p_map.R
#' Bayesian p-value based on the density at the Maximum A Posteriori (MAP)
#'
#' Compute a Bayesian equivalent of the *p*-value, related to the odds that a parameter (described by its posterior distribution) has against the null hypothesis (*h0*) using Mills' (2014, 2017) *Objective Bayesian Hypothesis Testing* framework. It corresponds to the density value at 0 divided by the density at the Maximum A Posteriori (MAP).
#'
#' @details Note that this method is sensitive to the density estimation method (see the section in the examples below).
#' \subsection{Strengths and Limitations}{
#' **Strengths:** Straightforward computation. Objective property of the posterior distribution.
#' \cr \cr
#' **Limitations:** Limited information favoring the null hypothesis. Relates on density approximation. Indirect relationship between mathematical definition and interpretation. Only suitable for weak / very diffused priors.
#' }
#'
#' @inheritParams hdi
#' @inheritParams density_at
#'
#' @examples
#' library(bayestestR)
#'
#' p_map(rnorm(1000, 0, 1))
#' p_map(rnorm(1000, 10, 1))
#' \dontrun{
#' library(rstanarm)
#' model <- stan_glm(mpg ~ wt + gear, data = mtcars, chains = 2, iter = 200, refresh = 0)
#' p_map(model)
#'
#' library(emmeans)
#' p_map(emtrends(model, ~1, "wt"))
#'
#' library(brms)
#' model <- brms::brm(mpg ~ wt + cyl, data = mtcars)
#' p_map(model)
#'
#' library(BayesFactor)
#' bf <- ttestBF(x = rnorm(100, 1, 1))
#' p_map(bf)
#'
#' # ---------------------------------------
#' # Robustness to density estimation method
#' set.seed(333)
#' data <- data.frame()
#' for (iteration in 1:250) {
#'   x <- rnorm(1000, 1, 1)
#'   result <- data.frame(
#'     "Kernel" = p_map(x, method = "kernel"),
#'     "KernSmooth" = p_map(x, method = "KernSmooth"),
#'     "logspline" = p_map(x, method = "logspline")
#'   )
#'   data <- rbind(data, result)
#' }
#' data$KernSmooth <- data$Kernel - data$KernSmooth #' data$logspline <- data$Kernel - data$logspline
#'
#' summary(data$KernSmooth) #' summary(data$logspline)
#' boxplot(data[c("KernSmooth", "logspline")])
#' }
#'
#' @references \itemize{
#'   \item Makowski D, Ben-Shachar MS, Chen SHA, Lüdecke D (2019) Indices of Effect Existence and Significance in the Bayesian Framework. Frontiers in Psychology 2019;10:2767. \doi{10.3389/fpsyg.2019.02767}
#'   \item Mills, J. A. (2018). Objective Bayesian Precise Hypothesis Testing. University of Cincinnati.
#' }
#'
#' @export
p_map <- function(x, precision = 2^10, method = "kernel", ...) {
UseMethod("p_map")
}

