Q1 I have a multiple regression model with two continuous variables (Cont1 and Cont2) and one categorical variable (Cat1) with three levels. If I run a model containing all possible interactions (so two and three way), how many parameters would that be in my maximal model?
I suppose my confusion is to do with how many parameters the interactions consist of. For example, since I want to include all two and three way interactions in the model, would the number of parameters be:
- 5 for the direct effects (1 for each of Cont1 and Cont 2, and 3 for Cat1 since it has three levels)
- 3 for each of the two way interactions with Cat 1 (so Cont1*Cat1 = 3 AND Cont2*Cat1 = 3 as again there are three levels for Cat1)
- 1 for the two-way interaction between Cont1 and Cont2
- 6 for the three way interaction (this is the one I am most unsure about)
- 1 for the interval term
Or is that incorrect?
Q2 I read that n=30 is a reasonable proxy for the sample size needed per variable in a model - would I need n=30 for every parameter in the model, or simply every direct effect (taking account of the fact that the categorical variable has three levels)? If it is per parameter, does this include n=30 for the interval term too?
Apologies for the simple questions, am just getting myself a bit confused with the interaction terms/levels of the categorical!
Let me know if you need further info. (No data at the moment, this is hypothetical...). Thanks.