Test for moderation effect in multiple regression

Question

I am trying to build a regression model to find the correlation between the features of thumbnails and the popularity of videos. I am proposing that category of videos is the moderator of the correlations, and I selected two categories for comparison (dichotomous).

As I have 3 independent variables (features of thumbnails), do I include an interaction term for each feature? I understand that it could cause my model to be overly complex and multicollinearity could cause problems. Alternatively, is it possible to only test for one moderation effect in each model, and build three of them - is this an appropriate way to do it?

I would also like to ask why can't I just separate my dataset by category and construct two models and compare the coefficients?

Thank you!

Answer 1

The interaction terms included should correspond to your hypothesis. While each thumbnail feature is a separate variable, it sounds like you do not have a specific hypothesis about which feature is important. This is fine. You can either A) run a separate model for each feature and correct for multiple comparisons; or B) Run a single model with all three features and all 3 interaction terms. You can use a model comparison test (i.e., an anova) to compare models with and without all three interaction terms. This will give you an index of the overall effect of the interactions, and you would then have to probe deeper to test which is driving the effect. Both options are fine, it just depends on what you're will to sacrifice (A = power, B = specificity).

As to the second question, separate models for each level of a moderator is a valid way to test whether the slope in that group is different from 0, but it isn't a test of whether the slopes differ between groups - that's what an interaction tells you.