since I have a little trouble making sense of the role of interaction effects in my ACBC study, I´d be very grateful for your help.

1. First-order interaction effects

I can´t get my head around interaction effects between attributes, e.g. there is always "size" and "color" (attributes) involved with many different interactions based on the combination of their levels. "Size XL" and "color pink" (levels) on the other hand might have a specific interaction, I can understand.

* How do you interpret first-order interaction effects between attributes?

* Are the interactions between levels called "second-order interaction effects"?

2. Identification of relevant interaction effects

Regarding first-order interactions I have e.g. one interaction that is highly significant (p-value: 0,000000171), but that only marginally improves the model over the main effects (0,12%). I would therefore argue that in order to avoid overfitting, the interaction effect is ignored.

* Does that make sense?

* How is the "Gain in Pct. Cert. over Main Effects" calculated?

* Is it possible to derive any statements about the relevance of interactions between levels from the first-order interaction effects?

I understand that with ACBC the best approach to assessing the model´s improvement through interaction effects is based on predictive hit rates. I therefore derived some potential interactions between levels from theory and would like to test, if their consideration in the model improves predictive hit rates.

3. Calculation of total utilities including interaction effects between levels

I understand that the formula to calculate total stimuli utilities is as follows:

Utility(Att1_level1 x Att2_level1) =

main_effect(Att1_level1)+main_effect(Att2_level2)+interaction_effect (Att1_level1 x Att2_level1)

The CBC/HB allows me to calculate the interactions between levels. In the file ACBCExport_utilities.csv respectively ACBCExport_alpha.csv there is only one sheet that contains raw utilities.

* How do I aggregate the main effects and interaction effects?

* How do get the Zero-Centered Diffs for the main effects and interaction effects, as well as the importances?

Thank you very much for your support!

Best

Christian