Create the Diffusion Model for Conflict Tasks

This function creates a drift_dm object that corresponds to the Diffusion Model for Conflict Tasks by Ulrich et al. (2015) .

Usage

dmc_dm(
  var_non_dec = TRUE,
  var_start = TRUE,
  instr = NULL,
  obs_data = NULL,
  sigma = 1,
  t_max = 3,
  dt = 0.0075,
  dx = 0.02,
  b_coding = NULL
)

Arguments

var_non_dec, var_start: logical, indicating whether the model should have a normally-distributed non-decision time or beta-shaped starting point distribution, respectively. (see nt_truncated_normal and x_beta in component_shelf). Defaults are TRUE. If FALSE, a constant non-decision time and starting point is set (see nt_constant and x_dirac_0 in component_shelf).
instr: optional string with "instructions", see modify_flex_prms().
obs_data: data.frame, an optional data.frame with the observed data. See obs_data.
sigma, t_max, dt, dx: numeric, providing the settings for the diffusion constant and discretization (see drift_dm)
b_coding: list, an optional list with the boundary encoding (see b_coding)

Value

An object of type drift_dm (parent class) and dmc_dm (child class), created by the function drift_dm().

Details

The Diffusion Model for Conflict Tasks is a model for describing conflict tasks like the Stroop, Simon, or flanker task.

It has the following properties (see component_shelf):

a constant boundary (parameter b)
an evidence accumulation process that results from the sum of two subprocesses:
- a controlled process with drift rate muc
- a gamma-shaped process with a scale parameter tau, a shape parameter a, and an amplitude A.

If var_non_dec = TRUE, a (truncated) normally distributed non-decision with mean non_dec and standard deviation sd_non_dec is assumed. If var_start = TRUE, a beta-shaped starting point distribution is assumed with shape and scale parameter alpha.

If var_non_dec = TRUE, a constant non-decision time at non_dec is set. If var_start = FALSE, a starting point centered between the boundaries is assumed (i.e., a dirac delta over 0).

Per default the shape parameter a is set to 2 and not allowed to vary. This is because the derivative of the scaled gamma-distribution function does not exist at t = 0 for a < 2. Currently, we recommend keeping a fixed to 2. If users decide to set a != 2, then a small value of tol = 0.001 (default) is added to the time vector t_vec before calculating the derivative of the scaled gamma-distribution as originally introduced by Ulrich et al. (2015) . Users can control this value by passing a value via ddm_opts() (see the example below). Note, however, that varying a can lead to large numerical inaccuracies if a gets smaller.

The model assumes the amplitude A to be negative for incompatible trials. Also, the model contains the custom parameter peak_l, containing the peak latency ((a-2)*tau).

Note

The scaling of the parameters in dRiftDM is different to Ulrich et al. (2015) . This is because dRiftDM works in seconds and with a diffusion constant of 1, while the original DMC parameterization is in milliseconds and with a diffusion constant of 4. We describe how to convert the parameters on our website.

References

Ulrich R, Schröter H, Leuthold H, Birngruber T (2015). “Automatic and controlled stimulus processing in conflict tasks: Superimposed diffusion processes and delta functions.” Cognitive Psychology, 78, 148–174. doi:10.1016/j.cogpsych.2015.02.005 .

Examples

# the model with default settings
my_model <- dmc_dm()

# the model with no variability in the starting point and a finer
# discretization
my_model <- dmc_dm(var_start = FALSE, dt = .005, dx = .01)

# we don't recommend this, but if you really want a != 2, just do...
# (see the Details for more warnings/information about this)
my_model <- dmc_dm(instr = "a ~!")
coef(my_model)["a"] <- 1.9
# -> if you want to control the small value that is added to t_vec when
# calculating the drift rate for a != 2, just use ...
ddm_opts(my_model) <- 0.0001 # ==> t_vec + 0.0001
ddm_opts(my_model) <- NULL # default ==> t_vec + 0.001