R/tepsilonhat.R

In jeksterslabds/jeksterslabRlinreg: Jekster's Lab Linear Regression Utilities

#' @author Ivan Jacob Agaloos Pesigan
#'
#' @title Studentized Residuals
#'
#' @description Calculates studentized residuals using
#'   \deqn{
#'     t_i = \frac{\hat{\varepsilon}_{i}}{\hat{\sigma}_{\varepsilon}^{2} \sqrt{1 - h_{ii}}}
#'   }
#'
#' @details If `epsilonhat`, `h`, or `sigma2hatepsilonhat` are `NULL`,
#'   they are calculated using `X` and `y`.
#'
#' @family residuals functions
#' @keywords residuals
#' @inheritParams .RSS
#' @inheritParams .vcovhatbetahat
#' @inherit .h references
#' @param h Numeric vector of length `n` or `n` by 1 numeric matrix.
#'   \eqn{n \times 1} vector of leverage values.
#' @return Returns studentized residuals.
#' @export
.tepsilonhat <- function(epsilonhat = NULL,
                         h = NULL,
                         sigma2hatepsilonhat = NULL,
                         X = NULL,
                         y = NULL) {
  if (is.null(epsilonhat)) {
    epsilonhat <- epsilonhat(
      X = X,
      y = y
    )
  }
  if (is.null(h)) {
    h <- h(X)
  }
  if (is.null(sigma2hatepsilonhat)) {
    sigma2hatepsilonhat <- sigma2hatepsilonhat(
      X = X,
      y = y
    )
  }
  epsilonhat / sqrt(sigma2hatepsilonhat * (1 - h))
}

#' @author Ivan Jacob Agaloos Pesigan
#'
#' @title Studentized Residuals
#' @family residuals functions
#' @keywords residuals
#' @inherit .tepsilonhat description return
#' @inheritParams .tepsilonhat
#' @examples
#' # Simple regression------------------------------------------------
#' X <- jeksterslabRdatarepo::wages.matrix[["X"]]
#' X <- X[, c(1, ncol(X))]
#' y <- jeksterslabRdatarepo::wages.matrix[["y"]]
#' tepsilonhat <- tepsilonhat(X = X, y = y)
#' hist(tepsilonhat)
#'
#' # Multiple regression----------------------------------------------
#' X <- jeksterslabRdatarepo::wages.matrix[["X"]]
#' # age is removed
#' X <- X[, -ncol(X)]
#' tepsilonhat <- tepsilonhat(X = X, y = y)
#' hist(tepsilonhat)
#' @export
tepsilonhat <- function(X,
                        y) {
  .tepsilonhat(
    epsilonhat = NULL,
    h = NULL,
    sigma2hatepsilonhat = NULL,
    X = X,
    y = y
  )
}