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

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

  precision = 2^10,
  method = "kernel",
  effects = c("fixed", "random", "all"),
  parameters = NULL,

  precision = 2^10,
  method = "kernel",
  effects = c("fixed", "random", "all"),
  component = c("conditional", "zi", "zero_inflated", "all"),
  parameters = NULL,
\item{x}{Vector representing a posterior distribution, or a data frame of such
vectors. Can also be a Bayesian model (\code{stanreg}, \code{brmsfit},
\code{MCMCglmm}, \code{mcmc} or \code{bcplm}) or a \code{BayesFactor} model.}

\item{precision}{Number of points of density data. See the \code{n} parameter in \code{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.}
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).
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.

p_map(rnorm(1000, 0, 1))
p_map(rnorm(1000, 10, 1))

model <- stan_glm(mpg ~ wt + gear, data = mtcars, chains = 2, iter = 200, refresh = 0)

p_map(emtrends(model, ~1, "wt"))

model <- brms::brm(mpg ~ wt + cyl, data = mtcars)

bf <- ttestBF(x = rnorm(100, 1, 1))

# ---------------------------------------
# Robustness to density estimation method
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

boxplot(data[c("KernSmooth", "logspline")])
  \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.
\href{}{Jeff Mill's talk}
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