LIM | R Documentation |
SDDM modified to encode leaky integration in the drift rate. Also known as an
Ornstein-Uhlenbeck model, its drift rate is v(x,t) = \mu - L*x
where L
is the
leakage rate. All other parameters are unchanged from the SDDM. Leakage describes
the rate at which old information is lost from the accumulator, occurring on a
time scale of approximately 1/L
. The LIM is used to model decay of excitatory
currents in decision neurons (Usher & McClelland, 2001; Wong & Wang, 2006) and
has been proposed as a mechanism for preference reversals under time pressure
(Busemeyer & Townsend, 1993). Due to its neural plausibility and simple functional
form, recent work has proposed it as an alternative psychometric tool to the SDDM
(Wang & Donkin, 2024).
dLIM(rt, resp, phi, x_res = "default", t_res = "default")
pLIM(rt, resp, phi, x_res = "default", t_res = "default")
rLIM(n, phi, dt = 1e-05)
rt |
vector of response times |
resp |
vector of responses ("upper" and "lower") |
phi |
parameter vector in the following order:
|
x_res |
spatial/evidence resolution |
t_res |
time resolution |
n |
number of samples |
dt |
step size of time. We recommend 0.00001 (1e-5) |
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).
Raphael Hartmann & Matthew Murrow
Busemeyer, J. R., & Townsend, J. T. (1993). Decision field theory: A dynamic-cognitive approach to decision making in an uncertain environment. Psychological Review, 100(3), 432-459.
Usher, M., & McClelland, J. L. (2001). The time course of perceptual choice: The leaky, competing accumulator model. Psychological Review, 108(3), 550-592.
Wang, J.-S., & Donkin, C. (2024). The neural implausibility of the diffusion decision model doesn’t matter for cognitive psychometrics, but the Ornstein-Uhlenbeck model is better. Psychonomic Bulletin & Review.
Wong, K.-F., & Wang, X.-J. (2006). A Recurrent Network Mechanism of Time Integration in Perceptual Decisions. The Journal of Neuroscience, 26(4), 1314-1328.
# Probability density function
dLIM(rt = c(1.2, 0.6, 0.4), resp = c("upper", "lower", "lower"),
phi = c(0.3, 0.5, 1.0, 0.5, 1.0, 0.5, 0.0, 0.0, 1.0))
# Cumulative distribution function
pLIM(rt = c(1.2, 0.6, 0.4), resp = c("upper", "lower", "lower"),
phi = c(0.3, 0.5, 1.0, 0.5, 1.0, 0.5, 0.0, 0.0, 1.0))
# Random sampling
rLIM(n = 100, phi = c(0.3, 0.5, 1.0, 0.5, 1.0, 0.5, 0.0, 0.0, 1.0))
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