#' @title Find Default Equivalence (ROPE) Region Bounds
#'
#' @description This function attempts at automatically finding suitable "default"
#'   values for the Region Of Practical Equivalence (ROPE).
#'
#' @details \cite{Kruschke (2018)} suggests that the region of practical
#'   equivalence could be set, by default, to a range from \code{-0.1} to
#'   \code{0.1} of a standardized parameter (negligible effect size
#'   according to Cohen, 1988).
#'
#'   \itemize{
#'     \item For \strong{linear models (lm)}, this can be generalised to \ifelse{html}{\out{-0.1 * SD<sub>y</sub>, 0.1 * SD<sub>y</sub>}}{\eqn{[-0.1*SD_{y}, 0.1*SD_{y}]}}.
#'     \item For \strong{logistic models}, the parameters expressed in log odds ratio can be converted to standardized difference through the formula \ifelse{html}{\out{&pi;/&radic;(3)}}{\eqn{\pi/\sqrt{3}}}, resulting in a range of \code{-0.18} to \code{0.18}.
#'     \item For other models with \strong{binary outcome}, it is strongly recommended to manually specify the rope argument. Currently, the same default is applied that for logistic models.
#'     \item For models from \strong{count data}, the residual variance is used. This is a rather experimental threshold and is probably often similar to \code{-0.1, 0.1}, but should be used with care!
#'     \item For \strong{t-tests}, the standard deviation of the response is used, similarly to linear models (see above).
#'     \item For \strong{correlations}, \code{-0.05, 0.05} is used, i.e., half the value of a negligible correlation as suggested by Cohen's (1988) rules of thumb.
#'     \item For all other models, \code{-0.1, 0.1} is used to determine the ROPE limits, but it is strongly advised to specify it manually.
#'   }
#'
#' @param x A \code{stanreg}, \code{brmsfit} or \code{BFBayesFactor} object.
#' @param verbose Toggle warnings.
#' @inheritParams rope
#'
#' @examples
#' \dontrun{
#' if (require("rstanarm")) {
#'   model <- stan_glm(
#'     mpg ~ wt + gear,
#'     data = mtcars,
#'     chains = 2,
#'     iter = 200,
#'     refresh = 0
#'   )
#'   rope_range(model)
#'
#'   model <- stan_glm(vs ~ mpg, data = mtcars, family = "binomial", refresh = 0)
#'   rope_range(model)
#' }
#'
#' if (require("brms")) {
#'   model <- brm(mpg ~ wt + cyl, data = mtcars)
#'   rope_range(model)
#' }
#'
#' if (require("BayesFactor")) {
#'   model <- ttestBF(mtcars[mtcars$vs == 1, "mpg"], mtcars[mtcars$vs == 0, "mpg"])
#'   rope_range(model)
#'
#'   model <- lmBF(mpg ~ vs, data = mtcars)
#'   rope_range(model)
#' }
#' }
#' @references Kruschke, J. K. (2018). Rejecting or accepting parameter values in Bayesian estimation. Advances in Methods and Practices in Psychological Science, 1(2), 270-280. \doi{10.1177/2515245918771304}.
#'
#' @importFrom insight get_response model_info is_multivariate
#' @importFrom stats sd
#' @export
rope_range <- function(x, ...) {
  UseMethod("rope_range")
}


#' @rdname rope_range
#' @export
rope_range.default <- function(x, verbose = TRUE, ...) {
  response <- insight::get_response(x)
  information <- insight::model_info(x)

  if (insight::is_multivariate(x)) {
    ret <- mapply(function(i, j) .rope_range(x, i, j), information, response)

    # return matrix as named list
    # see https://stackoverflow.com/questions/6819804/how-to-convert-a-matrix-to-a-list-of-column-vectors-in-r
    # this is not the fastest solution bot keeps columns names
    as.list(as.data.frame(ret))
  } else {
    .rope_range(x, information, response, verbose)
  }
}


# Exceptions --------------------------------------------------------------

#' @export
rope_range.mlm <- function(x, verbose = TRUE, ...) {
  response <- insight::get_response(x)
  information <- insight::model_info(x)

  lapply(response, function(i) .rope_range(x, information, i, verbose))
}



# helper ------------------


#' @importFrom stats sigma sd
.rope_range <- function(x, information = NULL, response = NULL, verbose = TRUE) {

  # if(method != "legacy") {
  #   message("Other ROPE range methods than 'legacy' are currently not implemented. See https://github.com/easystats/bayestestR/issues/364", call. = FALSE)
  # }


  negligible_value <- tryCatch({
    if (!is.null(response) && information$link == "identity") {
      # Linear Models
      0.1 * stats::sd(response, na.rm = TRUE)
      # 0.1 * stats::sigma(x) # https://github.com/easystats/bayestestR/issues/364
    } else if (information$link == "logit") {
      # Logistic Models (any)
      # Sigma==pi / sqrt(3)
      0.1 * pi / sqrt(3)
    } else if (information$link == "probit") {
      # Probit models
      # Sigma==1
      0.1 * 1
    } else if (information$is_correlation) {
      # Correlations
      # https://github.com/easystats/bayestestR/issues/121
      0.05
    } else if (information$is_count) {
      # Not sure about this
      sig <- stats::sigma(x)
      if (is.null(sig) || length(sig) == 0 || is.na(sig)) stop()
      0.1 * sig
    } else {
      # Default
      stop()
    }
  }, error = function(e) {
    if (isTRUE(verbose)) {
      warning("Could not estimate a good default ROPE range. Using 'c(-0.1, 0.1)'.", call. = FALSE)
    }
    0.1
  })

  c(-1, 1) * negligible_value
}