pfddm  R Documentation 
Density function for the Ratcliff diffusion decision model (DDM) with
following parameters: v
(drift rate), a
(threshold
separation), t0
(nondecision time/response time constant), w
(relative starting point), sv
(intertrial variability of drift), and
sigma
(diffusion coefficient of underlying Wiener process).
pfddm(
rt,
response,
v,
a,
t0,
w = 0.5,
sv = 0,
sigma = 1,
err_tol = 1e06,
log = FALSE,
method = "Mills"
)
rt 
A vector of response times (in seconds). If a response time is
nonpositve, then its density will evaluate to 
response 
Binary response(s) that correspond(s) to either the "lower" or "upper" threshold. This model parameter can either be a singular value or a vector. The value(s) in 'response' can be of the following data types:

v 
Drift rate. Average slope of the information accumulation process.
The drift gives information about the speed and direction of the
accumulation of information. Large (absolute) values of drift indicate a
good performance. If received information supports the response linked to
the upper threshold, then the sign will be positive; similarly a negative
value indicates that the received information supports the response linked
to the lower threshold. Allowed range: 
a 
Threshold separation. Amount of information that is considered for
a decision. Large values indicate a conservative decisional style. Allowed
range: 
t0 
Nondecision time or response time constant (in seconds). Lower
bound for the duration of all nondecisional processes (encoding and
response execution). If this value is greater than 
w 
Relative starting point. Indicator of an a priori bias in decision
making. When the relative starting point 
sv 
Intertrialvariability of drift rate. Standard deviation of a
normal distribution with mean 
sigma 
Diffusion coefficient of the underlying Wiener process. Allowed
range:
. 
err_tol 
Allowed error tolerance of the density function. Since the
density function contains an infinite sum, this parameter defines the
precision of the approximation to that infinite sum. If the provided
error tolerance is less than 
log 
Logical; if 
method 
Which method of calculating the CDF to use. Can be one of
{ 
All of the model inputs and parameters (rt
, response
,
v
, a
, t0
, w
, sv
, sigma
) can be
input as a single value or as a vector of values. If input as a vector of
values, then the standard R
input wrapping will occur.
sigma
 The default value of this parameter is 1
because it
only scales the parameters v
, a
, and sv
, as shown
above. However, other formulations of the DDM may set sigma = 0.1
(see Ratcliff (1978), the fourth reference), so care must be taken when
comparing the results of different formulations.
A vector containing the distribution of the DDM with precision
err_tol
whose length matches that of the longest input parameter
(usually rt
).
Navarro, D. J., & Fuss, I. G. (2009). Fast and accurate calculations for firstpassage times in Wiener diffusion models. Journal of Mathematical Psychology, 53(4), 222230.
Gondan, M., Blurton, S. P., & Kesselmeier, M. (2014). Even faster and even more accurate firstpassage time densities and distributions for the Wiener diffusion model. Journal of Mathematical Psychology, 60, 2022.
Blurton, S. P., Kesselmeier, M., & Gondan, M. (2017). The firstpassage time distribution for the diffusion model with variable drift. Journal of Mathematical Psychology, 76, 712.
Ratcliff, R. (1978). A theory of memory retrieval. Psychological review, 85(2), 59.
# minimal example
pfddm(rt = 1.2, response = "lower", a = 1, v = 1, t0 = 0.3)
# example with all function parameters set to default or a practical value
pfddm(rt = c(1.2, 0.9, 1.1, 1.4, 0.8, 1.3),
response = c("lower", "upper", "upper", "lower", "upper", "lower"),
a = 1, v = 1, t0 = 0.2, w = 0.5, sv = 0, sigma = 1,
err_tol = 1e6, log = FALSE, method = "Mills")
# example of mismatched input lengths
pfddm(rt = c(1.2, 0.9, 1.1, 1.4, 0.8, 1.3),
response = c("lower", "upper", "upper", "lower", "upper", "lower"),
a = c(1, 3), v = c(2, 2, 2, 2, 2, 2),
t0 = 0.3, w = c(0.4, 0.5, 0.6), sv = 0.9,
err_tol = 1e10, log = FALSE, method = "NCDF")
# example with Wiener diffusion coefficient (sigma) not equal to 1
pfddm(rt = c(1.2, 0.9, 1.1, 1.4, 0.8, 1.3),
response = c("lower", "upper", "upper", "lower", "upper", "lower"),
a = 1, v = 1, t0 = 0.3, w = 0.5, sv = 0, sigma = 0.1,
err_tol = 1e10, log = TRUE, method = "Mills")
### examples of different response inputs
# integer
resp_int < as.integer(c(1, 2, 2, 1, 2, 1))
pfddm(rt = c(1.2, 0.9, 1.1, 1.4, 0.8, 1.3), response = resp_int,
a = 1, v = 2, t0 = 0.3, w = 0.5, sv = 0.1,
err_tol = 1e10, log = FALSE, method = "Mills")
# double
resp_dbl < as.double(c(1, 2, 2, 1, 2, 1))
pfddm(rt = c(1.2, 0.9, 1.1, 1.4, 0.8, 1.3), response = resp_dbl,
a = 1, v = 2, t0 = 0.3, w = 0.5, sv = 0.1,
err_tol = 1e10, log = FALSE, method = "Mills")
# factor (first level is mapped to "lower")
days < c("Monday", "Friday", "Friday", "Monday", "Friday", "Monday")
resp_fac < factor(days, levels = c("Monday", "Friday"))
pfddm(rt = c(1.2, 0.9, 1.1, 1.4, 0.8, 1.3), response = resp_fac,
a = 1, v = 2, t0 = 0.3, w = 0.5, sv = 0.1,
err_tol = 1e10, log = FALSE, method = "Mills")
# string
resp_str < c("lower", "upper", "upper", "lower", "upper", "lower")
pfddm(rt = c(1.2, 0.9, 1.1, 1.4, 0.8, 1.3), response = resp_str,
a = 1, v = 2, t0 = 0.3, w = 0.5, sv = 0.1,
err_tol = 1e10, log = FALSE, method = "Mills")
# logical
resp_log < c(FALSE, TRUE, TRUE, FALSE, TRUE, FALSE)
pfddm(rt = c(1.2, 0.9, 1.1, 1.4, 0.8, 1.3), response = resp_log,
a = 1, v = 2, t0 = 0.3, w = 0.5, sv = 0.1,
err_tol = 1e10, log = FALSE, method = "Mills")
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