R/statliu.R

In fastliu: Fast Functions for Liu Regression with Regularization Parameter and Statistics

#' Liu Regression Statistics
#'
#' \code{statliu} computes the statistics related to the Liu regression.
#'
#' @param obj An object of class \code{liureg}.
#'
#' @details
#' \tabular{ll}{
#' \code{EDF} (Liu, 1993; Hastie et al., 2009) \tab Effective degrees of freedom, \eqn{n-\mathrm{trace}\left(2\mathbf{H}_\lambda\right)-\mathbf{H}_\lambda\mathbf{H}_\lambda^T} for each \eqn{\lambda} where \eqn{n} is the number of the observations in the design matrix and \eqn{\mathbf{H}_\lambda} is the hat matrix of Liu regression at \eqn{\lambda}.\cr
#' \tab \cr
#' \code{sigma2} \tab Computed \eqn{\hat{\sigma}^2} from the Liu regression for each \eqn{\lambda}.\cr
#' \tab \cr
#' \code{VAR} \tab Variance from the Liu regression for each \eqn{\lambda}.\cr
#' \tab \cr
#' \code{BIAS2} \tab Squared-bias from the Liu regression for each \eqn{\lambda}.\cr
#' \tab \cr
#' \code{MSE} \tab Mean squared error (MSE) from the Liu regression for each \eqn{\lambda}.\cr
#' \tab \cr
#' \code{FVal} \tab F-statistics value from the Liu regression for each \eqn{\lambda}.\cr
#' \tab \cr
#' \code{GCV} \tab Generalized cross-validation (GCV) from the Liu regression for each \eqn{\lambda}. The GCV is computed by \eqn{\frac{\mathrm{SSR}_{\lambda}}{n-1-\mathrm{trace}\left(\mathbf{H}_{\lambda}\right)}} where \eqn{\mathrm{SSR}_{\lambda}} is the residual sum of squares and \eqn{\mathrm{trace}\left(\mathbf{H}_{\lambda}\right)} is the trace of the hat matrix at corresponding value of \eqn{\lambda} from Liu regression.\cr
#' \tab \cr
#' \code{R2} \tab R-squared from the Liu regression for each \eqn{\lambda}.\cr
#' \tab \cr
#' \code{AdjR2} \tab Adjusted R-squared from the Liu regression for each \eqn{\lambda}.\cr
#' \tab \cr
#' }
#'
#' @return The return object is the statistics related to the Liu regression.
#' @author Murat Genç
#' @references Liu, K. (1993). A new class of blased estimate in linear regression.
#' *Communications in Statistics-Theory and Methods*, **22**(2), 393-402.
#' \doi{10.1080/03610929308831027}.
#'
#' Hastie, T., Tibshirani, R., Friedman, J. H., Friedman, J. H. (2009).
#' The elements of statistical learning: data mining, inference,
#' and prediction (Vol. 2, pp. 1-758). *New York: Springer*.
#' @export
#'
#' @seealso [liureg()], [summary()], [pressliu()], [residuals()]
#'
#' @examples
#' Hitters <- na.omit(Hitters)
#' X <- model.matrix(Salary ~ ., Hitters)[, -1]
#' y <- Hitters$Salary
#' lam <- seq(0, 1, 0.01)
#' liu.mod <- liureg(X, y, lam)
#' stats <- statliu(liu.mod)
#' print(stats)
statliu <- function(obj){

  liust <- as.data.frame(liustatscpp(obj))
  rownames(liust) <- obj$lnames
  colnames(liust) <- c("EDF", "sigma2", "VAR", "BIAS2", "MSE", "FVal",
                       "GCV", "R2", "AdjR2")
  res <- structure(liust, class = "statliu")
  res

}