# How to decide between additive vs. multiplicative logistic regression model?

I want to collect data in an experiment where I manipulate two treatment factors. Factor A has two possible nominal values, Factor B has three possible nominal values. The outcome is binary.

Therefore, I have six treatment groups. I assume that there is a multiplicative connection of my two factors because of the experimental setting. I want to generate an logistic regression model and test the impact of the factors.

Although I do not treat independently with these factors: Is it useful or allowed to generate an additional additive model and compare both models to maybe find out that the additional model is more appropriate?

Am I correct in interpreting the question as whether it's possible to test whether a model with an interaction between the factors fits better than a model without one? If so, yes, a straightforward way to do this would be to fit a model with the interaction (i.e., y ~ F1 + F2 + F1:F2) and one without (i.e., y ~ F1 + F2) and perform a likelihood ratio test for the two models. A significant p-value for this test indicates that the interaction is (statistically) important (i.e., that including the interaction yields a model that fits the data better).