R/harvey.R

In skedastic: Handling Heteroskedasticity in the Linear Regression Model

#' Harvey Test for Heteroskedasticity in a Linear Regression Model
#'
#' This function implements the method of
#'    \insertCite{Harvey76;textual}{skedastic} for testing for "multiplicative"
#'    heteroskedasticity in a linear regression model.
#'    \insertCite{Mittelhammer00;textual}{skedastic} gives the
#'    formulation of the test used here.
#'
#' @details Harvey's Test entails fitting an auxiliary regression model in
#'    which the response variable is the log of the  vector of squared
#'    residuals from the original model and the design matrix \eqn{Z}
#'    consists of one or more exogenous variables that are suspected of being
#'    related to the error variance. In the absence of prior information on
#'    a possible choice of \eqn{Z}, one would typically use the explanatory
#'    variables from the original model. Under the null hypothesis of
#'    homoskedasticity, the distribution of the test statistic is
#'    asymptotically chi-squared with \code{parameter} degrees of freedom.
#'    The test is right-tailed.
#' @inheritParams breusch_pagan
#'
#' @return An object of \code{\link[base]{class}} \code{"htest"}. If object is
#'    not assigned, its attributes are displayed in the console as a
#'    \code{\link[tibble]{tibble}} using \code{\link[broom]{tidy}}.
#' @references{\insertAllCited{}}
#' @importFrom Rdpack reprompt
#' @export
#' @seealso the description of the test in
#'   \href{http://www.econometrics.com/intro/testhet.htm}{SHAZAM} software
#'   (which produces identical results).
#'
#' @examples
#' mtcars_lm <- lm(mpg ~ wt + qsec + am, data = mtcars)
#' harvey(mtcars_lm)
#' harvey(mtcars_lm, auxdesign = "fitted.values")
#'

harvey <- function(mainlm, auxdesign = NA, statonly = FALSE) {

  auxfitvals <- ifelse(all(is.na(auxdesign)) | is.null(auxdesign), FALSE,
                                    auxdesign == "fitted.values")
  processmainlm(m = mainlm, needy = auxfitvals, needyhat = auxfitvals,
                needp = FALSE)

  if (all(is.na(auxdesign)) || is.null(auxdesign)) {
    Z <- X
  } else if (is.character(auxdesign)) {
    if (auxdesign == "fitted.values") {
      Z <- t(t(yhat))
    } else stop("Invalid character value for `auxdesign`")
  } else {
    Z <- auxdesign
    if (nrow(auxdesign) != nrow(X)) stop("No. of observations in `auxdesign`
                                         must match\nno. of observations in
                                         original model.")
  }

  hasintercept <- columnof1s(Z)
  if (!hasintercept[[1]]) {
    Z <- cbind(1, Z)
    message("Column of 1's added to `auxdesign`")
  }

  p <- ncol(Z) - 1
  n <- nrow(Z)
  auxresponse <- log(e ^ 2)
  auxres <- stats::lm.fit(Z, auxresponse)$residuals

  teststat <- (sum(auxresponse ^ 2) - n * mean(auxresponse) ^ 2
               - sum(auxres ^ 2)) / pracma::psi(1, 1 / 2)
  if (statonly) return(teststat)

  pval <- stats::pchisq(teststat, df = p, lower.tail = FALSE)

  rval <- structure(list(statistic = teststat, parameter = p, p.value = pval,
               null.value = "Homoskedasticity",
               alternative = "greater"), class = "htest")
  broom::tidy(rval)
}