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#' Forstmann et al.'s Data
#'
#' A dataset containing the speed or accuracy manipulation for a Random Dot
#' Motion experiment.
#'
#' Details on the dataset can be found in the following paper:
#'
#' \strong{Striatum and pre-SMA facilitate decision-making under time pressure}
#'
#' Birte U. Forstmann, Gilles Dutilh, Scott Brown, Jane Neumann,
#' D. Yves von Cramon, K. Richard Ridderinkhof, Eric-Jan Wagenmakers.
#'
#' \emph{Proceedings of the National Academy of Sciences Nov 2008, 105 (45)
#' 17538-17542; DOI: 10.1073/pnas.0805903105}
#'
#' @format A data frame with 15818 rows and 5 variables:
#' \describe{
#' \item{E}{Factor with 3 levels for Speed, Accuracy and
#' Neutral}
#' \item{R}{Factor with 2 levels for Left and Right responses}
#' \item{S}{Factor with 2 levels for Left and Right trials}
#' \item{rt}{reaction time for each trial as a double}
#' \item{subjects}{integer ID for each subject}
#' }
#' @source \url{https://www.pnas.org/doi/10.1073/pnas.0805903105}
"forstmann"
#' LNR Model of Forstmann Data (First 3 Subjects)
#'
#' An emc object with a limited number of samples and subjects of the Forstmann dataset.
#' The object is a nested list of lenght three, each list containing the MCMC samples
#' of the respective chain. The MCMC samples are stored in the samples element.
#'
#'
#' @section Samples Element:
#'
#' The samples element of a emc object contains the different types of samples
#' estimated by EMC2. These include the three main types of samples
#' \code{theta_mu}, \code{theta_var} and \code{alpha} as well as a number of
#' other items which are detailed here.
#' \describe{
#' \item{theta_mu}{samples used for estimating the model parameters (group
#' level), an array of size (n_pars x n_samples)}
#' \item{theta_var}{samples used for estimating the parameter covariance
#' matrix, an array of size (n_pars x n_pars x n_samples)}
#' \item{alpha}{samples used for estimating the subject random effects, an
#' array of size (n_pars x n_subjects x n_samples)}
#' \item{stage}{A vector containing what PMwG stage each sample was drawn in}
#' \item{subj_ll}{The winning particles log-likelihood for each subject and
#' sample}
#' \item{a_half}{Mixing weights used during the Gibbs step when creating a
#' new sample for the covariance matrix}
#' \item{last_theta_var_inv}{The inverse of the last samples covariance
#' matrix}
#' \item{idx}{The index of the last sample drawn}
#' }
#'
#' @format An emc object. An emc object is a list with a
#' specific structure and elements, as outlined below.
#' \describe{
#' \item{data}{A list of dataframes, one for each subject included}
#' \item{par_names}{A character vector containing the model parameter names}
#' \item{n_pars}{The number of parameters in the model}
#' \item{n_subjects}{The number of unique subject ID's in the data}
#' \item{model}{A list containing the model functions}
#' \item{nuisance}{A logical vector indicating which parameters are nuisance parameters}
#' \item{subjects}{A vector containing the unique subject ID's}
#' \item{type}{The type of model e.g., "standard" or "diagonal"}
#' \item{prior}{A list that holds the prior for \code{theta_mu} (the model
#' parameters). Contains the mean (\code{theta_mu_mean}), covariance matrix
#' (\code{theta_mu_var}), degrees of freedom (\code{v}), and scale (\code{A})
#' and inverse covariance matrix (\code{theta_mu_invar})}
#' \item{samples}{A list with defined structure containing the samples, see
#' the Samples Element section for more detail}
#' \item{sampler_nuis}{A sampler list for nuisance parameters (in this case there are none),
#' similarly structured to the overall samples list of one of the MCMC chains.}
#' }
#' @source \url{https://www.pnas.org/doi/10.1073/pnas.0805903105}
"samples_LNR"
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