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

Comments

• EJ

  December 2016

  In your final analysis, you did not test 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.
• duplex_

  December 2016

  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?
• EJ

  December 2016

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

  December 2016 edited December 2016

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

  January 2017

  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 "