R/dataME.R

In saeME: Small Area Estimation with Measurement Error

#' @title dataME
#' @description This data generated by simulation based on Fay-Herriot with Measurement Error Model by following these steps:
#' \enumerate{
#'   \item Generate \eqn{x_{i}}{xi} from a UNIF(5, 10) distribution, \eqn{\psi_{i}}{\psii} = 3, \eqn{c_{i}}{ci} = 0.25, and \eqn{\sigma_{v}^{2}}{\sigma2v} = 2.
#'   \item Generate \eqn{u_{i}}{ui} from a N(0, \eqn{c_{i}}{ci}) distribution, \eqn{e_{i}}{ei} from a N(0, \eqn{\psi_{i}}{\psii}) distribution, and \eqn{v_{i}}{vi} from a N(0, \eqn{\sigma_{v}^{2}}{\sigma2v}) distribution.
#'   \item Generate \eqn{\hat{x}_{i}}{x.hati} = \eqn{x_{i}}{xi} + \eqn{u_{i}}{ui}.
#'   \item Then for each iteration, we generated \eqn{Y_{i}}{Yi} = \eqn{2 + 0.5 \hat{x}_{i} + v_{i}}{2 + 0.5*x.hati + vi} and \eqn{y_{i}}{yi} = \eqn{Y_{i} + e_{i}}{Yi + ei}.
#' }
#' Direct estimator \code{y}, auxiliary variable \eqn{\hat{x}}{x.hat}, sampling variance \eqn{\psi}{\psi}, and  \eqn{c}{c} are arranged in a dataframe called \code{dataME}.
#' @usage data(dataME)
#' @format A data frame with 100 observations on the following 4 variables.
#' \describe{
#'  \item{\code{small_area}}{areas of interest.}
#'  \item{\code{y}}{direct estimator for each domain.}
#'  \item{\code{x.hat}}{auxiliary variable for each domain.}
#'  \item{\code{vardir}}{sampling variances for each domain.}
#'  \item{\code{var.x}}{mean squared error of auxiliary variable and sorted as \code{x.hat}}
#' }
#' @name dataME
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