Compute the probability of Practical Significance (ps), which can be conceptualized as a unidirectional equivalence test. It returns the probability that effect is above a given threshold corresponding to a negligible effect in the median's direction. Mathematically, it is defined as the proportion of the posterior distribution of the median sign above the threshold.
p_significance(x, ...)
# S3 method for class 'numeric'
p_significance(x, threshold = "default", ...)
# S3 method for class 'get_predicted'
p_significance(
x,
threshold = "default",
use_iterations = FALSE,
verbose = TRUE,
...
)
# S3 method for class 'data.frame'
p_significance(x, threshold = "default", rvar_col = NULL, ...)
# S3 method for class 'brmsfit'
p_significance(
x,
threshold = "default",
effects = "fixed",
component = "conditional",
parameters = NULL,
verbose = TRUE,
...
)Vector representing a posterior distribution. Can also be a
stanreg or brmsfit model.
Currently not used.
The threshold value that separates significant from negligible effect, which can have following possible values:
"default", in which case the range is set to 0.1 if input is a vector,
and based on rope_range() if a (Bayesian) model is provided.
a single numeric value (e.g., 0.1), which is used as range around zero (i.e. the threshold range is set to -0.1 and 0.1, i.e. reflects a symmetric interval)
a numeric vector of length two (e.g., c(-0.2, 0.1)), useful for
asymmetric intervals
a list of numeric vectors, where each vector corresponds to a parameter
a list of named numeric vectors, where names correspond to parameter
names. In this case, all parameters that have no matching name in threshold
will be set to "default".
Logical, if TRUE and x is a get_predicted object,
(returned by insight::get_predicted()), the function is applied to the
iterations instead of the predictions. This only applies to models that return
iterations for predicted values (e.g., brmsfit models).
Toggle off warnings.
A single character - the name of an rvar column in the data
frame to be processed. See example in p_direction().
Should variables for fixed effects ("fixed"), random effects
("random") or both ("all") be returned? Only applies to mixed models. May
be abbreviated.
For models of from packages brms or rstanarm there are additional options:
"fixed" returns fixed effects.
"random_variance" return random effects parameters (variance and
correlation components, e.g. those parameters that start with sd_ or
cor_).
"grouplevel" returns random effects group level estimates, i.e. those
parameters that start with r_.
"random" returns both "random_variance" and "grouplevel".
"all" returns fixed effects and random effects variances.
"full" returns all parameters.
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):
component = "all" returns all possible parameters.
If component = "location", location parameters such as conditional,
zero_inflated, smooth_terms, or instruments are returned (everything
that are fixed or random effects - depending on the effects argument -
but no auxiliary parameters).
For component = "distributional" (or "auxiliary"), components like
sigma, dispersion, beta or precision (and other auxiliary
parameters) are returned.
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.
Values between 0 and 1 corresponding to the probability of practical significance (ps).
p_significance() returns the proportion of a probability
distribution (x) that is outside a certain range (the negligible
effect, or ROPE, see argument threshold). If there are values of the
distribution both below and above the ROPE, p_significance() returns
the higher probability of a value being outside the ROPE. Typically, this
value should be larger than 0.5 to indicate practical significance. However,
if the range of the negligible effect is rather large compared to the
range of the probability distribution x, p_significance()
will be less than 0.5, which indicates no clear practical significance.
There is also a plot()-method implemented in the see-package.
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 as conditional,
zero_inflated, or smooth_terms (everything that are fixed or random
effects - depending on the effects argument - but no auxiliary
parameters).
"distributional" (or "auxiliary"): components like sigma,
dispersion, beta or precision (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.
library(bayestestR)
# Simulate a posterior distribution of mean 1 and SD 1
# ----------------------------------------------------
posterior <- rnorm(1000, mean = 1, sd = 1)
p_significance(posterior)
#> Practical Significance (threshold: 0.10)
#>
#> Parameter | ps
#> ----------------
#> Posterior | 0.80
# Simulate a dataframe of posterior distributions
# -----------------------------------------------
df <- data.frame(replicate(4, rnorm(100)))
p_significance(df)
#> Practical Significance (threshold: 0.10)
#>
#> Parameter | ps
#> ----------------
#> X1 | 0.51
#> X2 | 0.53
#> X3 | 0.46
#> X4 | 0.47
# \donttest{
# rstanarm models
# -----------------------------------------------
model <- rstanarm::stan_glm(mpg ~ wt + cyl,
data = mtcars,
chains = 2, refresh = 0
)
p_significance(model)
#> Practical Significance (threshold: 0.60)
#>
#> Parameter | ps
#> ------------------
#> (Intercept) | 1.00
#> wt | 1.00
#> cyl | 0.98
# multiple thresholds - asymmetric, symmetric, default
p_significance(model, threshold = list(c(-10, 5), 0.2, "default"))
#> Practical Significance
#>
#> Parameter | ps | ROPE
#> -----------------------------------
#> (Intercept) | 1.00 | [-10.00, 5.00]
#> wt | 1.00 | [ -0.20, 0.20]
#> cyl | 0.98 | [ -0.60, 0.60]
# named thresholds
p_significance(model, threshold = list(wt = 0.2, `(Intercept)` = c(-10, 5)))
#> Practical Significance
#>
#> Parameter | ps | ROPE
#> -----------------------------------
#> (Intercept) | 1.00 | [-10.00, 5.00]
#> wt | 1.00 | [ -0.20, 0.20]
#> cyl | 0.98 | [ -0.60, 0.60]
# }