#' Practical Significance (ps)
#'
#' Compute the probability of \strong{Practical Significance} (\strong{\emph{ps}}), which can be conceptualized as a unidirectional equivalence test. It returns the probability that effect is above a given threshold corresponding to a negligible effect in the median's direction. Mathematically, it is defined as the proportion of the posterior distribution of the median sign above the threshold.
#'
#' @inheritParams rope
#' @param threshold The threshold value that separates significant from negligible effect. If \code{"default"}, the range is set to \code{0.1} if input is a vector, and based on \code{\link[=rope_range]{rope_range()}} if a Bayesian model is provided.
#'
#' @return Values between 0 and 1 corresponding to the probability of practical significance (ps).
#'
#' @details \code{p_significance()} returns the proportion of a probability
#'   distribution (\code{x}) that is outside a certain range (the negligible
#'   effect, or ROPE, see argument \code{threshold}). If there are values of the
#'   distribution both below and above the ROPE, \code{p_significance()} returns
#'   the higher probability of a value being outside the ROPE. Typically, this
#'   value should be larger than 0.5 to indicate practical significance. However,
#'   if the range of the negligible effect is rather large compared to the
#'   range of the probability distribution \code{x}, \code{p_significance()}
#'   will be less than 0.5, which indicates no clear practical significance.
#'
#' @examples
#' library(bayestestR)
#'
#' # Simulate a posterior distribution of mean 1 and SD 1
#' # ----------------------------------------------------
#' posterior <- rnorm(1000, mean = 1, sd = 1)
#' p_significance(posterior)
#'
#' # Simulate a dataframe of posterior distributions
#' # -----------------------------------------------
#' df <- data.frame(replicate(4, rnorm(100)))
#' p_significance(df)
#'
#' \dontrun{
#' # rstanarm models
#' # -----------------------------------------------
#' if (require("rstanarm")) {
#'   model <- rstanarm::stan_glm(mpg ~ wt + cyl,
#'     data = mtcars,
#'     chains = 2, refresh = 0
#'   )
#'   p_significance(model)
#' }
#' }
#' @export
p_significance <- function(x, ...) {
UseMethod("p_significance")
}

#' @rdname p_significance
#' @export
p_significance.numeric <- function(x, threshold = "default", ...) {
threshold <- .select_threshold_ps(x = x, threshold = threshold)

psig <- max(
c(
length(x[x > abs(threshold)]) / length(x), # ps positive
length(x[x < -abs(threshold)]) / length(x) # ps negative
)
)

attr(psig, "threshold") <- threshold
attr(psig, "data") <- x

class(psig) <- unique(c("p_significance", "see_p_significance", class(psig)))

psig
}

#' @export
p_significance.data.frame <- function(x, threshold = "default", ...) {
threshold <- .select_threshold_ps(x = x, threshold = threshold)
x <- .select_nums(x)

if (ncol(x) == 1) {
ps <- p_significance(x[, 1], threshold = threshold, ...)
} else {
ps <- sapply(x, p_significance, threshold = threshold, simplify = TRUE, ...)
}

out <- data.frame(
"Parameter" = names(x),
"ps" = as.numeric(ps),
row.names = NULL,
stringsAsFactors = FALSE
)

attr(out, "threshold") <- threshold
attr(out, "object_name") <- .safe_deparse(substitute(x))
class(out) <- unique(c("p_significance", "see_p_significance", class(out)))

out
}

#' @export
p_significance.MCMCglmm <- function(x, threshold = "default", ...) {
nF <- x$Fixed$nfl
out <- p_significance(as.data.frame(x$Sol[, 1:nF, drop = FALSE]), threshold = threshold, ...) attr(out, "object_name") <- .safe_deparse(substitute(x)) out } #' @export p_significance.BFBayesFactor <- function(x, threshold = "default", ...) { out <- p_significance(insight::get_parameters(x), threshold = threshold, ...) attr(out, "object_name") <- .safe_deparse(substitute(x)) out } #' @export p_significance.mcmc <- function(x, threshold = "default", ...) { p_significance(as.data.frame(x), threshold = threshold, ...) } #' @rdname p_significance #' @export p_significance.emmGrid <- function(x, threshold = "default", ...) { if (!requireNamespace("emmeans")) { stop("Package 'emmeans' required for this function to work. Please install it by running install.packages('emmeans').") } xdf <- as.data.frame(as.matrix(emmeans::as.mcmc.emmGrid(x, names = FALSE))) out <- p_significance(xdf, threshold = threshold, ...) attr(out, "object_name") <- .safe_deparse(substitute(x)) out } #' @rdname p_significance #' @export p_significance.stanreg <- function(x, threshold = "default", effects = c("fixed", "random", "all"), parameters = NULL, verbose = TRUE, ...) { effects <- match.arg(effects) threshold <- .select_threshold_ps(model = x, threshold = threshold) data <- p_significance( insight::get_parameters(x, effects = effects, parameters = parameters), threshold = threshold ) out <- .prepare_output(data, insight::clean_parameters(x)) attr(out, "threshold") <- threshold attr(out, "object_name") <- .safe_deparse(substitute(x)) class(out) <- class(data) out } #' @rdname p_significance #' @export p_significance.brmsfit <- function(x, threshold = "default", effects = c("fixed", "random", "all"), component = c("conditional", "zi", "zero_inflated", "all"), parameters = NULL, verbose = TRUE, ...) { effects <- match.arg(effects) component <- match.arg(component) threshold <- .select_threshold_ps(model = x, threshold = threshold) data <- p_significance( insight::get_parameters(x, effects = effects, component = component, parameters = parameters), threshold = threshold ) out <- .prepare_output(data, insight::clean_parameters(x)) attr(out, "threshold") <- threshold attr(out, "object_name") <- .safe_deparse(substitute(x)) class(out) <- class(data) out } #' @rdname as.numeric.p_direction #' @export as.numeric.p_significance <- function(x, ...) { if ("data.frame" %in% class(x)) { return(as.numeric(as.vector(x$ps)))
} else {
return(as.vector(x))
}
}

#' @method as.double p_significance
#' @export
as.double.p_significance <- as.numeric.p_significance

#' @keywords internal
.select_threshold_ps <- function(x = NULL, model = NULL, threshold = "default") {
# If a range is passed
if (length(threshold) > 1) {
if(length(unique(abs(threshold))) == 1) { # If symetric range
threshold <- abs(threshold[2])
} else{
stop("threshold should be 'default' or a numeric value (e.g., 0.1).")
}
}
# If default
if (all(threshold == "default")) {
if (!is.null(model)) {
threshold <- rope_range(model)[2]
} else {
threshold <- 0.1
}
} else if (!all(is.numeric(threshold))) {
stop("threshold should be 'default' or a numeric value (e.g., 0.1).")
}
threshold
}