Inclusion Bayes Factors for testing predictors across Bayesian models
Source:R/bayesfactor_inclusion.R
bayesfactor_inclusion.RdThe 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()orBFBayesFactor.- 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.
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
# }