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

For more info, see the Bayes factors vignette.

## Usage

``````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`.

match_models

See details.

prior_odds

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 (Use `as.numeric()` to extract the non-log Bayes factors; see examples).

## 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.

## See also

`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)
(bf_inc <- 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-equal

as.numeric(bf_inc)
#> [1] 2.021143e+55 3.575448e+26 1.131202e-01

# \donttest{
# BayesFactor
# -------------------------------
BF <- BayesFactor::generalTestBF(len ~ supp * dose, ToothGrowth, progress = FALSE)
bayesfactor_inclusion(BF)
#> Inclusion Bayes Factors (Model Averaged)
#>
#>           P(prior) P(posterior) Inclusion BF
#> supp          0.60         0.98        35.18
#> dose          0.60         1.00     5.77e+12
#> dose:supp     0.20         0.56         5.08
#>
#> * Compared among: all models
#> *    Priors odds: uniform-equal

# compare only matched models:
bayesfactor_inclusion(BF, match_models = TRUE)
#> Inclusion Bayes Factors (Model Averaged)
#>
#>           P(prior) P(posterior) Inclusion BF
#> supp          0.40         0.42        22.68
#> dose          0.40         0.44     3.81e+12
#> dose:supp     0.20         0.56         1.33
#>
#> * Compared among: matched models only
#> *    Priors odds: uniform-equal
# }
``````