Fits the parameters of different models of response time and confidence, including
the 2DSD model (Pleskac & Busemeyer, 2010), dynWEV, DDMConf, and various
flavors of race models (Hellmann et al., 2023). Which model to fit is
specified by the argument model.
Only a ML method is implemented.
See dWEV, d2DSD, and dRM for more
information about the parameters and Details for not-fitted parameters.
fitRTConf(data, model = "dynWEV", fixed = list(sym_thetas = FALSE),
init_grid = NULL, grid_search = TRUE, data_names = list(),
nRatings = NULL, restr_tau = Inf, precision = 1e-05, logging = FALSE,
opts = list(), optim_method = "bobyqa", useparallel = FALSE,
n.cores = NULL, ...)Gives a one-row data frame with columns for the different parameters as
fitted result as well as additional information about the fit (negLogLik (for
final parameters), k (number of parameters), N (number of data rows),
BIC, AICc and AIC) and the column fixed, which includes all information
about fixed and not fitted parameters.
a data.frame where each row is one trial, containing following
variables (column names can be changed by passing additional arguments of
the form condition="contrast"):
condition (not necessary; for different levels of stimulus quality, will be transformed to a factor),
rating (discrete confidence judgments, should be given as integer vector; otherwise will be transformed to integer),
rt (giving the reaction times for the decision task),
either 2 of the following (see details for more information about the accepted formats):
stimulus (encoding the stimulus category in a binary choice task),
response (encoding the decision response),
correct (encoding whether the decision was correct; values in 0, 1)
sbj or participant (optional; giving the subject ID; only relevant if logging = TRUE;
if unique the ID is used in saved files with interim results
and logging messages;
if non-unique or missing and logging =TRUE, 999 will be used then)
character scalar. One of "dynWEV", "2DSD", "IRM", "PCRM", "IRMt", "PCRMt", or "DDMConf" for the model to be fit.
list. List with parameter-value pairs for parameters that should not be fitted. See Details.
data.frame or NULL. Grid for the initial parameter search. Each row is one parameter constellation.
See details for more information. If NULL a default grid will be used.
logical. If FALSE, the grid search before the optimization
algorithm is omitted. The fitting is then started with a mean parameter set
from the default grid (if init_grid=NULL) or directly with the rows from
init_grid, if not NULL. (Default: TRUE)
named list (e.g. c(rating="confidence")). Alternative
possibility of giving other column names for the variables in the data. By default
column names are identical to the ones given in the data argument description.
integer. Number of rating categories. If NULL, the maximum of
rating and length(unique(rating)) is used. This argument is especially
important for data sets where not the whole range of rating categories is realized.
If given, ratings has to be given as factor or integer.
numerical or Inf or "simult_conf". For 2DSD and dynWEV only.
Upper bound for tau. Fits will be in the interval (0,restr_tau). If FALSE tau will be unbound.
For "simult_conf", see the documentation of d2DSD and dWEV
numerical scalar. For 2DSD and dynWEV only. Precision of calculation.
(in the respective models) for the density functions (see dWEV for more information).
logical. If TRUE, a folder 'autosave/fitmodel' is created and
messages about the process are printed in a logging file and to console (depending
on OS). Additionally intermediate results are saved in a .RData file with the
participant ID in the name.
list. A list for more control options in the optimization routines
(depending on the optim_method). See details for more information.
character. Determines which optimization function is used for
the parameter estimation. Either "bobyqa" (default), "L-BFGS-B" or "Nelder-Mead".
"bobyqa" uses a box-constrained optimization with quadratic interpolation.
(See bobyqa for more information.) The first two use a
box-constraint optimization. For Nelder-Mead a transfinite function rescaling is used
(i.e. the constrained arguments are suitably transformed to the whole real line).
logical. If TRUE the grid search in the beginning is done with a
parallel back-end, using the parallel package.
integer or NULL. Number of cores used for parallelization. If NULL
(default) the number of available cores -1 is used.
Possibility of giving alternative variable names in data frame
(in the form condition = "SOA", or response="pressedKey").
Sebastian Hellmann.
The fitting involves a first grid search through computation of the
likelihood on an initial grid with possible sets of parameters to start the
optimization routine. Then the best nAttempts parameter sets are
chosen for an optimization, which is done with an algorithm, depending on the
argument optim-method. The Nelder-Mead algorithm uses the R function
optim. The optimization routine is restarted
nRestarts times with the starting parameter set equal to the
best parameters from the previous routine.
stimulus, response and correct. Two of these columns must be given in
data. If all three are given, correct will have no effect (and will be not checked!).
stimulus can always be given in numerical format with values -1 and 1. response
can always be given as a character vector with "lower" and "upper" as values.
