bayesfactor_methods: Methods for Bayes factors

In bayestestR: Understand and Describe Bayesian Models and Posterior Distributions

Methods for Bayes factors

Description

Methods for Bayes factors

Usage

## S3 method for class 'bayestestRBF'
as.matrix(x, log = TRUE, ...)

## S3 method for class 'bayesfactor_models'
update(object, subset = NULL, reference = NULL, ...)

## S3 method for class 'bayestestRBF'
as.numeric(x, log = FALSE, ...)

## S3 method for class 'bayesfactor_restricted'
as.logical(x, which = c("posterior", "prior"), ...)

Arguments

x, object	Bayes factor object
log	Return log(BF) (default), or BF values.
...	Additional arguments (currently not used).
subset	Vector of model indices to keep or remove.
reference	Index of model to reference to, or "top" to reference to the best model, or "bottom" to reference to the worst model.
which	Should the logical matrix be of the posterior or prior distribution(s)?

Value

• as.numeric() / as.double(): a numeric vector of (log) Bayes factors.

• as.logical(): a logical data frame with a column for each order-restricted hypothesis.

• as.matrix(): a square matrix of (log) Bayes factors, with rows as denominators and columns as numerators.

• update(): an updated bayesfactor_models object.

Interpreting Bayes Factors

A Bayes factor greater than 1 can be interpreted as evidence against the null, at which one convention is that a Bayes factor greater than 3 can be considered as "substantial" evidence against the null (and vice versa, a Bayes factor smaller than 1/3 indicates substantial evidence in favor of the null-model). See also effectsize::interpret_bf().

Transitivity of Bayes factors

For multiple inputs (models or hypotheses), the function will return multiple Bayes factors between each model and the same reference model (the denominator or un-restricted model). However, we can take advantage of the transitivity of Bayes factors - where if we have two Bayes factors for Model A and model B against the same reference model C, we can obtain a Bayes factor for comparing model A to model B by dividing them:

BF_{AB} = \frac{BF_{AC}}{BF_{BC}} = \frac{\frac{ML_{A}}{ML_{C}}}{\frac{ML_{B}}{ML_{C}}} = \frac{ML_{A}}{ML_{B}}

(Where ML is the marginal likelihood.)

A full matrix comparing all models can be obtained with as.matrix().

Prior and posterior considerations

In order to correctly and precisely estimate Bayes factors, a rule of thumb are the 4 P's: Proper Priors and Plentiful Posteriors.

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) (Note that by default, brms::brm() uses flat priors for fixed-effects); Wide priors result in smaller marginal likelihoods, and thus models with wider priors are trivially less likely than models with narrower priors - where, at the extreme, that a model with completely flat priors is infinitely less favorable than a point null model (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.

Additionally, for models using MCMC estimation the number of posterior samples needed for testing is substantially larger than for estimation (the default of 4000 samples may not be enough in many cases). A conservative rule of thumb is to obtain 10 times more samples than would be required for estimation (Gronau, Singmann, & Wagenmakers, 2017). If less than 40,000 samples are detected, a warning is issued.

bayestestR documentation built on May 22, 2026, 1:06 a.m.