Compute Support Intervals

Source: R/si.R

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.

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 = "fixed",
  component = "location",
  parameters = NULL,
  ...
)

# 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 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.

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):

  • 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.

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.

use_iterations

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).

rvar_col

A single character - the name of an rvar column in the data frame to be processed. See example in p_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 an rvar 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. See unupdate().

    • If prior is set to NULL, unupdate() is called internally (not supported for brmsfit_multiple model).

  • Output from a {marginaleffects} function - prior should also be an equivalent output from a {marginaleffects} function based on a prior-model (See unupdate()).

  • Output from an {emmeans} function

    • prior should also be an equivalent output from an {emmeans} function based on a prior-model (See unupdate()).

    • 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 any regriding).

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(), 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)
#> 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 5e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.5 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: 0.299 seconds (Warm-up)
#> Chain 1:                0.195 seconds (Sampling)
#> Chain 1:                0.494 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 1.8e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.18 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: 0.197 seconds (Warm-up)
#> Chain 2:                0.171 seconds (Sampling)
#> Chain 2:                0.368 seconds (Total)
#> Chain 2: 
#> 
#> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 3).
#> Chain 3: 
#> Chain 3: Gradient evaluation took 1.7e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.17 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: 0.163 seconds (Warm-up)
#> Chain 3:                0.178 seconds (Sampling)
#> Chain 3:                0.341 seconds (Total)
#> Chain 3: 
#> 
#> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 4).
#> Chain 4: 
#> Chain 4: Gradient evaluation took 2.8e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.28 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: 0.297 seconds (Warm-up)
#> Chain 4:                0.176 seconds (Sampling)
#> Chain 4:                0.473 seconds (Total)
#> Chain 4: 
si(stan_model, verbose = FALSE)
#> Support Interval
#> 
#> Parameter   |    BF = 1 SI | Effects |   Component
#> --------------------------------------------------
#> (Intercept) | [0.39, 2.64] |   fixed | conditional
#> group1      | [0.39, 2.73] |   fixed | conditional
si(stan_model, BF = 3, verbose = FALSE)
#> Support Interval
#> 
#> Parameter   |    BF = 3 SI | Effects |   Component
#> --------------------------------------------------
#> (Intercept) | [0.73, 2.32] |   fixed | conditional
#> group1      | [0.68, 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 | [-2.75, -0.37]

# 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
# }