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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?

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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).

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  • $\begingroup$ What if I want to compare more than two models? Do I test every single one against the reduced-model (β_1=β_2=0) and take the one with the lowest AIC if all models are significant or is there some better approach? Is it reasonable to take the simple addiditve model (like y~F1+F2) if it is significant compared to the reduced model because it is easier to interpret? Or should I strive for "the best" model (however this is accomplished) $\endgroup$ – laka Aug 3 '18 at 19:51

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