bayestestR: p_map – R documentation

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p_map

Bayesian p-value based on the density at the Maximum A Posteriori (MAP)

Description

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).

Usage

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

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

## S3 method for class '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 class 'brmsfit'
p_map(
  x,
  precision = 2^10,
  method = "kernel",
  effects = c("fixed", "random", "all"),
  component = c("conditional", "zi", "zero_inflated", "all"),
  parameters = NULL,
  ...
)

Arguments

`x`	Vector representing a posterior distribution, or a data frame of such vectors. Can also be a Bayesian model (`stanreg`, `brmsfit`, `MCMCglmm`, `mcmc` or `bcplm`) or a `BayesFactor` model.
`precision`	Number of points of density data. See the `n` parameter in `density`.
`method`	Density estimation method. Can be `"kernel"` (default), `"logspline"` or `"KernSmooth"`.
`...`	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 `lp__` or `prior_`) are filtered by default, so only parameters that typically appear in the `summary()` are returned. Use `parameters` to select specific parameters for the output.

Details

Note that this method is sensitive to the density estimation method (see the section in the examples below).

Strengths and Limitations

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.

References

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.

Examples

library(bayestestR)

p_map(rnorm(1000, 0, 1))
p_map(rnorm(1000, 10, 1))
## Not run: 
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")])

## End(Not run)

bayestestR

Understand and Describe Bayesian Models and Posterior Distributions

v0.10.0

GPL-3

Authors

Dominique Makowski [aut, cre] (<https://orcid.org/0000-0001-5375-9967>, @Dom_Makowski), Daniel Lüdecke [aut] (<https://orcid.org/0000-0002-8895-3206>, @strengejacke), Mattan S. Ben-Shachar [aut] (<https://orcid.org/0000-0002-4287-4801>, @mattansb), Indrajeet Patil [aut] (<https://orcid.org/0000-0003-1995-6531>, @patilindrajeets), Michael D. Wilson [aut] (<https://orcid.org/0000-0003-4143-7308>), Paul-Christian Bürkner [rev], Tristan Mahr [rev] (<https://orcid.org/0000-0002-8890-5116>), Henrik Singmann [ctb] (<https://orcid.org/0000-0002-4842-3657>), Quentin F. Gronau [ctb] (<https://orcid.org/0000-0001-5510-6943>), Sam Crawley [ctb] (<https://orcid.org/0000-0002-7847-0411>)

Initial release