How to find the BF of a main effect when the best model includes interactions.
Hello. I am using anovaBF from the BayesFactor package for R. Usually to find the BF of a main effect, I compare the best model with this main effect, against the model that has the same main effects and interactions except for the one I am looking for.
I want to find the BF for the main effect of A, but the best model  contains also two interactions (A:C and A:B) and the best model without A (4) has no interactions. If I comparte 18 against 4 (sort(Anova)/sort(Anova)) I get a BF of 1.587706e+14, but it includes the interactions.
The other option would be 12 (with only main effects) against 4, which gives 1.606811e+12.
> sort(Anova) Bayes factor analysis  B + S : 35319663 ±0.41%  C + S : 35932312 ±0.2%  C + B + C:B + S : 1.107802e+13 ±0.81%  C + B + S : 9.975825e+13 ±0.58%  A + S : 1.510931e+15 ±0.31%  A + C + S : 2.025998e+18 ±1.27%  A + C + A:C + S : 1.408867e+19 ±0.76%  A + C + B + A:B + C:B + S : 1.098129e+25 ±4.21%  A + C + B + C:B + S : 1.935634e+25 ±0.93%  A + C + B + A:B + S : 7.503825e+25 ±3.19%  A + B + A:B + S : 9.598767e+25 ±1.01%  A + C + B + S : 1.602926e+26 ±1.86%  A + C + A:C + B + C:B + S : 2.149663e+26 ±1.14%  A + B + S : 2.969097e+26 ±1.38%  A + C + A:C + B + A:B + C:B + A:C:B + S : 6.400354e+26 ±1.47%  A + C + A:C + B + S : 1.63816e+27 ±1.27%  A + C + A:C + B + A:B + C:B + S : 2.496953e+27 ±1.14%  A + C + A:C + B + A:B + S : 1.583868e+28 ±0.84%
Then to find the BF of A:B I would compare 18/16, and for A:C it would be 18/10?
Which option is better and why? Do I need to use my best model to find the BF of each main effect and interaction, or can I compare two models that allow me to make a fair comparison even if I don´t use the best model?