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 Savage-Dickey 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, rvar_col = NULL, verbose = TRUE, ...)
Arguments
- posterior
A numerical vector,
stanreg
/brmsfit
object,emmGrid
or a data frame - representing a posterior distribution(s) from (see 'Details').- ...
Arguments passed to and from other methods. (Can be used to pass arguments to internal
logspline::logspline()
.)- 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 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__
orprior_
) are filtered by default, so only parameters that typically appear in thesummary()
are returned. Useparameters
to select specific parameters for the output.- use_iterations
Logical, if
TRUE
andx
is aget_predicted
object, (returned byinsight::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).- rvar_col
A single character - the name of an
rvar
column in the data frame to be processed. See example inp_direction()
.
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]
.
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 fixed-effects; see example below).
Note
There is also a plot()
-method implemented in the see-package.
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 point-null 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 Jeffreys-Lindley-Bartlett 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 fixed-effects;
See example below.)
It is important to provide the correct prior
for meaningful results,
to match the posterior
-type input:
A numeric vector -
prior
should also be a numeric vector, representing the prior-estimate.A data frame -
prior
should also be a data frame, representing the prior-estimates, in matching column order.If
rvar_col
is specified,prior
should be the name of anrvar
column that represents the prior-estimates.
Supported Bayesian model (
stanreg
,brmsfit
, etc.)prior
should be a model an equivalent model with MCMC samples from the priors only. Seeunupdate()
.If
prior
is set toNULL
,unupdate()
is called internally (not supported forbrmsfit_multiple
model).
Output from a
{marginaleffects}
function -prior
should also be an equivalent output from a{marginaleffects}
function based on a prior-model (Seeunupdate()
).Output from an
{emmeans}
functionprior
should also be an equivalent output from an{emmeans}
function based on a prior-model (Seeunupdate()
).prior
can also be the original (posterior) model, in which case the function will try to "unupdate" the estimates (not supported if the estimates have undergone any transformations –"log"
,"response"
, etc. – or anyregrid
ing).
References
Wagenmakers, E., Gronau, Q. F., Dablander, F., & Etz, A. (2018, November 22). The Support Interval. doi:10.31234/osf.io/zwnxb
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)
#> BF = 1 SI: [0.04, 1.04]
# \donttest{
# rstanarm models
# ---------------
library(rstanarm)
contrasts(sleep$group) <- contr.equalprior_pairs # see vignette
stan_model <- stan_lmer(extra ~ group + (1 | ID), data = sleep)
#>
#> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).
#> Chain 1:
#> Chain 1: Gradient evaluation took 2.9e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.29 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1:
#> Chain 1:
#> Chain 1: Iteration: 1 / 2000 [ 0%] (Warmup)
#> Chain 1: Iteration: 200 / 2000 [ 10%] (Warmup)
#> Chain 1: Iteration: 400 / 2000 [ 20%] (Warmup)
#> Chain 1: Iteration: 600 / 2000 [ 30%] (Warmup)
#> Chain 1: Iteration: 800 / 2000 [ 40%] (Warmup)
#> Chain 1: Iteration: 1000 / 2000 [ 50%] (Warmup)
#> Chain 1: Iteration: 1001 / 2000 [ 50%] (Sampling)
#> Chain 1: Iteration: 1200 / 2000 [ 60%] (Sampling)
#> Chain 1: Iteration: 1400 / 2000 [ 70%] (Sampling)
#> Chain 1: Iteration: 1600 / 2000 [ 80%] (Sampling)
#> Chain 1: Iteration: 1800 / 2000 [ 90%] (Sampling)
#> Chain 1: Iteration: 2000 / 2000 [100%] (Sampling)
#> Chain 1:
#> Chain 1: Elapsed Time: 0.214 seconds (Warm-up)
#> Chain 1: 0.23 seconds (Sampling)
#> Chain 1: 0.444 seconds (Total)
#> Chain 1:
#>
#> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2).
#> Chain 2:
#> Chain 2: Gradient evaluation took 1.5e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.15 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2:
#> Chain 2:
#> Chain 2: Iteration: 1 / 2000 [ 0%] (Warmup)
#> Chain 2: Iteration: 200 / 2000 [ 10%] (Warmup)
#> Chain 2: Iteration: 400 / 2000 [ 20%] (Warmup)
#> Chain 2: Iteration: 600 / 2000 [ 30%] (Warmup)
#> Chain 2: Iteration: 800 / 2000 [ 40%] (Warmup)
#> Chain 2: Iteration: 1000 / 2000 [ 50%] (Warmup)
#> Chain 2: Iteration: 1001 / 2000 [ 50%] (Sampling)
#> Chain 2: Iteration: 1200 / 2000 [ 60%] (Sampling)
#> Chain 2: Iteration: 1400 / 2000 [ 70%] (Sampling)
#> Chain 2: Iteration: 1600 / 2000 [ 80%] (Sampling)
#> Chain 2: Iteration: 1800 / 2000 [ 90%] (Sampling)
#> Chain 2: Iteration: 2000 / 2000 [100%] (Sampling)
#> Chain 2:
#> Chain 2: Elapsed Time: 0.218 seconds (Warm-up)
#> Chain 2: 0.192 seconds (Sampling)
#> Chain 2: 0.41 seconds (Total)
#> Chain 2:
#>
#> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 3).
