#' Test for Practical Equivalence
#'
#' Perform a **Test for Practical Equivalence** for Bayesian and frequentist models.
#'
#' Documentation is accessible for:
#' \itemize{
#'   \item [Bayesian models](https://easystats.github.io/bayestestR/reference/equivalence_test.html)
#'   \item [Frequentist models](https://easystats.github.io/parameters/reference/equivalence_test.lm.html)
#' }
#'
#' For Bayesian models, the **Test for Practical Equivalence** is based on the *"HDI+ROPE decision rule"* (\cite{Kruschke, 2014, 2018}) to check whether parameter values should be accepted or rejected against an explicitly formulated "null hypothesis" (i.e., a ROPE). In other words, it checks the percentage of the `89%` [HDI][hdi] that is the null region (the ROPE). If this percentage is sufficiently low, the null hypothesis is rejected. If this percentage is sufficiently high, the null hypothesis is accepted.
#'
#'
#' @inheritParams rope
#'
#' @details Using the [ROPE][rope] and the [HDI][hdi], \cite{Kruschke (2018)}
#'   suggests using the percentage of the `95%` (or `89%`, considered more stable)
#'   HDI that falls within the ROPE as a decision rule. If the HDI
#'   is completely outside the ROPE, the "null hypothesis" for this parameter is
#'   "rejected". If the ROPE completely covers the HDI, i.e., all most credible
#'   values of a parameter are inside the region of practical equivalence, the
#'   null hypothesis is accepted. Else, it’s undecided whether to accept or
#'   reject the null hypothesis. If the full ROPE is used (i.e., `100%` of the
#'   HDI), then the null hypothesis is rejected or accepted if the percentage
#'   of the posterior within the ROPE is smaller than to `2.5%` or greater than
#'   `97.5%`. Desirable results are low proportions inside the ROPE  (the closer
#'   to zero the better).
#'   \cr \cr
#'   Some attention is required for finding suitable values for the ROPE limits
#'   (argument `range`). See 'Details' in [`rope_range()`][rope_range]
#'   for further information.
#'   \cr \cr
#'   **Multicollinearity: Non-independent covariates**
#'   \cr \cr
#'   When parameters show strong correlations, i.e. when covariates are not
#'   independent, the joint parameter distributions may shift towards or
#'   away from the ROPE. In such cases, the test for practical equivalence may
#'   have inappropriate results. Collinearity invalidates ROPE and hypothesis
#'   testing based on univariate marginals, as the probabilities are conditional
#'   on independence. Most problematic are the results of the "undecided"
#'   parameters, which may either move further towards "rejection" or away
#'   from it (\cite{Kruschke 2014, 340f}).
#'   \cr \cr
#'   `equivalence_test()` performs a simple check for pairwise correlations
#'   between parameters, but as there can be collinearity between more than two variables,
#'   a first step to check the assumptions of this hypothesis testing is to look
#'   at different pair plots. An even more sophisticated check is the projection
#'   predictive variable selection (\cite{Piironen and Vehtari 2017}).
#'
#'
#' @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}
#' - Kruschke, J. K. (2014). Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan. Academic Press
#' - Piironen, J., & Vehtari, A. (2017). Comparison of Bayesian predictive methods for model selection. Statistics and Computing, 27(3), 711–735. \doi{10.1007/s11222-016-9649-y}
#'
#' @return A data frame with following columns:
#'   \itemize{
#'     \item `Parameter` The model parameter(s), if `x` is a model-object. If `x` is a vector, this column is missing.
#'     \item `CI` The probability of the HDI.
#'     \item `ROPE_low`, `ROPE_high` The limits of the ROPE. These values are identical for all parameters.
#'     \item `ROPE_Percentage` The proportion of the HDI that lies inside the ROPE.
#'     \item `ROPE_Equivalence` The "test result", as character. Either "rejected", "accepted" or "undecided".
#'     \item `HDI_low` , `HDI_high` The lower and upper HDI limits for the parameters.
#'   }
#'
#' @note There is a `print()`-method with a `digits`-argument to control
#'   the amount of digits in the output, and there is a
#'   [`plot()`-method](https://easystats.github.io/see/articles/bayestestR.html)
#'   to visualize the results from the equivalence-test (for models only).
#'
#' @examplesIf require("rstanarm") && require("brms") && require("emmeans") && require("BayesFactor")
#' library(bayestestR)
#'
#' equivalence_test(x = rnorm(1000, 0, 0.01), range = c(-0.1, 0.1))
#' equivalence_test(x = rnorm(1000, 0, 1), range = c(-0.1, 0.1))
#' equivalence_test(x = rnorm(1000, 1, 0.01), range = c(-0.1, 0.1))
#' equivalence_test(x = rnorm(1000, 1, 1), ci = c(.50, .99))
#'
#' # print more digits
#' test <- equivalence_test(x = rnorm(1000, 1, 1), ci = c(.50, .99))
#' print(test, digits = 4)
#' \donttest{
#' model <- rstanarm::stan_glm(mpg ~ wt + cyl, data = mtcars)
#' equivalence_test(model)
#'
#' # plot result
#' test <- equivalence_test(model)
#' plot(test)
#'
#' equivalence_test(emmeans::emtrends(model, ~1, "wt", data = mtcars))
#'
#' model <- brms::brm(mpg ~ wt + cyl, data = mtcars)
#' equivalence_test(model)
#'
#' bf <- BayesFactor::ttestBF(x = rnorm(100, 1, 1))
#' # equivalence_test(bf)
#' }
#' @export
equivalence_test <- function(x, ...) {
  UseMethod("equivalence_test")
}


