CDSTP: Continuous Dual-Stage Two-Phase Model of Selective Attention

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

Continuous 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. The target selection process is an SDDM, while 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

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

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

rCDSTP(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). Target selection drift rate (\mu_{ts}). Noise scale (\sigma). Model scaling parameter. Effective noise scale of continuous approximation (\sigma_{eff}). See ream publication for full description. 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.

Examples

# Probability density function
dCDSTP(rt = c(1.2, 0.6, 0.4), resp = c("upper", "lower", "lower"),
       phi = c(0.3, 0.5, 0.5, -0.5, -1.0, -0.5, 8.0, 4.0, 1.0, 2.0, 1.3, 1.3, 0.0, 0.0, 1.0))

# Cumulative distribution function
pCDSTP(rt = c(1.2, 0.6, 0.4), resp = c("upper", "lower", "lower"),
       phi = c(0.3, 0.5, 0.5, -0.5, -1.0, -0.5, 8.0, 4.0, 1.0, 2.0, 1.3, 1.3, 0.0, 0.0, 1.0))

# Random sampling
rCDSTP(n = 100, phi = c(0.3, 0.5, 0.5, -0.5, -1.0, -0.5, 8.0, 4.0, 1.0, 2.0, 1.3, 1.3,
                        0.0, 0.0, 1.0), dt = 0.001)

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