Positive BF inclusion for interaction but model with interaction not best model

Comments

• MSB

  May 2019

  Your conclusions seem correct. One option would be to report these results. Another option might be to fit and test your specified model (one main effect and the interaction) in R:

  library(BayesFactor)
  
  data(puzzles) # example of 2*2 data
  
  
  # This is what JASP does
  Models <- anovaBF(RT ~ shape*color, data = puzzles)
  
  
  # specific model
  new_model <- lmBF(RT ~ shape + shape:color, data = puzzles)
  
  
  all_models <- c(Models,new_model)
  all_models
  #> Bayes factor analysis
  #> --------------
  #> [1] shape                       : 0.6114754 ±0.01%
  #> [2] color                       : 0.6114754 ±0.01%
  #> [3] shape + color               : 0.3843659 ±2.11%
  #> [4] shape + color + shape:color : 0.1448699 ±1.13%
  #> [5] shape + shape:color         : 0.2291015 ±0.87%
  #> 
  #> Against denominator:
  #>   Intercept only 
  #> ---
  #> Bayes factor type: BFlinearModel, JZS
  
  
  # also get inclusion BFs:
  library(bayestestR)
  bayesfactor_inclusion(all_models)
  #>             Pr(prior) Pr(posterior) Inclusion BF
  #> shape            0.67          0.46         0.43
  #> color            0.50          0.38         0.62
  #> shape:color      0.33          0.13         0.29
  #> ---
  #> Inclusion BFs compared among all models.
  
  

  
  
• EJ

  May 2019

  Yes. Depends how principled you are about the principle of marginality, I guess :-)

  E.J.
• AugustCollsiöö

  May 2019 edited May 2019

  Thanks for the quick replies!

  By including Main1 in the null-model I (kind of) test the models, although now not the full model with Main1, Main2 and the interaction, and against a somewhat different null model. Is such an approach absurd, or could it be feasible? Maybe best just to move to a r-analysis as suggested though..

  
  

  /August
• EJ

  June 2019

  If you are interested in the interaction, you can also compare the 2-main effect model against the full model. With few models you don't always need the inclusion BF.

  Cheers,

  E.J.