R/rob_F_test.R

In robmed: (Robust) Mediation Analysis

# --------------------------------------
# Author: Andreas Alfons
#         Erasmus Universiteit Rotterdam
# --------------------------------------

## compute a robust F-test (which actually uses the chi-squared distribution)

# generic function
#' @noRd
rob_F_test <- function(object, ...) UseMethod("rob_F_test")

# # method for mediation model fits via regression
# rob_F_test.reg_fit_mediation <- function(object, ...) {
#   # check if Tukey bisquare loss function is used, otherwise return NULL
#   control <- object$control
#   if (control$psi != "bisquare" || is.null(control$efficiency)) return()
#   # extract the full model and fit the null model
#   fit_full <- object$fit_ymx
#   y <- object$data[, object$y]
#   x_null <- matrix(1, nrow = length(y), ncol = 1)
#   fit_null <- lmrob.fit(x_null, y, control = control)
#   # perform robust F-test
#   s <- fit_full$scale
#   df <- fit_full$rank - fit_null$rank
#   chi_full <- Mchi(residuals(fit_full) / s, control$tuning.psi, control$psi)
#   chi_null <- Mchi(residuals(fit_null) / s, control$tuning.psi, control$psi)
#   tau <- (2 / df) * sum(chi_null - chi_full)
#   if(control$efficiency == 0.8)       const <- 0.4140647
#   else if(control$efficiency == 0.85) const <- 0.3572601  # default
#   else if(control$efficiency == 0.9)  const <- 0.2953806
#   else if(control$efficiency == 0.95) const <- 0.2180425
#   # Y = df1*X ~ chi-squared(df1) if X ~ F(df1, df2) and df2 goes to infinity
#   chi2 <- tau / const
#   p_value <- pchisq(chi2, df = df, lower.tail = FALSE)
#   # return results
#   list(statistic = chi2 / df, df = c(df, Inf), p_value = p_value)
# }

# method for mediation model fits via regression
# This does not work for all "lmrob" methods, only for those generated by
# package 'robmed'.  Some additional information is stored:  the object itself
# has an additional component 'response' that contains the values of the
# response variable, and the control object has an extra component 'efficiency'
# that contains the efficiency to which the estimator was tuned.
#' @noRd
rob_F_test.lmrob <- function(object, ...) {
  # check if Tukey bisquare loss function is used, otherwise return NULL
  control <- object$control
  if (control$psi != "bisquare" || is.null(control$efficiency)) return()
  # extract the response variable and fit the null model
  y <- object$response
  x_null <- matrix(1, nrow = length(y), ncol = 1)
  fit_null <- lmrob.fit(x_null, y, control = control)
  # perform robust F-test
  s <- object$scale
  df <- object$rank - fit_null$rank
  chi_full <- Mchi(residuals(object) / s, control$tuning.psi, control$psi)
  chi_null <- Mchi(residuals(fit_null) / s, control$tuning.psi, control$psi)
  tau <- (2 / df) * sum(chi_null - chi_full)
  if(control$efficiency == 0.8)       const <- 0.4140647
  else if(control$efficiency == 0.85) const <- 0.3572601  # default
  else if(control$efficiency == 0.9)  const <- 0.2953806
  else if(control$efficiency == 0.95) const <- 0.2180425
  # Y = df1*X ~ chi-squared(df1) if X ~ F(df1, df2) and df2 goes to infinity
  chi2 <- tau / const
  p_value <- pchisq(chi2, df = df, lower.tail = FALSE)
  # return results
  list(statistic = chi2 / df, df = c(df, Inf), p_value = p_value)
}