#' @rdname equivalence_test
#' @export
equivalence_test.default <- function(x, ...) {
  NULL
}


#' @export
equivalence_test.numeric <- function(x, range = "default", ci = 0.95, verbose = TRUE, ...) {
  rope_data <- rope(x, range = range, ci = ci, verbose = verbose)
  out <- as.data.frame(rope_data)

  if (all(ci < 1)) {
    out$ROPE_Equivalence <- datawizard::recode_into(
      out$ROPE_Percentage == 0 ~ "Rejected",
      out$ROPE_Percentage == 1 ~ "Accepted",
      default = "Undecided"
    )
  } else {
    # Related to guidelines for full rope (https://easystats.github.io/bayestestR/articles/4_Guidelines.html)
    out$ROPE_Equivalence <- datawizard::recode_into(
      out$ROPE_Percentage < 0.025 ~ "Rejected",
      out$ROPE_Percentage > 0.975 ~ "Accepted",
      default = "Undecided"
    )
  }

  out$HDI_low <- attr(rope_data, "HDI_area", exact = TRUE)$CI_low
  out$HDI_high <- attr(rope_data, "HDI_area", exact = TRUE)$CI_high

  # remove attribute
  attr(out, "HDI_area") <- NULL
  attr(out, "data") <- x

  class(out) <- unique(c("equivalence_test", "see_equivalence_test", class(out)))
  out
}



#' @rdname equivalence_test
#' @export
equivalence_test.data.frame <- function(x, range = "default", ci = 0.95, verbose = TRUE, ...) {
  l <- insight::compact_list(lapply(
    x,
    equivalence_test,
    range = range,
    ci = ci,
    verbose = verbose
  ))

  dat <- do.call(rbind, l)
  out <- data.frame(
    Parameter = rep(names(l), each = nrow(dat) / length(l)),
    dat,
    stringsAsFactors = FALSE
  )
  row.names(out) <- NULL

  attr(out, "object_name") <- insight::safe_deparse_symbol(substitute(x))
  class(out) <- unique(c("equivalence_test", "see_equivalence_test_df", class(out)))

  out
}


#' @export
equivalence_test.draws <- function(x, range = "default", ci = 0.95, verbose = TRUE, ...) {
  equivalence_test(.posterior_draws_to_df(x), range = range, ci = ci, verbose = verbose, ...)
}

#' @export
equivalence_test.rvar <- equivalence_test.draws


#' @export
equivalence_test.emmGrid <- function(x, range = "default", ci = 0.95, verbose = TRUE, ...) {
  xdf <- insight::get_parameters(x)

  out <- equivalence_test(xdf, range = range, ci = ci, verbose = verbose, ...)
  attr(out, "object_name") <- insight::safe_deparse_symbol(substitute(x))
  out
}

#' @export
equivalence_test.emm_list <- equivalence_test.emmGrid


#' @export
equivalence_test.BFBayesFactor <- function(x, range = "default", ci = 0.95, verbose = TRUE, ...) {
  out <- equivalence_test(insight::get_parameters(x), range = range, ci = ci, verbose = verbose, ...)
  attr(out, "object_name") <- insight::safe_deparse_symbol(substitute(x))
  out
}




#' @keywords internal
.equivalence_test_models <- function(x,
                                     range = "default",
                                     ci = 0.95,
                                     effects = "fixed",
                                     component = "conditional",
                                     parameters = NULL,
                                     verbose = TRUE) {
  if (all(range == "default")) {
    range <- rope_range(x, verbose = verbose)
  } else if (!all(is.numeric(range)) || length(range) != 2L) {
    insight::format_error("`range` should be 'default' or a vector of 2 numeric values (e.g., c(-0.1, 0.1)).")
  }

  if (verbose && !inherits(x, "blavaan")) .check_multicollinearity(x)
  params <- insight::get_parameters(
    x,
    component = component,
    effects = effects,
    parameters = parameters,
    verbose = verbose
  )

  l <- sapply(
    params,
    equivalence_test,
    range = range,
    ci = ci,
    verbose = verbose,
    simplify = FALSE
  )

  dat <- do.call(rbind, l)
  out <- data.frame(
    Parameter = rep(names(l), each = nrow(dat) / length(l)),
    dat,
    stringsAsFactors = FALSE
  )

  class(out) <- unique(c("equivalence_test", "see_equivalence_test", class(out)))
  out
}


