frac_bayes_factors: Fractional Bayes factors

In bayesics: Bayesian Analyses for One- and Two-Sample Inference and Regression Methods

Fractional Bayes factors

Description

Compute fractional Bayes factors for lm_b objects

Usage

frac_bayes_factors(object1, object2, fractional_proportion)

Arguments

object1	object of class lm_b
object2	object of class lm_b
fractional_proportion	The fraction of the data used to create the prior in turn used to compute the marginal likelihood. By default, O'Hagan's recommendation of max(log(n),ncol(X) + 1) / n) is used.

Details

Fractional Bayes factors, devised by O'Hagan, are a way to use flat, even improper, priors to obtain valid Bayes factors. The idea is built on the notion of partial Bayes factors, where a part of the data is used to determine the prior, and the remaining is used to compare the models.

References

O’Hagan, Anthony. “Fractional Bayes Factors for Model Comparison.” Journal of the Royal Statistical Society. Series B (Methodological), vol. 57, no. 1, 1995, pp. 99–138. https://doi.org/10.1111/j.2517-6161.1995.tb02017.x

Examples

set.seed(2026)
N = 500
test_data <-
  data.frame(x1 = rnorm(N),
             x2 = rnorm(N),
             x3 = letters[1:5])
test_data$outcome <-
  rnorm(N,-1 + test_data$x1 + 2 * (test_data$x3 %in% c("d","e")) )
fit_full <-
  lm_b(outcome ~ x1 + x2 + x3,
       data = test_data)
fit_no_x1 <-
  lm_b(outcome ~ x2 + x3,
       data = test_data)
fit_no_x2 <-
  lm_b(outcome ~ x1 + x3,
       data = test_data)

frac_bayes_factors(fit_full,
                   fit_no_x1)
frac_bayes_factors(fit_full,
                   fit_no_x2)

bayesics documentation built on March 11, 2026, 5:07 p.m.