Bayes Factors (BF) — bayesfactor • bayestestR

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)

prior <- distribution_normal(1000, mean = 0, sd = 1)
posterior <- distribution_normal(1000, mean = .5, sd = .3)

bayesfactor(posterior, prior = prior, verbose = FALSE)
#> Bayes Factor (Savage-Dickey density ratio)
#> 
#> BF  
#> ----
#> 1.21
#> 
#> * Evidence Against The Null: 0
#> 

# \donttest{
# rstanarm models
# ---------------
model <- suppressWarnings(rstanarm::stan_lmer(extra ~ group + (1 | ID), data = sleep))
#> 
#> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 3.6e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.36 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
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#> Chain 1: 
#> Chain 1:  Elapsed Time: 0.22 seconds (Warm-up)
#> Chain 1:                0.328 seconds (Sampling)
#> Chain 1:                0.548 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 1.4e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.14 seconds.
#> Chain 2: Adjust your expectations accordingly!
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#> Chain 2: 
#> Chain 2:  Elapsed Time: 0.194 seconds (Warm-up)
#> Chain 2:                0.193 seconds (Sampling)
#> Chain 2:                0.387 seconds (Total)
#> Chain 2: 
#> 
#> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 3).
#> Chain 3: 
#> Chain 3: Gradient evaluation took 1.3e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.13 seconds.
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#> Chain 3: 
#> Chain 3:  Elapsed Time: 0.213 seconds (Warm-up)
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#> Chain 3:                0.347 seconds (Total)
#> Chain 3: 
#> 
#> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 4).
#> Chain 4: 
#> Chain 4: Gradient evaluation took 1.3e-05 seconds
#> Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.13 seconds.
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#> Chain 4: 
#> Chain 4:  Elapsed Time: 0.194 seconds (Warm-up)
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#> Chain 4:                0.416 seconds (Total)
#> Chain 4: 
bayesfactor(model, verbose = FALSE)
#> Bayes Factor (Savage-Dickey density ratio) 
#> 
#> Parameter   |    BF
#> -------------------
#> (Intercept) | 0.206
#> group2      |  2.66
#> 
#> * Evidence Against The Null: 0
#> 

# 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
#> Bayes Factors for Model Comparison
#> 
#>       Model            BF
#> [..2] group          1.30
#> [..3] group + ID 1.12e+04
#> 
#> * Against Denominator: [..1] (Intercept only)
#> *   Bayes Factor Type: BIC approximation

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
# }