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).

p_map(x, precision = 2^10, method = "kernel", ...) p_pointnull(x, precision = 2^10, method = "kernel", ...) # S3 method for stanreg p_map( x, precision = 2^10, method = "kernel", effects = c("fixed", "random", "all"), component = c("location", "all", "conditional", "smooth_terms", "sigma", "distributional", "auxiliary"), parameters = NULL, ... ) # S3 method for brmsfit p_map( x, precision = 2^10, method = "kernel", effects = c("fixed", "random", "all"), component = c("conditional", "zi", "zero_inflated", "all"), parameters = NULL, ... )

x | Vector representing a posterior distribution, or a data frame of such
vectors. Can also be a Bayesian model ( |
---|---|

precision | Number of points of density data. See the |

method | Density estimation method. Can be |

... | Currently not used. |

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

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 brms-models. |

parameters | Regular expression pattern that describes the parameters that
should be returned. Meta-parameters (like |

Note that this method is sensitive to the density estimation `method`

(see the section in the examples below).

**Strengths:** Straightforward computation. Objective property of the posterior distribution.

**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.

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

Mills, J. A. (2018). Objective Bayesian Precise Hypothesis Testing. University of Cincinnati.

#> MAP-based p-value: 0.98#> MAP-based p-value: 0.00if (FALSE) { 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")]) }