Interacted Fixed Effect in Small Sample

[Kien Hoang]

Hi, I have a sample of 6000 observations. I want to put an interacted fixed effect into my model. The interaction term includes 4 variables, each having 5 values (they are categorical variables with 5 levels).

However, I understand that by using such interaction terms, there will be 5^4 = 625 groups in my model. So, on average, each group will have only 10 observations, and that could lead to an overfitted result.

Do I understand this correctly?

[Clyde Schechter]

Yes. You will largely be fitting the noise in this way. In addition, because of the small cell sizes in the interaction, the coefficients you get will come with large standard errors, so they will be largely uninformative, to boot.

Imagine, however, that you had a sample of 6,000,000 observations, so that you would not face the overfitting and low precision problems. you add this 625-level interaction to your model, you will end up with 625 additional coefficients in your model. What would you do with them? What could you learn about your data from them? Is there a pre-existing theoretical reason to expect that this 625-level classification is important for understanding sources of variation in your outcome?

[Kien Hoang]

Thank you, Clyde for your helpful reply as usual!