si {bayestestR}  R Documentation 
Compute Support Intervals
Description
A support interval contains only the values of the parameter that predict the observed data better than average, by some degree k; these are values of the parameter that are associated with an updating factor greater or equal than k. From the perspective of the SavageDickey Bayes factor, testing against a point null hypothesis for any value within the support interval will yield a Bayes factor smaller than 1/k.
Usage
si(posterior, ...)
## S3 method for class 'numeric'
si(posterior, prior = NULL, BF = 1, verbose = TRUE, ...)
## S3 method for class 'stanreg'
si(
posterior,
prior = NULL,
BF = 1,
verbose = TRUE,
effects = c("fixed", "random", "all"),
component = c("location", "conditional", "all", "smooth_terms", "sigma", "auxiliary",
"distributional"),
parameters = NULL,
...
)
## S3 method for class 'brmsfit'
si(
posterior,
prior = NULL,
BF = 1,
verbose = TRUE,
effects = c("fixed", "random", "all"),
component = c("location", "conditional", "all", "smooth_terms", "sigma", "auxiliary",
"distributional"),
parameters = NULL,
...
)
## S3 method for class 'blavaan'
si(
posterior,
prior = NULL,
BF = 1,
verbose = TRUE,
effects = c("fixed", "random", "all"),
component = c("location", "conditional", "all", "smooth_terms", "sigma", "auxiliary",
"distributional"),
parameters = NULL,
...
)
## S3 method for class 'emmGrid'
si(posterior, prior = NULL, BF = 1, verbose = TRUE, ...)
## S3 method for class 'get_predicted'
si(
posterior,
prior = NULL,
BF = 1,
use_iterations = FALSE,
verbose = TRUE,
...
)
## S3 method for class 'data.frame'
si(posterior, prior = NULL, BF = 1, verbose = TRUE, ...)
Arguments
posterior 
A numerical vector, 
... 
Arguments passed to and from other methods. (Can be used to pass
arguments to internal 
prior 
An object representing a prior distribution (see 'Details'). 
BF 
The amount of support required to be included in the support interval. 
verbose 
Toggle off warnings. 
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 zeroinflated part of the model be returned? May be abbreviated. Only applies to brmsmodels. 
parameters 
Regular expression pattern that describes the parameters
that should be returned. Metaparameters (like 
use_iterations 
Logical, if 
Details
For more info, in particular on specifying correct priors for factors with more than 2 levels, see the Bayes factors vignette.
This method is used to compute support intervals based on prior and posterior distributions.
For the computation of support intervals, the model priors must be proper priors (at the very least
they should be not flat, and it is preferable that they be informative  note
that by default, brms::brm()
uses flat priors for fixedeffects; see example below).
Value
A data frame containing the lower and upper bounds of the SI.
Note that if the level of requested support is higher than observed in the data, the
interval will be [NA,NA]
.
Choosing a value of BF
The choice of BF
(the level of support) depends on what we want our interval
to represent:
A
BF
= 1 contains values whose credibility is not decreased by observing the data.A
BF
> 1 contains values who received more impressive support from the data.A
BF
< 1 contains values whose credibility has not been impressively decreased by observing the data. Testing against values outside this interval will produce a Bayes factor larger than 1/BF
in support of the alternative. E.g., if an SI (BF = 1/3) excludes 0, the Bayes factor against the pointnull will be larger than 3.
Setting the correct prior
For the computation of Bayes factors, the model priors must be proper priors
(at the very least they should be not flat, and it is preferable that
they be informative); As the priors for the alternative get wider, the
likelihood of the null value(s) increases, to the extreme that for completely
flat priors the null is infinitely more favorable than the alternative (this
is called the JeffreysLindleyBartlett paradox). Thus, you should
only ever try (or want) to compute a Bayes factor when you have an informed
prior.
(Note that by default, brms::brm()
uses flat priors for fixedeffects;
See example below.)
It is important to provide the correct prior
for meaningful results.
When
posterior
is a numerical vector,prior
should also be a numerical vector.When
posterior
is adata.frame
,prior
should also be adata.frame
, with matching column order.When
posterior
is astanreg
,brmsfit
or other supported Bayesian model:
prior
can be set toNULL
, in which case prior samples are drawn internally. 
prior
can also be a model equivalent toposterior
but with samples from the priors only. Seeunupdate()
. 
Note: When
posterior
is abrmsfit_multiple
model,prior
must be provided.

When
posterior
is anemmGrid
/emm_list
object:
prior
should also be anemmGrid
/emm_list
object equivalent toposterior
but created with a model of priors samples only. Seeunupdate()
. 
prior
can also be the original (posterior) model. If so, the function will try to update theemmGrid
/emm_list
to use theunupdate()
d priormodel. (This cannot be done forbrmsfit
models.) 
Note: When the
emmGrid
has undergone any transformations ("log"
,"response"
, etc.), orregrid
ing, thenprior
must be anemmGrid
object, as stated above.

Note
There is also a plot()
method implemented in the seepackage.
References
Wagenmakers, E., Gronau, Q. F., Dablander, F., & Etz, A. (2018, November 22). The Support Interval. doi:10.31234/osf.io/zwnxb
See Also
Other ci:
bci()
,
ci()
,
cwi()
,
eti()
,
hdi()
,
spi()
Examples
library(bayestestR)
prior < distribution_normal(1000, mean = 0, sd = 1)
posterior < distribution_normal(1000, mean = 0.5, sd = 0.3)
si(posterior, prior, verbose = FALSE)
# rstanarm models
# 
library(rstanarm)
contrasts(sleep$group) < contr.equalprior_pairs # see vignette
stan_model < stan_lmer(extra ~ group + (1  ID), data = sleep)
si(stan_model, verbose = FALSE)
si(stan_model, BF = 3, verbose = FALSE)
# emmGrid objects
# 
library(emmeans)
group_diff < pairs(emmeans(stan_model, ~group))
si(group_diff, prior = stan_model, verbose = FALSE)
# brms models
# 
library(brms)
contrasts(sleep$group) < contr.equalprior_pairs # see vingette
my_custom_priors <
set_prior("student_t(3, 0, 1)", class = "b") +
set_prior("student_t(3, 0, 1)", class = "sd", group = "ID")
brms_model < suppressWarnings(brm(extra ~ group + (1  ID),
data = sleep,
prior = my_custom_priors,
refresh = 0
))
si(brms_model, verbose = FALSE)