#' @rdname p_map
#' @export
p_pointnull <- p_map

#' @export
p_map.numeric <- function(x, precision = 2^10, method = "kernel", ...) {
# Density at MAP
map <- attributes(map_estimate(x, precision = precision, method = method, ...))$MAP_density # Density at 0 d_0 <- density_at(x, 0, precision = precision, method = method, ...) if (is.na(d_0)) d_0 <- 0 # Odds p <- d_0 / map class(p) <- c("p_map", class(p)) p } #' @export p_map.data.frame <- function(x, precision = 2^10, method = "kernel", ...) { x <- .select_nums(x) if (ncol(x) == 1) { p_MAP <- p_map(x[, 1], precision = precision, method = method, ...) } else { p_MAP <- sapply(x, p_map, precision = precision, method = method, simplify = TRUE, ...) } out <- data.frame( "Parameter" = names(x), "p_MAP" = p_MAP, row.names = NULL, stringsAsFactors = FALSE ) class(out) <- c("p_map", class(out)) out } #' @export p_map.emmGrid <- function(x, precision = 2^10, method = "kernel", ...) { xdf <- insight::get_parameters(x) out <- p_map(xdf, precision = precision, method = method, ...) attr(out, "object_name") <- .safe_deparse(substitute(x)) out } #' @export p_map.emm_list <- p_map.emmGrid #' @keywords internal .p_map_models <- function(x, precision, method, effects, component, parameters, ...) { p_map(insight::get_parameters(x, effects = effects, component = component, parameters = parameters), precision = precision, method = method, ...) } #' @export p_map.mcmc <- function(x, precision = 2^10, method = "kernel", parameters = NULL, ...) { out <- .p_map_models( x = x, precision = precision, method = method, effects = "fixed", component = "conditional", parameters = parameters, ... ) attr(out, "data") <- insight::get_parameters(x, parameters = parameters) out } #' @export p_map.bcplm <- p_map.mcmc #' @export p_map.blrm <- p_map.mcmc #' @export p_map.mcmc.list <- p_map.mcmc #' @export p_map.BGGM <- p_map.mcmc #' @export p_map.bamlss <- function(x, precision = 2^10, method = "kernel", component = c("all", "conditional", "location"), parameters = NULL, ...) { component <- match.arg(component) out <- .p_map_models( x = x, precision = precision, method = method, effects = "all", component = component, parameters = parameters, ... ) out <- .add_clean_parameters_attribute(out, x) attr(out, "data") <- insight::get_parameters(x, parameters = parameters) out } #' @export p_map.sim.merMod <- function(x, precision = 2^10, method = "kernel", effects = c("fixed", "random", "all"), parameters = NULL, ...) { effects <- match.arg(effects) out <- .p_map_models( x = x, precision = precision, method = method, effects = effects, component = "conditional", parameters = parameters, ... ) attr(out, "data") <- insight::get_parameters(x, effects = effects, parameters = parameters) out } #' @export p_map.sim <- function(x, precision = 2^10, method = "kernel", parameters = NULL, ...) { out <- .p_map_models( x = x, precision = precision, method = method, effects = "fixed", component = "conditional", parameters = parameters, ... ) attr(out, "data") <- insight::get_parameters(x, parameters = parameters) out } #' @rdname p_map #' @export p_map.stanreg <- function(x, precision = 2^10, method = "kernel", effects = c("fixed", "random", "all"), component = c("location", "all", "conditional", "smooth_terms", "sigma", "distributional", "auxiliary"), parameters = NULL, ...) { effects <- match.arg(effects) component <- match.arg(component) cleaned_parameters <- insight::clean_parameters(x) out <- .prepare_output( p_map(insight::get_parameters(x, effects = effects, component = component, parameters = parameters), precision = precision, method = method), cleaned_parameters, inherits(x, "stanmvreg") ) attr(out, "clean_parameters") <- cleaned_parameters class(out) <- unique(c("p_map", class(out))) attr(out, "object_name") <- .safe_deparse(substitute(x)) out } #' @export p_map.stanfit <- p_map.stanreg #' @export p_map.blavaan <- p_map.stanreg #' @rdname p_map #' @export p_map.brmsfit <- function(x, precision = 2^10, method = "kernel", effects = c("fixed", "random", "all"), component = c("conditional", "zi", "zero_inflated", "all"), parameters = NULL, ...) { effects <- match.arg(effects) component <- match.arg(component) cleaned_parameters <- insight::clean_parameters(x) out <- .prepare_output( p_map(insight::get_parameters(x, effects = effects, component = component, parameters = parameters), precision = precision, method = method, ...), cleaned_parameters ) attr(out, "clean_parameters") <- cleaned_parameters class(out) <- unique(c("p_map", class(out))) attr(out, "object_name") <- .safe_deparse(substitute(x)) out } #' @export p_map.BFBayesFactor <- function(x, precision = 2^10, method = "kernel", ...) { out <- p_map(insight::get_parameters(x), precision = precision, method = method, ...) attr(out, "object_name") <- .safe_deparse(substitute(x)) out } #' @export p_map.MCMCglmm <- function(x, precision = 2^10, method = "kernel", ...) { nF <- x$Fixed$nfl out <- p_map(as.data.frame(x$Sol[, 1:nF, drop = FALSE]), precision = precision, method = method, ...)
attr(out, "object_name") <- .safe_deparse(substitute(x))
out
}

#' @export
p_map.bayesQR <- function(x, precision = 2^10, method = "kernel", ...) {
out <- p_map(insight::get_parameters(x), precision = precision, method = method, ...)
attr(out, "object_name") <- .safe_deparse(substitute(x))
out
}

#' @rdname as.numeric.p_direction
#' @method as.numeric p_map
#' @export
as.numeric.p_map <- function(x, ...) {
if ("data.frame" %in% class(x)) {
return(as.numeric(as.vector(x\$p_MAP)))
} else {
return(as.vector(x))
}
}

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