Bayes Factors (BF)

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)
}
#> Loading required package: logspline
#> Warning: Bayes factors might not be precise.
#> For precise Bayes factors, sampling at least 40,000 posterior samples is recommended.
#> Bayes Factor (Savage-Dickey density ratio)
#> 
#> BF  
#> ----
#> 1.21
#> 
#> * Evidence Against The Null: 0
if (FALSE) {
# rstanarm models
# ---------------
if (require("rstanarm")) {
  model <- stan_lmer(extra ~ group + (1 | ID), data = sleep)
  bayesfactor(model)
}
}

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