The bf_* function is an alias of the main function.

bayesfactor_inclusion(models, match_models = FALSE, prior_odds = NULL, ...)

bf_inclusion(models, match_models = FALSE, prior_odds = NULL, ...)

## Arguments

models An object of class bayesfactor_models or BFBayesFactor. See details. Optional vector of prior odds for the models. See BayesFactor::priorOdds<-. Arguments passed to or from other methods.

## Value

a data frame containing the prior and posterior probabilities, and log(BF) for each effect.

## Details

Inclusion Bayes factors answer the question: Are the observed data more probable under models with a particular effect, than they are under models without that particular effect? In other words, on average - are models with effect $$X$$ more likely to have produced the observed data than models without effect $$X$$?

### Match Models

If match_models=FALSE (default), Inclusion BFs are computed by comparing all models with a term against all models without that term. If TRUE, comparison is restricted to models that (1) do not include any interactions with the term of interest; (2) for interaction terms, averaging is done only across models that containe the main effect terms from which the interaction term is comprised.

## Note

Random effects in the lmer style are converted to interaction terms: i.e., (X|G) will become the terms 1:G and X:G.

## 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) (Wetzels et al. 2011).

## References

• Hinne, M., Gronau, Q. F., van den Bergh, D., and Wagenmakers, E. (2019, March 25). A conceptual introduction to Bayesian Model Averaging. doi: 10.31234/osf.io/wgb64

• Clyde, M. A., Ghosh, J., & Littman, M. L. (2011). Bayesian adaptive sampling for variable selection and model averaging. Journal of Computational and Graphical Statistics, 20(1), 80-101.

• Mathot, S. (2017). Bayes like a Baws: Interpreting Bayesian Repeated Measures in JASP [Blog post]. Retrieved from https://www.cogsci.nl/blog/interpreting-bayesian-repeated-measures-in-jasp

weighted_posteriors for Bayesian parameter averaging.

## Author

Mattan S. Ben-Shachar

## Examples

library(bayestestR)

# Using bayesfactor_models:
# ------------------------------
mo0 <- lm(Sepal.Length ~ 1, data = iris)
mo1 <- lm(Sepal.Length ~ Species, data = iris)
mo2 <- lm(Sepal.Length ~ Species + Petal.Length, data = iris)
mo3 <- lm(Sepal.Length ~ Species * Petal.Length, data = iris)

BFmodels <- bayesfactor_models(mo1, mo2, mo3, denominator = mo0)
bayesfactor_inclusion(BFmodels)
#> Inclusion Bayes Factors (Model Averaged)
#>
#>                      P(prior) P(posterior) Inclusion BF
#> Species                  0.75         1.00     2.02e+55
#> Petal.Length             0.50         1.00     3.58e+26
#> Petal.Length:Species     0.25         0.04        0.113
#>
#> * Compared among: all models
#> *    Priors odds: uniform-equalif (FALSE) {
# BayesFactor
# -------------------------------
library(BayesFactor)

BF <- generalTestBF(len ~ supp * dose, ToothGrowth, progress = FALSE)

bayesfactor_inclusion(BF)

# compare only matched models:
bayesfactor_inclusion(BF, match_models = TRUE)
}