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#' Simulated data set
#'
#' The simulated data set \code{simul2} considers a situation with clustered
#' observations and four binary covariates in both sub-models of the Pogit
#' model, i.e.
#' \code{X} = \code{W}. The respective design matrix is
#' built by computing all 2^4 possible 0/1 combinations and one observation
#' is generated for each covariate pattern. C=50 clusters are built containing
#' one unit with each of the resulting 16 covariate patterns, i.e. a total of
#' I=800 units. The regression effects are set to \code{beta = {0.75,0.1,0.1,0,0}}
#' in the Poisson and to \code{alpha = {2.2,-0.3,0,-0.3,0}} in the logit model.
#' Random intercepts in both sub-models are simulated from a normal distribution
#' with standard deviations \eqn{\theta_\beta}=\code{0.1} and
#' \eqn{\theta_\alpha}=\code{0.3}. Additionally to the main study sample,
#' validation data are available for each covariate pattern and cluster.
#' For details concerning the simulation setup, see Dvorzak and Wagner (2016).
#'
#' @docType data
#' @usage data(simul2)
#' @format A data frame with 800 rows and the following 10 variables:
#' \describe{
#' \item{\code{y}}{number of observed counts for each covariate pattern
#' in each cluster}
#' \item{\code{E}}{total exposure times for each unit}
#' \item{\code{cID}}{cluster ID for each unit}
#' \item{\code{X.0}}{intercept}
#' \item{\code{X.1}, \code{X.2}, \code{X.3}, \code{X.4}}{binary covariates}
#' \item{\code{v}}{number of reported cases for each covariate pattern in each
#' cluster in the validation sample}
#' \item{\code{m}}{number of true cases subject to the fallible reporting
#' process (sample size of validation data)}
#' }
#'
#' @source Dvorzak, M. and Wagner, H. (2016). Sparse Bayesian modelling
#' of underreported count data. \emph{Statistical Modelling}, \strong{16}(1),
#' 24 - 46, \doi{10.1177/1471082x15588398}.
#'
#' @seealso \code{\link{pogitBvs}}
#' @name simul2
#' @keywords datasets
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