% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/p_map.R
\name{p_map}
\alias{p_map}
\alias{p_pointnull}
\alias{p_map.stanreg}
\alias{p_map.brmsfit}
\title{Bayesian p-value based on the density at the Maximum A Posteriori (MAP)}
\usage{
p_map(x, precision = 2^10, method = "kernel", ...)

p_pointnull(x, precision = 2^10, method = "kernel", ...)

\method{p_map}{stanreg}(
  x,
  precision = 2^10,
  method = "kernel",
  effects = c("fixed", "random", "all"),
  parameters = NULL,
  ...
)

\method{p_map}{brmsfit}(
  x,
  precision = 2^10,
  method = "kernel",
  effects = c("fixed", "random", "all"),
  component = c("conditional", "zi", "zero_inflated", "all"),
  parameters = NULL,
  ...
)
}
\arguments{
\item{x}{Vector representing a posterior distribution. Can also be a
\code{stanreg}, \code{brmsfit} or a \code{BayesFactor} model.}

\item{precision}{Number of points of density data. See the \code{n} parameter in \link[=density]{density}.}

\item{method}{Density estimation method. Can be \code{"kernel"} (default), \code{"logspline"} or \code{"KernSmooth"}.}

\item{...}{Currently not used.}

\item{effects}{Should results for fixed effects, random effects or both be returned?
Only applies to mixed models. May be abbreviated.}

\item{parameters}{Regular expression pattern that describes the parameters that
should be returned. Meta-parameters (like \code{lp__} or \code{prior_}) are
filtered by default, so only parameters that typically appear in the
\code{summary()} are returned. Use \code{parameters} to select specific parameters
for the output.}

\item{component}{Should results for all parameters, parameters for the conditional model
or the zero-inflated part of the model be returned? May be abbreviated. Only
applies to \pkg{brms}-models.}
}
\description{
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 secion 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.
}
}
\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")])
}
}
\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.
}
}
\seealso{
\href{https://www.youtube.com/watch?v=Ip8Ci5KUVRc}{Jeff Mill's talk}
}