Stochastic Diffusion Models are used in cognitive science to analyse cognitive processes in fast binary decisions. It is assumed that the information supporting one and refuting the other decision can be described by a Wiener Diffusion process with constant drift over time. In the model, the decision process is terminated when the process exits from a given interval (see also Voss, Nagler, & Lerche, 2013).
The diffusion-model data analysis was introduced in psychology by Roger Ratcliff (1978). Ratcliff's diffusion model is specified by the following parameters: The distance of thresholds (a), the starting point (z), the drift rate (v), a non-decisional part of the response time (t0), and three so-called inter-trial variability parameters concerning the starting point (sz), the drift (sv), and the non- decisional response-time constant (st0).
FastRdm estimates values for this parameters from response-time distributions for both alternative decisions. FastRdm is based on a fast numerical approach for solving the Partial Differential Equation defining the above sketched diffusion model (cf. Voss & Voss, 2008). A detailed description of the core C functions that fastRdm relies on is given by Voss and Voss (2007).
FastRdm comes with NO WARRANTY, to the extent permitted by law. You may redistribute copies of fastRdm under the terms of the GNU General Public License.
Ratcliff, R., 1978. A theory of memory retrieval. Psychological Review, 85, 59-108.
Ratcliff, R., Rouder, J. N., 1998. Modelling response times for two-choice decisions. Psychological Science 9 (5), 347-356.
Voss, A., Rothermund, K., Voss, J., 2004. Interpreting the parameters of the diffusion model: An empirical validation. Memory & Cognition 32, 1206-1220.
Voss, Nagler, & Lerche (in press). Diffusion Models in Experimental Psychology: A Practical Introduction. Experimental Psychology.
Voss, A., Voss, J., 2008. A fast numerical algorithm for the estimation of diffusion-model parameters. Journal of Mathematiocal Psychology.
Voss, A., Voss, J., 2007. Fast-dm: A free program for efficient diffusion model analysis. Behavioral Research Methods, 39, 767-775.
Wagenmakers, E.-J., van der Maas, H. L. J., & Grasman, R. P. P. P., 2007. An ez-diffusion model for response time and accuracy. Psychonomic Bulletin & Review, 14, 3-22.
The core of the package is split into several source files. The common header file for all of these is "fast-dm.h".
cdf.c - compute the CDF for the diffusion model
container.c - container types (sets, dictionaries, arrays)
dataset.c - read and store data files
density.c - calculate the density of the predicted response-time distributions
experiment.c - read and store the control file
EZ-diff.c - compute approximate parameters using the EZ-model
file.c - auxiliary funcitons to read control and data files
main.c - main program for the fast-dm project
method-cs.c - implementation of the CS method
method-ks.c - implementation of the KS method
method-ml.c - implementation of the ML method
pde.c - numerically solve the Fokker-Planck equation
phi.c - the CDF and inverse CDF of the standard normal distribution
precision.c - tune parameters for the precision of CDF and density
simplex2.c - the downhill simplex method of Nelder and Mead
win32dir.c - emulate opendir/readdir/closedir on MS Windows systems
win32.erf.c - emulate Gaussian error function (erf) on MS Windows systems
win32getopt.c - emulate getopt on MS Windows systems
xmalloc.c - memory management
plot-cdf.c - plot cumulative distribution functions
construct-samples.c - simulate sample data
Fast-dm is a program to efficiently estimate parameters in Ratcliff's diffusion model. Valid parameters are
a = the boundary separation
zr = the mean of the starting point of the diffusion relative to
threshold separation
szr = the width of the support of the distribution of zr
v = the mean of the drift
sv = the standard deviation of the drift
t0 = the mean of the non-decisional component of the reaction time
st0 = the width of the support of the distribution of t0
d = differences in the non-decisional component between upper and
lower threshold
The relative starting point is assumend to be uniformly distributed on the interval [zr-0.5szr,zr+0.5szr], the drift is assumed to be normally distributed with mean v and variance sv^2, and t0 is assumed to be uniformly distributed on the interval [t0-0.5st0,t0+0.5st0].
For each run of the fast-dm program you need two kinds of input files: one control file which describes the experiment and one or more data files which contain the measured reaction times and responses. In addition there are two types of output files. All files are plain text files, the exact format is described below.
An experiment control file describes one experiment. By convention these files use the file name extension ".ctl". By default fast-dm tries to read an experiment description from the file "experiment.ctl". On systems which support command line arguments, you can choose a different experiment control file by calling fast-dm with the name of a control file as the first argument.
Control files are evaluated line by line. Empty lines and lines starting with "#" are ignored. For all other lines the first word is interpreted as a command and the subsequent words are used as arguments to this command.
Example 1: A simple control file could look as follows
format RESPONSE TIME
load "*.dat"
save "*.out"
The first line specifies that the data files will have just two entries per line, namely first a 0/1 value giving the response and then a reaction time (in seconds). The second line instructs fast-dm to analyse the data files "1.dat", "2.dat", etc. The results are written to the screen and to files named "1.out", "2.out", etc.
