WDSTP: Weibull Dual-Stage Two-Phase Model of Selective Attention

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

Weibull Dual-Stage Two-Phase Model of Selective Attention

Description

A continuous approximation of the Dual-Stage Two-Phase model of conflict tasks. The Dual-Stage Two-Phase model assumes that choice in conflict tasks involves two processes: a decision process and a target selection process. Unlike the CDSTP, the target selection process here is a Weibull cumulative distribution function. The decision process is an SDDM but with drift rate

v(x,t) = (1 - w(t))*(\mu_t + c*\mu_{nt}) + w(t)*\mu_2,

where w(t) = 0 before target selection and w(t) = 1 after target selection. A full derivation of this model is in the ream publication.

Usage

dWDSTP(rt, resp, phi, x_res = "default", t_res = "default")

pWDSTP(rt, resp, phi, x_res = "default", t_res = "default")

rWDSTP(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). Relative start of the target selection process (w_{ts}). Sets the start point of accumulation for the target selection process as a ratio of the two decision thresholds. Related to the absolute start z_{ts} point via equation z_{ts} = b_{lts} + w_ts*(b_{uts} – b_{lts}). Target stimulus strength (\mu_t). Congruence parameter (c). Set experiment congruency. In congruent condition c = 1, in incongruent condition c = -1, and in neutral condition c = 0. Non-target stimulus strength (\mu_{nt}). Drift rate following target selection i.e. stage 2 (\mu_2). Scale parameter for Weibull function (\lambda). Shape parameter for Weibull function (\kappa). 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. Target selection decision thresholds (b_{ts}). Sets the location of each decision threshold for the target selection process. The upper threshold b_{uts} is above 0 and the lower threshold b_{lts} is below 0 such that b_{uts} = -b_{lts} = b_{ts}. The threshold separation a_{ts} = 2b_{ts}. 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

Hübner, R., Steinhauser, M., & Lehle, C. (2010). A dual-stage two-phase model of selective attention. Psychological Review, 117(3), 759-784.

Examples

# Probability density function
dWDSTP(rt = c(1.2, 0.6, 0.4), resp = c("upper", "lower", "lower"),
       phi = c(0.3, 0.5, 1.0, 1.0, -1.0, -0.5, 8.0, 1.0, 1.0, 1.0, 2.0, 1.3, 0.0, 0.0, 1.0))

# Cumulative distribution function
pWDSTP(rt = c(1.2, 0.6, 0.4), resp = c("upper", "lower", "lower"),
       phi = c(0.3, 0.5, 1.0, 1.0, -1.0, -0.5, 8.0, 1.0, 1.0, 1.0, 2.0, 1.3, 0.0, 0.0, 1.0))

# Random sampling
rWDSTP(n = 100, phi = c(0.3, 0.5, 1.0, 1.0, -1.0, -0.5, 8.0, 1.0, 1.0, 1.0, 2.0, 1.3,
                        0.0, 0.0, 1.0))

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