variance_inflation.R

#' Variance inflation factor
#'
#' @param mod A model object (or data.frame). For the moment only `lm` and a
#' plain dataset is implemented
#' @param ... not used
#' @rdname vif
#' @return a matrix with for each variable de variance inflation factor,
#' the degrees of freedom  en the rescaled variance inflation factor based on
#' the degrees of freedom.
#' @export
#'
#' @family Statistics

vif <- function(mod, ...) {
  UseMethod("vif")
}

#---------------------------

#' Variance inflation factor (`lm` model)
#'
#' @export
#' @method vif lm
#' @rdname vif
vif.lm <- function(mod, ...) {
  vif.default(mod, ...)
}



#' Variance inflation factor (data.frame)
#'
#' @export
#' @method vif data.frame
#' @rdname vif
vif.data.frame <- function(mod, ...) {
  mod <- cbind(dummyResponse = 1, mod)
  my_formula <- as.formula(mod)
  mod <- lm(my_formula, data = mod)
  vif.default(mod, ...)
}


#' Variance inflation factor (default routine)
#'
#' @export
#' @method vif default
#' @rdname vif
#' @examples{
#' vif(airquality)
#' }
#' @importFrom stats as.formula coef coefficients cov2cor lm model.matrix vcov
vif.default <- function(mod, ...) {
  if (any(is.na(coef(mod)))) {
    stop("there are aliased coefficients in the model")
  }
  v <- vcov(mod)
  assign <- attr(model.matrix(mod), "assign")
  if (names(coefficients(mod)[1]) == "(Intercept)") {
    v <- v[-1, -1]
    assign <- assign[-1]
  } else {
    warning("No intercept: vifs may not be sensible.")
  }
  terms <- labels(terms(mod))
  n_terms <- length(terms)
  if (n_terms < 2) {
    stop("model contains fewer than 2 terms")
  }
  r <- cov2cor(v)
  det_r <- det(r)
  result <- matrix(0, n_terms, 3)
  rownames(result) <- terms
  colnames(result) <- c("GVIF", "Df", "GVIF^(1/(2*Df))")
  for (term in 1:n_terms) {
    subs <- which(assign == term)
    result[term, 1] <- det(as.matrix(r[subs, subs])) * det(as.matrix(r[
      -subs,
      -subs
    ])) / det_r
    result[term, 2] <- length(subs)
  }
  result[, 3] <- result[, 1]^(1 / (2 * result[, 2]))
  result
}