bayesics (version 2.1.0)

frac_bayes_factors: 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

# \donttest{
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)

# }