#> Chain 3:
#> Chain 3: Gradient evaluation took 1.5e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.15 seconds.
#> Chain 3: Adjust your expectations accordingly!
#> Chain 3:
#> Chain 3:
#> Chain 3: Iteration: 1 / 2000 [ 0%] (Warmup)
#> Chain 3: Iteration: 200 / 2000 [ 10%] (Warmup)
#> Chain 3: Iteration: 400 / 2000 [ 20%] (Warmup)
#> Chain 3: Iteration: 600 / 2000 [ 30%] (Warmup)
#> Chain 3: Iteration: 800 / 2000 [ 40%] (Warmup)
#> Chain 3: Iteration: 1000 / 2000 [ 50%] (Warmup)
#> Chain 3: Iteration: 1001 / 2000 [ 50%] (Sampling)
#> Chain 3: Iteration: 1200 / 2000 [ 60%] (Sampling)
#> Chain 3: Iteration: 1400 / 2000 [ 70%] (Sampling)
#> Chain 3: Iteration: 1600 / 2000 [ 80%] (Sampling)
#> Chain 3: Iteration: 1800 / 2000 [ 90%] (Sampling)
#> Chain 3: Iteration: 2000 / 2000 [100%] (Sampling)
#> Chain 3:
#> Chain 3: Elapsed Time: 0.189 seconds (Warm-up)
#> Chain 3: 0.279 seconds (Sampling)
#> Chain 3: 0.468 seconds (Total)
#> Chain 3:
#>
#> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 4).
#> Chain 4:
#> Chain 4: Gradient evaluation took 1.5e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.15 seconds.
#> Chain 4: Adjust your expectations accordingly!
#> Chain 4:
#> Chain 4:
#> Chain 4: Iteration: 1 / 2000 [ 0%] (Warmup)
#> Chain 4: Iteration: 200 / 2000 [ 10%] (Warmup)
#> Chain 4: Iteration: 400 / 2000 [ 20%] (Warmup)
#> Chain 4: Iteration: 600 / 2000 [ 30%] (Warmup)
#> Chain 4: Iteration: 800 / 2000 [ 40%] (Warmup)
#> Chain 4: Iteration: 1000 / 2000 [ 50%] (Warmup)
#> Chain 4: Iteration: 1001 / 2000 [ 50%] (Sampling)
#> Chain 4: Iteration: 1200 / 2000 [ 60%] (Sampling)
#> Chain 4: Iteration: 1400 / 2000 [ 70%] (Sampling)
#> Chain 4: Iteration: 1600 / 2000 [ 80%] (Sampling)
#> Chain 4: Iteration: 1800 / 2000 [ 90%] (Sampling)
#> Chain 4: Iteration: 2000 / 2000 [100%] (Sampling)
#> Chain 4:
#> Chain 4: Elapsed Time: 0.19 seconds (Warm-up)
#> Chain 4: 0.205 seconds (Sampling)
#> Chain 4: 0.395 seconds (Total)
#> Chain 4:
si(stan_model, verbose = FALSE)
#> Support Interval
#>
#> Parameter | BF = 1 SI | Effects | Component
#> --------------------------------------------------
#> (Intercept) | [0.41, 2.72] | fixed | conditional
#> group1 | [0.44, 2.75] | fixed | conditional
si(stan_model, BF = 3, verbose = FALSE)
#> Support Interval
#>
#> Parameter | BF = 3 SI | Effects | Component
#> --------------------------------------------------
#> (Intercept) | [0.83, 2.33] | fixed | conditional
#> group1 | [0.66, 2.44] | fixed | conditional
# emmGrid objects
# ---------------
library(emmeans)
group_diff <- pairs(emmeans(stan_model, ~group))
si(group_diff, prior = stan_model, verbose = FALSE)
#> Support Interval
#>
#> contrast | BF = 1 SI
#> --------------------------------
#> group1 - group2 | [-2.76, -0.34]
# 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
))
#> Compiling Stan program...
#> Start sampling
si(brms_model, verbose = FALSE)
#> Support Interval
#>
#> Parameter | BF = 1 SI | Effects | Component
#> --------------------------------------------------
#> b_Intercept | [0.65, 2.47] | fixed | conditional
#> b_group1 | [0.70, 2.43] | fixed | conditional
# }