# Including many interaction terms in a logistic regression

I have a logistic regression model that is currently of the form:

Event ~ Vacc + Age


I want to start including interaction terms for different types of vaccine. I have been able to do:

Event ~ Vacc + Age + Vacc*VaccRoute


Where VaccRoute = 0 for intramuscular and = 1 for intranasal. This gives me nice results.

Now I want to look at the effect of vaccine brand. There are approximately 20 different vaccine brands in my data. I have made dummy variables for them all.

My question is, do I model this as A or as B?

A, i.e. a single model

Event ~ Vacc + Age + Vacc*Brand1 + Vacc*Brand2... + Vacc*Brand20


B, i.e. multiple runs of the model changing the interaction term each time

Event ~ Vacc + Age + Vacc*Brand1
Event ~ Vacc + Age + Vacc*Brand2
...
Event ~ Vacc + Age + Vacc*Brand20


Do I "use up" statistical power more doing it one way? Do I generate erroneous confidence intervals doing it the other?

Apologies for such a basic question but I haven't been able to find a succinct answer anywhere on CV or elsewhere.

• At least you should not run the model 20 times with a new interaction term each time! How do you want to interpret that? But with 20 brands you get a lot of parameters ... maybe let the brand interactions be random effects, or use some form of regularization? Some ideas here: stats.stackexchange.com/questions/64414/… – kjetil b halvorsen Jun 29 '18 at 18:45