PAM: Piecewise Attention Model

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

Piecewise Attention Model

Description

The PAM (aka dual-process model) is an evidence accumulation model developed to study cognition in conflict tasks like the Eriksen flanker task. It is similar to the SSP, but instead of a gradual narrowing of attention, target selection is discrete. Its total drift rate is

v(x,t) = 2*a_{outer}*p_{outer} + 2*a_{inner}*p_{inner} + a_{target}*p_{target},

where a_{inner} and a_{outter} are 0 if t >= t_s and 1 otherwise. The PAM otherwise maintains the parameters of the SDDM.

Usage

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

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

rPAM(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). Perceptual input strength of outer units (p_{outer}). Perceptual input strength of inner units (p_{inner}). Perceptual input strength of target (p_{target}). Target selection time (t_s). Noise scale (\sigma). Model noise scale 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

White, C. N., Ratcliff, R., & Starns, J. J. (2011). Diffusion models of the flanker task: Discrete versus gradual attentional selection. Cognitive Psychology, 63(4), 210-238.

Examples

# Probability density function
dPAM(rt = c(1.2, 0.6, 0.4), resp = c("upper", "lower", "lower"),
     phi = c(0.25, 0.5, -0.3, -0.3, 0.3, 0.25, 1.0, 0.5, 0.0, 0.0, 1.0))

# Cumulative distribution function
pPAM(rt = c(1.2, 0.6, 0.4), resp = c("upper", "lower", "lower"),
     phi = c(0.25, 0.5, -0.3, -0.3, 0.3, 0.25, 1.0, 0.5, 0.0, 0.0, 1.0))

# Random sampling
rPAM(n = 100, phi = c(0.25, 0.5, -0.3, -0.3, 0.3, 0.25, 1.0, 0.5, 0.0, 0.0, 1.0))

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