Correct must always be given as a 0-1-vector. If the stimulus column is given
together with a response column and they both do not match the above format,
they need to have the same values/levels (if factor).
In the case that only stimulus/response is given in any other format together with
correct, the unique values will be sorted increasingly and
the first value will be encoded as "lower"/-1 and the second as "upper"/+1.
fixed. Parameters that should not be fitted but kept constant. These will
be dropped from the initial grid search
but will be present in the output, to keep all parameters for prediction in the result.
Includes the possibility for symmetric confidence thresholds for both alternative
(sym_thetas=logical). Other examples are
z =.5, sv=0, st0=0, sz=0. For race models, the possibility
of setting a='b' (or vice versa)
leads to identical upper bounds on the decision processes, which is the equivalence for
z=.5 in a diffusion process.
Parameters not fitted. The models get developed continuously and not all changes are adopted in the fitting function instantly. Following parameters are currently not included in the fitting routine:
in race models: sza, szb, smu1, and smu2
init_grid. Each row should be one parameter set to check. The column names
should include the parameters of the desired model, which are the following for 2DSD:
a, vmin and vmax (will be equidistantly spanned across conditions), sv, z (as the
relative starting point between 0 and a), sz (also in relative terms), t0, st0, theta0
(minimal threshold), thetamax (maximal threshold; the others will be equidistantly
spanned symmetrically for both decisions), and tau. For dynWEV,
additionally w , svis, and sigvis are required. For the race models the parameters
are: vmin, vmax (will be equidistantly
spanned across conditions), a and b (decision thresholds), t0, st0, theta0
(minimal threshold), thetamax (maximal threshold;
the others will be equidistantly spanned symmetrically for both decisions), and for
time-dependent confidence race models
additionally wrt and wint (as weights compared to wx=1).
opts. A list with numerical values. Possible options are listed below (together with the optimization method they are used for).
nAttempts (all) number of best performing initial parameter sets used for
optimization; default 5, if grid_search is TRUE.
If grid_search is FALSE and init_grid is NULL, then nAttempts will be set to 1 (and
any input will be ignored).
If grid_search is FALSE and init_grid is not NULL, the rows of init_grid will be used
from top to bottom
(since no initial grid search is done) with not more than nAttempts rows used.
nRestarts (all) number of successive optim routines for each of the starting parameter sets; default 5,
maxfun ('bobyqa') maximum number of function evaluations; default: 5000,
maxit ('Nelder-Mead' and 'L-BFGS-B') maximum iterations; default: 2000,
reltol ('Nelder-Mead') relative tolerance; default: 1e-6),
factr ('L-BFGS-B') tolerance in terms of reduction factor of the objective, default: 1e-10)
Hellmann, S., Zehetleitner, M., & Rausch, M. (2023). Simultaneous modeling of choice, confidence and response time in visual perception. Psychological Review 2023 Mar 13. doi: 10.1037/rev0000411. Epub ahead of print. PMID: 36913292.
https://nashjc.wordpress.com/2016/11/10/why-optim-is-out-of-date/
# We use one of the implemented models, "dynWEV"
# 1. Generate data
# data with positive drift (stimulus = "upper")
data <- rWEV(20, a=2,v=0.5,t0=0.2,z=0.5, sz=0.1,sv=0.1, st0=0, tau=4, s=1, w=0.3)
data$stimulus <- "upper"
# data with negtive drift (stimulus = "lower") but same intensity
data2 <- rWEV(100, a=2,v=-0.5,t0=0.2,z=0.5,sz=0.1,sv=0.1, st0=0, tau=4, s=1, w=0.3)
data2$stimulus <- "lower"
data <- rbind(data, data2)
# Transfer response column and add dummy condition column
data$response <- ifelse(data$response==1, "upper", "lower")
data$condition <- 1
# Take some confidence thresholds for discrete ratings
threshs <- c(-Inf, 1, 2, Inf)
data$rating <- as.numeric(cut(data$conf, breaks = threshs, include.lowest = TRUE))
head(data)
# 2. Use fitting function
# Fitting the model with these opts results in a pretty bad fit
# (especially because of omitting the grid_search)
# \donttest{
fitRTConf(data, "dynWEV", fixed=list(sym_thetas=TRUE, z=0.5, st0=0),
grid_search = FALSE, logging=FALSE,
opts = list(nAttempts=1, nRestarts=2, maxfun=2000))
# }
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