#' Bayesian p-value based on the density at the Maximum A Posteriori (MAP) #' #' Compute a Bayesian equivalent of the \emph{p}-value, related to the odds that a parameter (described by its posterior distribution) has against the null hypothesis (\emph{h0}) using Mills' (2014, 2017) \emph{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 \code{method} (see the section in the examples below). #' \subsection{Strengths and Limitations}{ #' \strong{Strengths:} Straightforward computation. Objective property of the posterior distribution. #' \cr \cr #' \strong{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) #' } #' #' \donttest{ #' # --------------------------------------- #' # 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")]) #' } #' @seealso \href{https://www.youtube.com/watch?v=Ip8Ci5KUVRc}{Jeff Mill's talk} #' #' @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. #' } #' #' @importFrom stats density #' @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 #' @importFrom insight get_parameters #' @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.mcmc.list <- p_map.mcmc #' @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"), parameters = NULL, ...) { effects <- match.arg(effects) out <- .prepare_output( p_map(insight::get_parameters(x, effects = effects, parameters = parameters), precision = precision, method = method), insight::clean_parameters(x), inherits(x, "stanmvreg") ) class(out) <- unique(c("p_map", class(out))) attr(out, "object_name") <- .safe_deparse(substitute(x)) out } #' @export p_map.stanfit <- 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) out <- .prepare_output( p_map(insight::get_parameters(x, effects = effects, component = component, parameters = parameters), precision = precision, method = method, ...), insight::clean_parameters(x) ) 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