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# 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 [18] 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)[18]/sort(Anova)[4]) 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 [1] B + S : 35319663 ±0.41% [2] C + S : 35932312 ±0.2% [3] C + B + C:B + S : 1.107802e+13 ±0.81% [4] C + B + S : 9.975825e+13 ±0.58% [5] A + S : 1.510931e+15 ±0.31% [6] A + C + S : 2.025998e+18 ±1.27% [7] A + C + A:C + S : 1.408867e+19 ±0.76% [8] A + C + B + A:B + C:B + S : 1.098129e+25 ±4.21% [9] A + C + B + C:B + S : 1.935634e+25 ±0.93% [10] A + C + B + A:B + S : 7.503825e+25 ±3.19% [11] A + B + A:B + S : 9.598767e+25 ±1.01% [12] A + C + B + S : 1.602926e+26 ±1.86% [13] A + C + A:C + B + C:B + S : 2.149663e+26 ±1.14% [14] A + B + S : 2.969097e+26 ±1.38% [15] A + C + A:C + B + A:B + C:B + A:C:B + S : 6.400354e+26 ±1.47% [16] A + C + A:C + B + S : 1.63816e+27 ±1.27% [17] A + C + A:C + B + A:B + C:B + S : 2.496953e+27 ±1.14% [18] 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?

Thanks.