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Bayes Factors (BF)

Source: R/bayesfactor.R
bayesfactor.Rd

This function compte the Bayes factors (BFs) that are appropriate to the input. For vectors or single models, it will compute BFs for single parameters(), or is hypothesis is specified, BFs for restricted models(). For multiple models, it will return the BF corresponding to comparison between models() and if a model comparison is passed, it will compute the inclusion BF().

For a complete overview of these functions, read the Bayes factor vignette.

Usage

bayesfactor(
  ...,
  prior = NULL,
  direction = "two-sided",
  null = 0,
  hypothesis = NULL,
  effects = c("fixed", "random", "all"),
  verbose = TRUE,
  denominator = 1,
  match_models = FALSE,
  prior_odds = NULL
)

Arguments

...

A numeric vector, model object(s), or the output from bayesfactor_models.

prior

An object representing a prior distribution (see 'Details').

direction

Test type (see 'Details'). One of 0, "two-sided" (default, two tailed), -1, "left" (left tailed) or 1, "right" (right tailed).

null

Value of the null, either a scalar (for point-null) or a range (for a interval-null).

hypothesis

A character vector specifying the restrictions as logical conditions (see examples below).

effects

Should results for fixed effects, random effects or both be returned? Only applies to mixed models. May be abbreviated.

verbose

Toggle off warnings.

denominator

Either an integer indicating which of the models to use as the denominator, or a model to be used as a denominator. Ignored for BFBayesFactor.

match_models

See details.

prior_odds

Optional vector of prior odds for the models. See BayesFactor::priorOdds<-.

Value

Some type of Bayes factor, depending on the input. See bayesfactor_parameters(), bayesfactor_models() or bayesfactor_inclusion()

Note

There is also a plot()-method implemented in the see-package.

Examples

library(bayestestR)

if (require("logspline")) {
  prior <- distribution_normal(1000, mean = 0, sd = 1)
  posterior <- distribution_normal(1000, mean = .5, sd = .3)

  bayesfactor(posterior, prior = prior, verbose = FALSE)
}
#> Loading required package: logspline
#> Bayes Factor (Savage-Dickey density ratio)
#> 
#> BF  
#> ----
#> 1.21
#> 
#> * Evidence Against The Null: 0
#> 
# \dontrun{
# rstanarm models
# ---------------
if (require("rstanarm")) {
  model <- stan_lmer(extra ~ group + (1 | ID), data = sleep)
  bayesfactor(model, verbose = FALSE)
}
#> Loading required package: rstanarm
#> Loading required package: Rcpp
#> This is rstanarm version 2.21.3
#> - See https://mc-stan.org/rstanarm/articles/priors for changes to default priors!
#> - Default priors may change, so it's safest to specify priors, even if equivalent to the defaults.
#> - For execution on a local, multicore CPU with excess RAM we recommend calling
#>   options(mc.cores = parallel::detectCores())
#> 
#> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 4.3e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.43 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
#> Chain 1: Iteration:    1 / 2000 [  0%]  (Warmup)
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#> Chain 1: Iteration: 1800 / 2000 [ 90%]  (Sampling)
#> Chain 1: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 1: 
#> Chain 1:  Elapsed Time: 0.267143 seconds (Warm-up)
#> Chain 1:                0.22404 seconds (Sampling)
#> Chain 1:                0.491183 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 1.9e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.19 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2: 
#> Chain 2: 
#> Chain 2: Iteration:    1 / 2000 [  0%]  (Warmup)
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#> Chain 2: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 2: 
#> Chain 2:  Elapsed Time: 0.245042 seconds (Warm-up)
#> Chain 2:                0.200461 seconds (Sampling)
#> Chain 2:                0.445503 seconds (Total)
#> Chain 2: 
#> 
#> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 3).
#> Chain 3: 
#> Chain 3: Gradient evaluation took 1.8e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.18 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)
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#> Chain 3: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 3: 
#> Chain 3:  Elapsed Time: 0.23583 seconds (Warm-up)
#> Chain 3:                0.241212 seconds (Sampling)
#> Chain 3:                0.477042 seconds (Total)
#> Chain 3: 
#> 
#> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 4).
#> Chain 4: 
#> Chain 4: Gradient evaluation took 1.7e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.17 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)
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#> Chain 4: Iteration: 1001 / 2000 [ 50%]  (Sampling)
#> Chain 4: Iteration: 1200 / 2000 [ 60%]  (Sampling)
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#> Chain 4: Iteration: 2000 / 2000 [100%]  (Sampling)
#> Chain 4: 
#> Chain 4:  Elapsed Time: 0.249065 seconds (Warm-up)
#> Chain 4:                0.227155 seconds (Sampling)
#> Chain 4:                0.47622 seconds (Total)
#> Chain 4: 
#> Bayes Factor (Savage-Dickey density ratio) 
#> 
#> Parameter   |    BF
#> -------------------
#> (Intercept) | 0.214
#> group2      |  3.24
#> 
#> * Evidence Against The Null: 0
#> 
# }

if (require("logspline")) {
  # Frequentist models
  # ---------------
  m0 <- lm(extra ~ 1, data = sleep)
  m1 <- lm(extra ~ group, data = sleep)
  m2 <- lm(extra ~ group + ID, data = sleep)

  comparison <- bayesfactor(m0, m1, m2)
  comparison

  bayesfactor(comparison)
}
#> Inclusion Bayes Factors (Model Averaged)
#> 
#>       P(prior) P(posterior) Inclusion BF
#> group     0.67         1.00     5.61e+03
#> ID        0.33         1.00     9.77e+03
#> 
#> * Compared among: all models
#> *    Priors odds: uniform-equal