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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

# \dontrun{
library(bayestestR)

prior <- distribution_normal(1000, mean = 0, sd = 1)
posterior <- distribution_normal(1000, mean = 0.5, sd = 0.3)

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

# 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 3.9e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.39 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: 2000 / 2000 [100%]  (Sampling)
#> Chain 1: 
#> Chain 1:  Elapsed Time: 0.238 seconds (Warm-up)
#> Chain 1:                0.356 seconds (Sampling)
#> Chain 1:                0.594 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 1.6e-05 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.16 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2: 
#> Chain 2: 
#> Chain 2: Iteration:    1 / 2000 [  0%]  (Warmup)
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#> Chain 2: 
#> Chain 2:  Elapsed Time: 0.21 seconds (Warm-up)
#> Chain 2:                0.208 seconds (Sampling)
#> Chain 2:                0.418 seconds (Total)
#> Chain 2: 
#> 
#> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 3).
#> Chain 3: 
#> Chain 3: Gradient evaluation took 1.6e-05 seconds
#> Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.16 seconds.
#> Chain 3: Adjust your expectations accordingly!
#> Chain 3: 
#> Chain 3: 
#> Chain 3: Iteration:    1 / 2000 [  0%]  (Warmup)
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#> Chain 3: 
#> Chain 3:  Elapsed Time: 0.23 seconds (Warm-up)
#> Chain 3:                0.143 seconds (Sampling)
#> Chain 3:                0.373 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)
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#> Chain 4: 
#> Chain 4:  Elapsed Time: 0.209 seconds (Warm-up)
#> Chain 4:                0.239 seconds (Sampling)
#> Chain 4:                0.448 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
# }