#' @rdname equivalence_test
#' @export
equivalence_test.stanreg <- function(x,
                                     range = "default",
                                     ci = 0.95,
                                     effects = c("fixed", "random", "all"),
                                     component = c(
                                       "location",
                                       "all",
                                       "conditional",
                                       "smooth_terms",
                                       "sigma",
                                       "distributional",
                                       "auxiliary"
                                     ),
                                     parameters = NULL,
                                     verbose = TRUE,
                                     ...) {
  effects <- match.arg(effects)
  component <- match.arg(component)

  out <- .equivalence_test_models(x, range, ci, effects, component, parameters, verbose)

  out <- .prepare_output(
    out,
    insight::clean_parameters(x),
    inherits(x, "stanmvreg")
  )

  class(out) <- unique(c("equivalence_test", "see_equivalence_test", class(out)))
  attr(out, "object_name") <- insight::safe_deparse_symbol(substitute(x))
  out
}


#' @export
equivalence_test.stanfit <- equivalence_test.stanreg

#' @export
equivalence_test.blavaan <- equivalence_test.stanreg


#' @rdname equivalence_test
#' @export
equivalence_test.brmsfit <- function(x,
                                     range = "default",
                                     ci = 0.95,
                                     effects = c("fixed", "random", "all"),
                                     component = c("conditional", "zi", "zero_inflated", "all"),
                                     parameters = NULL,
                                     verbose = TRUE,
                                     ...) {
  effects <- match.arg(effects)
  component <- match.arg(component)

  out <- .equivalence_test_models(x, range, ci, effects, component, parameters, verbose)

  out <- .prepare_output(
    out,
    insight::clean_parameters(x),
    inherits(x, "stanmvreg")
  )

  class(out) <- unique(c("equivalence_test", "see_equivalence_test", class(out)))
  attr(out, "object_name") <- insight::safe_deparse_symbol(substitute(x))
  out
}



#' @export
equivalence_test.sim.merMod <- function(x,
                                        range = "default",
                                        ci = 0.95,
                                        parameters = NULL,
                                        verbose = TRUE,
                                        ...) {
  out <- .equivalence_test_models(
    x,
    range,
    ci,
    effects = "fixed",
    component = "conditional",
    parameters,
    verbose = verbose
  )

  attr(out, "object_name") <- insight::safe_deparse_symbol(substitute(x))
  out
}

#' @export
equivalence_test.sim <- equivalence_test.sim.merMod


#' @export
equivalence_test.mcmc <- function(x,
                                  range = "default",
                                  ci = 0.95,
                                  parameters = NULL,
                                  verbose = TRUE,
                                  ...) {
  out <- .equivalence_test_models(
    as.data.frame(x),
    range,
    ci,
    effects = "fixed",
    component = "conditional",
    parameters,
    verbose = verbose
  )

  attr(out, "object_name") <- insight::safe_deparse_symbol(substitute(x))
  out
}


#' @export
equivalence_test.bcplm <- function(x,
                                   range = "default",
                                   ci = 0.95,
                                   parameters = NULL,
                                   verbose = TRUE,
                                   ...) {
  out <- .equivalence_test_models(
    insight::get_parameters(x),
    range,
    ci,
    effects = "fixed",
    component = "conditional",
    parameters,
    verbose = verbose
  )

  attr(out, "object_name") <- insight::safe_deparse_symbol(substitute(x))
  out
}

#' @export
equivalence_test.blrm <- equivalence_test.bcplm

#' @export
equivalence_test.mcmc.list <- equivalence_test.bcplm

#' @export
equivalence_test.bayesQR <- equivalence_test.bcplm



#' @export
equivalence_test.bamlss <- function(x,
                                    range = "default",
                                    ci = 0.95,
                                    component = c("all", "conditional", "location"),
                                    parameters = NULL,
                                    verbose = TRUE,
                                    ...) {
  component <- match.arg(component)
  out <- .equivalence_test_models(
    insight::get_parameters(x, component = component),
    range,
    ci,
    effects = "fixed",
    component = "conditional",
    parameters,
    verbose = verbose
  )

  attr(out, "object_name") <- insight::safe_deparse_symbol(substitute(x))
  out
}