Example 2: A more complicated control file is the following one:
precision 2
set sv 0
depends v stimulus
format stimulus RESPONSE TIME
load "*.dat"
save "*.out"
log "protocol"
Here, the first two lines instruct fast-dm to use reduced precision for the computation and to not use variability for the v parameter (to speed up the analysis). The "format" statement specifies that each line of the data files will contain three values, one entry describing the stimulus used, then the participant's response and finally the response time. The "depends" statement specifies that different "v" parameters will be used for different stimuli, all other parameters are shared between all stimuli. Datasets are read from the files "1.dat", "2.dat", etc. and and the results are written to the files "1.out", "2.out", etc. (in addition to being printed to the screen). Also, a summary of all results, one line per input file, is written to the file "protocol".
The following commands are valid in control files. When present, they should be given in the order of the following list.
method M
Use a given estimation method. 'M' can either be "ks" (for the
Kolmogorov-Smirnov method; this is the default), "ml" (for the
maximum likelihood method), or "cs" (for the chi-square method).
precision VALUE
Set the precision used for the computations in the parameter
estimation procedure. 'VALUE' is a real number, the minimal
allowed value is 1. Larger values give higher accuracy but
greatly increase computation time, reasonable values are in the
range from 2 to 4.
This command is optional, the default precision is 3.
set PARAM VALUE
Fixes the parameter 'PARAM' to 'VALUE' instead of estimating it.
'PARAM' must be one of "a", "zr", "v", "t0", "d", "szr", "sv",
st0". Fixing parameters, especially the variability parameters,
can speed up the estimation procedure significantly.
This command is optional, default is to estimate all parameters.
depends PARAM ...
Specifies that parameter 'PARAM' depends on one or more
experimental conditions. 'PARAM' must be one of "a", "zr", "v",
"t0", "d", "szr", "sv", st0". All the remaining arguments must be
experimental conditions as defined on the "format" statement.
Parameters which are fixed to a value using "set" cannot depend on
experimental conditions. All parameters which are not mentioned
in a "depends" statement are shared between experimental
conditions.
This command is optional. Default is to share all parameters
between all experimental conditions.
format ...
Describes the format of the data files. The arguments can be
arbitrary strings. Each argument corresponds to one column in the
data files. The arguments "RESPONSE" and "TIME" must occur
exactly once each and define the position of the response column
and reaction time column, respectively, in the datafile. An
argument of "*" specifies that the corresponding column is to be
ignored. All other arguments are interpreted as experimental
conditions for use in "depends" statements.
This command is required, at least RESPONSE and TIME must be
specified.
load "FNAME"
Gives the name of the data files. This command is required. The
given name may contain a single "*" to consecutively read several
data files.
save "FNAME"
Gives the name of the per-dataset log files. The results of
parameter estimation, in addition to being printed to the screen,
are written to these files. If the file name in the 'load'
contains a star, the file name given in the log command must also
contain a star.
This command is optional, default is not to write a per-dataset
log file. If this command is not present, "log" must be used
instead.
log "FNAME"
Gives the name of the summary log file. This command is optional,
default is not to write a summary file. If this command is not
present, "save" must be used instead.
Data files contain the participants' responses and measured reaction times. Optionally they can also contain information about experimental conditions. Typically each data file describes one session of one participant in an experiment. By convention data files use the file name extension ".dat".
Data files are evaluated line by line. Empty lines and lines starting with "#" are ignored. All other lines must contain the entries given by the "format" statement in the control file.
Example 3. The beginning of data file "17.dat" for "Example 2" above could look as follows.
# participant 17, female
red 0 1.723
black 1 0.877
black 1 0.933
red 1 1.526
The values in the "RESPONSE" column must be either 0 or 1, corresponding to the two possible outcomes (a positive drift v or a large z both favour the outcome 1). The entries in the "TIME" column must be floating point numbers, giving the reaction time in seconds. All other entried correspond to experimental conditions and can be arbitrary strings.
per-dataset save files are written if the "save" statement is used in the control file. Each per-dataset log file corresponds to a data file. By convention, save files use the file name extension ".out".
Example 4. The save file "17.out" for Example 3 above could look as follows.
a = 2.134450
zr = 0.877730
v_red = 2.52287
v_black = -0.033281
t0 = 0.322186
d = 0.030334
szr = 0.100000
sv = 0.100000
st0 = 0.100000
p = 0.913227
time = 42.850000
It gives the estimated parameters, one per line. Since we allowed "v" to depend on the stimulus, several values for "v" are given. In addition to the parameter values there are two informational entries: 'p' gives the resulting p-value (values close to one indicate a good fit) and 'time' gives the CPU time used while processing this data set in seconds.
A summary log file is created when the "log" command is used in the control file. This log file contains one line of output for each dataset analysed plus a header line indicating which value is stored in which column. Summary log files can be useful to import fast-dm results into other programs for statistical analysis.
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