# Inclusion Bayes Factor across matched models

Hi,

I have got an experiment with two within variables with two conditions and a between subjects factor. I am interested in confirming (as requested by reviewers) the lack of interaction between the within variables and the between subjects factor. I have conducted a Bayesian repeated measures ANOVA and after reading about the baws factor, I assumed that I had to look at the analysis effects across matched models. I know that BFinclusion refers to change from prior to posterior inclusion odds but I don't know how to interpret the numbers I get nor how to report them. I have seen somewhere the criteria set by studies such as the one by Wetzels et al (2011) but I assume these are based on the BF10 comparison between the model and the null model -which it is much easy for me to understand, by the way-, aren't they? Could you please help me? I have got BFinclusion values as different as 19.75 and 0.30...Thank you very much for your help and for JASP which I recently discovered and seems terrific to me.

## Comments

BF inclusion is similar to a regular BF except that it compares two classes of models, one class with the factor of interest and one without. So you start with prior probabilities on the models; comparing the prior probability with vs without the factor yields the prior inclusion odds (usually 1, but not always). Then you do the same for the posterior probabilities on the models; the change from prior to posterior inclusion odds is the inclusion Bayes factor -- the extent to which the data support inclusion of the factor of interest, taking all models into account.

Thank you very much for your explanation. I am still not completely sure of properly interpreting the resulting number, though. So, if for instance I have a BFincl of let's say 19, it would mean that according to the current data a model taking into account this factor would be 19 times more likely that a model not considering it? What about a BFincl of for instance .30? Is this evidence against a model including this factor or nothing can be said with such a value? Again, thank you very much.

It means that the data have changed the odds in favor of models that include the predictor by a factor of 19. When BFincl = .30, you can interpret this as BFexcl = 1/.30 = 3.33, some change in the odds but nothing to get worked up about.

E.J.

Great, thanks again