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Compare models with a Bayes factor

Source: R/evaluation.R
bayes_factor.Rd

Estimates both marginal likelihoods with bridge sampling (Meng and Wong 1996; Frühwirth-Schnatter 2004) and compares the first model with the second model using bridgesampling::bf().

Usage

bayes_factor(
  model1,
  model2,
  log = FALSE,
  repetitions = 1L,
  ghk_draws = 500L,
  progress = interactive()
)

Arguments

model1, model2

[RprobitB_fit]
Fitted models to compare.

log

[logical(1)]
Return the logarithm of the Bayes factor?

repetitions

[integer(1)]
Number of bridge-sampling repetitions.

ghk_draws

[integer(1)]
Number of draws of the GHK simulator for multivariate normal probabilities of more than three dimensions, see oeli::pmvnorm().

progress

[logical(1)]
Show progress?

Value

A bf_bridge object from bridgesampling. Values greater than one (zero if log = TRUE) favor model1; smaller values favor model2.

References

Meng X, Wong WH (1996). “Simulating Ratios of Normalizing Constants via a Simple Identity: A Theoretical Exploration.” Statistica Sinica, 6(4), 831–860. https://www3.stat.sinica.edu.tw/statistica/j6n4/j6n43/j6n43.htm.

Frühwirth-Schnatter S (2004). “Estimating Marginal Likelihoods for Mixture and Markov Switching Models Using Bridge Sampling Techniques.” The Econometrics Journal, 7(1), 143–167. doi:10.1111/j.1368-423X.2004.00125.x .

Gronau QF, Singmann H, Wagenmakers E (2020). “bridgesampling: An R Package for Estimating Normalizing Constants.” Journal of Statistical Software, 92(10), 1–29. doi:10.18637/jss.v092.i10 .

Celeux G, Frühwirth-Schnatter S, Robert CP (2019). “Model Selection for Mixture Models – Perspectives and Strategies.” In Frühwirth-Schnatter S, Celeux G, Robert CP (eds.), Handbook of Mixture Analysis, 117–154. Chapman and Hall/CRC. doi:10.1201/9780429055911-7 .

Frühwirth-Schnatter S (2019). “Keeping the Balance – Bridge Sampling for Marginal Likelihood Estimation in Finite Mixture, Mixture of Experts and Markov Mixture Models.” Brazilian Journal of Probability and Statistics, 33(4), 706–733. doi:10.1214/19-BJPS446 .

Examples

### Simulate and fit the correctly specified model
set.seed(1)
correct_model <- fit(
  choice ~ x + z | 0,
  dgp_parameters = list(beta = c(x = 1, z = 0.5)),
  iterations = 500,
  chains = 1
)
simulated_data <- as.data.frame(correct_model$data)

### Fit the same data again, but omit the relevant regressor z
misspecified_model <- fit(
  choice ~ x | 0,
  data = simulated_data,
  iterations = 500,
  chains = 1
)

### A Bayes factor greater than one favors the correct first model
bayes_factor(correct_model, misspecified_model)
#> Estimated Bayes factor in favor of model1 over model2: 8.12778