (\mu_2). Strength of the stimulus after t_0. Log10-leakage (log_{10}(L)). Rate of leaky integration. 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)

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

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))

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