R/data.R

In pqrBayes: Bayesian Penalized Quantile Regression

#' Simulated data under high-dimensional linear, binary, group LASSO and quantile varying coefficient models
#'
#' @docType data
#' @keywords datasets
#' @name data
#' @format 
#' The data_linear object consists of 4 components: g, y, e and coeff. coeff contains the true values of parameters used for generating the response variable \eqn{y}.
#' The data_binary object consists of 4 components: g, y, e and coeff. coeff contains the true values of parameters used for generating the response variable \eqn{y}.
#' The data_group object consists of 4 components: g, y, e and coeff. coeff contains the true values of parameters used for generating the response variable \eqn{y}.
#' The data_varying object consists of five components: g, y, u, e and coeff. coeff contains the true values of parameters used for generating the response variable \eqn{y}.
#' 
#'
#' 
#'
#' @details
#'
#' \strong{Generating Y using a sparse linear (quantile) regression model}
#' 
#' The true data generating model under sparse linear regression:
#' \deqn{Y_i=\beta_0+\beta_{1}X_{i1}+\beta_{2}X_{i2}+\beta_{3}X_{i3}+\epsilon_i,}
#' where \eqn{\epsilon_i\sim N(0,1)}, \eqn{\beta_{0}=0}, \eqn{\beta_{1}=1 }, \eqn{\beta_{2}=1.5} and \eqn{\beta_3=2}.
#' 
#' \strong{Generating Y using a sparse binary (quantile) regression model}
#' 
#' The true data generating model under sparse linear regression:
#' \deqn{\tilde{Y}_i=\beta_0+\beta_{1}X_{i1}+\beta_{2}X_{i2}+\beta_{3}X_{i3}+\epsilon_i,}
#' where \eqn{\epsilon_i\sim N(0,1)}, \eqn{\beta_{0}=0}, \eqn{\beta_{1}=0.22 }, \eqn{\beta_{2}=0.18} and \eqn{\beta_3=0.14}.
#' 
#' \eqn{Y_i=1} if \eqn{\tilde{Y}_i>0} and \eqn{Y_i=0} otherwise.
#' 
#' \strong{Generating Y using a high-dimensional group LASSO model}
#' 
#' The true data generating model under a group LASSO model:
#' \deqn{Y_i=\beta_0+\beta_{1}X_{i1}+\beta_{2}X_{i2}+\beta_{3}X_{i3}+\beta_{7}X_{i7}+\beta_{8}X_{i8}+\beta_{9}X_{i9}+\epsilon_i,}
#' where \eqn{\epsilon_i\sim N(0,1)}, \eqn{\beta_{0}=0}, \eqn{\beta_{1}=0.6}, \eqn{\beta_{2}=0.7},\eqn{\beta_{3}=0.8},\eqn{\beta_{7}=0.65}, \eqn{\beta_{8}=0.75} and \eqn{\beta_{9}=0.85}.
#' 
#' \strong{Generating Y using a (quantile) varying coefficient model}
#'
#' Data generation under sparse (quantile) VC model:
#' \deqn{Y_i=\gamma_0(v_i)+\gamma_1(v_i)X_{i1}+\gamma_2(v_i)X_{i2}+\gamma_3(v_i)X_{i3}+\epsilon_i,}
#' where \eqn{\epsilon_i\sim N(0,1)}, \eqn{\gamma_{0}(v_i)=1.5\sin(0.2\pi*v_i}), \eqn{\gamma_{1}(v_i)=2\exp(0.2v_i-1)-1.5 }, \eqn{\gamma_{2}(v_i)=2-2v_i } and \eqn{\gamma_3(v_i)=-4+(v_i-2)^3/6}.
#'
#' @examples
#' data(data)
#' data = data$data_linear
#' g=data$g
#' dim(g)
#' y=data$y
#' coeff=data$coeff
#' print(coeff)
#' 
#' data = data$data_binary
#' g=data$g
#' dim(g)
#' y=data$y
#' coeff=data$coeff
#' print(coeff)
#' 
#' data = data$data_group
#' g=data$g
#' dim(g)
#' y=data$y
#' coeff=data$coeff
#' print(coeff)
#' 
#' data = data$data_varying
#' g=data$g
#' dim(g)
#' coeff=data$coeff
#' print(coeff)
#'
#'
#' @seealso \code{\link{pqrBayes}}
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