# Bayesian RM ANOVA - Does a model with interaction only make sense?

Hi,

I conducted two independent samples Bayesian ttests to test for a group difference before and after an experimental session:

I also did a dependent samples Bayesian ttest to see if there is a change within groups:

To check for an interaction, I conducted an ANOVA:

As you can see, clear support against the model with 2 main effects and interaction. However, if I have a model with interaction only, the BF is BF = 0.55, rather inconclusive.

Now my question: How much does a model with interaction term only make sense? I recall reading that a model should always include the main factors as well, but I do not remember the source. Can it be justified that I only have the interaction effect in the model? It sounds like cherry picking to me.

## Comments

In your final analysis, you did

nottest the model with the interaction only. JASP does not allow you to run such an analysis without including the constituent main effects. Instead, what the final analysis does is put the two main effects in as nuisance factors, such that they form the basis for comparison (instead of the usual null model that does not have any factors). So BF = 0.55 is simply the BF between the full model that includes the interaction and the model with main effects only. You can get that from the earlier table (using transitivity) as 0.079/0.153 (barring error from numerical approximation).So the full model does poorly against the model without any factors, but somewhat less poorly when it is compared to the model with two main effects. However, that model itself is not doing too well, and you may wonder what use it is to have a poor model as a standard for comparison. I would simply present the entire table and discuss the results for each of the models.

Cheers,

E.J.

Thanks for the fast clarification, EJ. I have done the analysis with the BF package as well, using whichModels="all" (VP = participant as random factor):

Is model [3] here an interaction only model?

Independent of my data, would it be legit to look at an interaction only model?

I'm not sure, we'll have to ask Richard. I'll forward this to him.

E.J.

I also posted this question on his twitter, without the image&data though. hope he responds. Thank you!

If anyone is interested, Jeff Rouder answered: "I cannot justify interactions without corresponding main effects. Seems like a magical model otherwise. The argument is in http://pcl.missouri.edu/sites/default/files/Rouder.etal_.pbr_.2016.pdf "