# How do I code interaction terms when I have dummy variables?

I have a dataset from an AB test. It shows the conversion rate per treatment group and the categories within each variant.

category     group         converted
green        control       0
green        control       0
green        control       1
blue         control       1
blue         control       0
purple       control       1
purple       control       1
yellow       control       1
yellow       control       0
green        treatment     0
green        treatment     0
blue         treatment     0
blue         treatment     1
purple       treatment     1
purple       treatment     1
yellow       treatment     0
yellow       treatment     1


I'm putting together a logistic regression to predict the likelihood of conversion as a function of the category + the group. I have about 10K records altogether.

I am encoding the category as is_green (0/1), is_blue (0/1), is_yellow(0/1) and is_purple(0/1). I am encoding the group as group(0/1).

I would like to see the group, but it also looks like there may be some interaction effect going on.

How do I capture the interaction in the logistic model when both variables are encoded?

Say you have dummy variables $$v_1$$ and $$v_2$$, both assuming either $$0$$ or $$1$$, and you want to capture their interaction. For this you could create $$w=v_1 v_2$$ to asses the effect they'd have when the events they represent happen together.
Naturally, you can also include, separately, $$v_1$$ and $$v_2$$ and asses their individual effects.