p_map {bayestestR} | R Documentation |
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 the null (e.g., 0) divided by the density at the Maximum A Posteriori (MAP).
Usage
p_map(x, ...)
p_pointnull(x, ...)
## S3 method for class 'numeric'
p_map(x, null = 0, precision = 2^10, method = "kernel", ...)
## S3 method for class 'get_predicted'
p_map(
x,
null = 0,
precision = 2^10,
method = "kernel",
use_iterations = FALSE,
verbose = TRUE,
...
)
## S3 method for class 'data.frame'
p_map(x, null = 0, precision = 2^10, method = "kernel", rvar_col = NULL, ...)
## S3 method for class 'brmsfit'
p_map(
x,
null = 0,
precision = 2^10,
method = "kernel",
effects = "fixed",
component = "conditional",
parameters = NULL,
...
)
Arguments
x |
Vector representing a posterior distribution, or a data frame of such
vectors. Can also be a Bayesian model. bayestestR supports a wide range
of models (see, for example, |
... |
Currently not used. |
null |
The value considered as a "null" effect. Traditionally 0, but could also be 1 in the case of ratios of change (OR, IRR, ...). |
precision |
Number of points of density data. See the |
method |
Density estimation method. Can be |
use_iterations |
Logical, if |
verbose |
Toggle off warnings. |
rvar_col |
A single character - the name of an |
effects |
Should variables for fixed effects ( For models of from packages brms or rstanarm there are additional options:
|
component |
Which type of parameters to return, such as parameters for the conditional model, the zero-inflated part of the model, the dispersion term, etc. See details in section Model Components. May be abbreviated. Note that the conditional component also refers to the count or mean component - names may differ, depending on the modeling package. There are three convenient shortcuts (not applicable to all model classes):
|
parameters |
Regular expression pattern that describes the parameters
that should be returned. Meta-parameters (like |
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.
Model components
Possible values for the component
argument depend on the model class.
Following are valid options:
-
"all"
: returns all model components, applies to all models, but will only have an effect for models with more than just the conditional model component. -
"conditional"
: only returns the conditional component, i.e. "fixed effects" terms from the model. Will only have an effect for models with more than just the conditional model component. -
"smooth_terms"
: returns smooth terms, only applies to GAMs (or similar models that may contain smooth terms). -
"zero_inflated"
(or"zi"
): returns the zero-inflation component. -
"location"
: returns location parameters such asconditional
,zero_inflated
, orsmooth_terms
(everything that are fixed or random effects - depending on theeffects
argument - but no auxiliary parameters). -
"distributional"
(or"auxiliary"
): components likesigma
,dispersion
,beta
orprecision
(and other auxiliary parameters) are returned.
For models of class brmsfit
(package brms), even more options are
possible for the component
argument, which are not all documented in detail
here. See also ?insight::find_parameters
.
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.
See Also
Examples
library(bayestestR)
p_map(rnorm(1000, 0, 1))
p_map(rnorm(1000, 10, 1))
model <- suppressWarnings(
rstanarm::stan_glm(mpg ~ wt + gear, data = mtcars, chains = 2, iter = 200, refresh = 0)
)
p_map(model)
p_map(suppressWarnings(
emmeans::emtrends(model, ~1, "wt", data = mtcars)
))
model <- brms::brm(mpg ~ wt + cyl, data = mtcars)
p_map(model)
bf <- BayesFactor::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 = as.numeric(p_map(x, method = "kernel")),
KernSmooth = as.numeric(p_map(x, method = "KernSmooth")),
logspline = as.numeric(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")])