Hello, rachard11, and welcome to the Grammar Exchange.
Is it grammatically correct to say "I study the interaction between factor A and factor B on outcome C?" Or do I have to explicitly mention the effects of the interaction, such as "I study the interactive effect of factor A and factor B on outcome C?"
I prefer the second version because the noun "interaction" does not collocate with the preposition "on," while "effect" does. Alternatively, and even if the preposition "of" followed by the definite article may not sound so idiomatic, this other version might be even clearer:
- I study the effect of the interaction between factor A and factor B/between factors A and B on outcome C.
To avoid the article, you might prefer the following:
- I study the effect of factor A-factor B interaction on outcome C.