# How to interpret interaction in bayesian linar regression [jasp 08.1.2]

I am very new to Bayesian analyses, I saw a presenation about JASP in a conference a few years ago and since then I have used JASP to recheck some of my results using Bayesian analyses (just to be sure).

I am now ready to make the next move, and try to actaully publish a manuscript using only JASP results for Bayesian analyses. However, as I am quite new to this way of doing analyses, I want to make sure I interpret the results in an appropriate manner.

As an example, I put some results here [example2.html].

I would now interpret this as follows:

Model without interaction / model with interaction: BF18.23, indicating strong evidence _against _ the inclusion of the interaction.

Then when I compare do: both main effects / only gender: BF2.77, indicating anecdotal evidence, meaning that based on the current model specifications and data I cannot determine whether or not RA may predict stress.

Could you let me know whether this interpretation is correct?

Second, let's assume for a minute that the BF's were actually reversed for the model with vs. without interaction (i.e., there would indeed be evidence to suggest that the model with interaction is more likely).

How would I then go about interpreting this interaction effect further? Could I just make a plot?

## Comments

Hi GerineL,

You might find some help in here: rdcu.be/tZ29

I think you probably forgot to set the OSF folder to public, because I can't view the html file.

Cheers,

E.J.

Hi E.J.,

You are right, my settings were on private (hadn't used it before, sorry about that).

I had looked at the paper before (also part I), but there are no examples of linear multiple regression in there (only of ANOVA's), and in all the examples the model with interaction is not preferred over the main effects models. It does say somewhere that post-hoc analyses for the ANOVA framework have not been developed yet.

Does that mean that if I do find myself in the situation where the model actually does have a better fit?

[for an example with moderate evidence, see example 3].

Perhaps you know an example of such a paper using JASP?

Gerine

Hi GerineL,

We will have Bayesian post-hoc tests for one-way ANOVA in the next version of JASP. I agree it would be nice to have a paper on how JASP does Bayesian regression, but we are in the midst of upgrading/overhauling that analysis, so this will have to wait. I will look at your data now...

E.J.

Yes, your interpretation is correct. Of course the BF of 2.77 is not a BF of 1, so there is

someevidence. I would interpret this BF to say that there is some evidence in favor of including RA on top of gender, but that this evidence is only weak. For a continuous interpretation of the BF see https://osf.io/3acm7/E.J.

Just wanted to ask a follow-up question to this. Is looking at the BF for inclusion of the interaction model in a Bayesian regression equivalent to a frequentist moderation analysis (i.e. where you might statistically compare a regression model with and without the interaction term)?

Dear powg,

The standard output allows you to compare a main-effects only model to a model with the interaction included (so only two models are involved). In the analysis of effects, the inclusion BF compares

allmodels with a particular term toallmodels without that particular term (all models are involved).Cheers,

E.J.