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

Hi,

I am contemplating how to use/interpret the BFinclusion factor in light of the principle of marginality used in JASP. I have a 2x2 between subject design where the BFinclusions for the respective main effects and the interaction are Main1: 0.225, Main2: 52.809 and Interaction: 3.042. Thus, while there is evidence for including the interaction, the model with the strongest support is the one only including main effect 2(BFm: 4.3, BF10: 53), while the model including both main effects and the interaction effect (BFm: 2.2, BF10:37) is clearly being "dragged down" by Main effect1.

It seems resonable to me to conclude that there is an effect of Main2 and an interaction. Although such a model is not tested in itself. How would you approach this situation?

Best,

August

## Comments

• 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.

```

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

E.J.

• 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

• 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.

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