# Comparing multiple regression models vs. using covariate

I have found from previous data that men and women differ significantly in the way that they interact with my variables.

I now want to make a regression model trying to ascertain the interactions between my dependent and independent variables and then compare the regressional weights and effect sizes on the basis of gender.

Is it more sensible to make two models and compared them - and if so, is there a test to see if two different models significantly differ from one another - or should I just include gender as a covariate?

• It'll help to provide information about the data, dependent & independent variables and the questions you want to answer with the analysis. In general, it's better to have one model and to interact gender with every independent variable that you want to compare between men and women, as suggested by @Sointu in their answer. Dec 3, 2022 at 11:55

## 1 Answer

Are you interested in whether y ~ x relationship is different for men and women or whether an interaction effect y ~ x*z is different for men and women? The way I see this, in the first case, you'd need to run a model predicting your outcome from your predictor x, gender, and their interaction. In the second case, you'd need to run a model predicting your outcome from x, z, gender and all the interactions between these three predictors. Then, if the interaction (or one of the interactions) involving gender is significant, you can run the relevant lower-order model(s) separately for men and women.

*Edited to remove confusing notation

• Can you explain the notation you use? It looks like R formula notation but then you don't need x*z in the second formula since it includes x*z*gender. In fact, the most succinct way to specify the second model in R is y ~ x*z*gender. Since the OP doesn't mention they use R, I suggest you use math notation instead (with explicit $\beta$ coefficients). Dec 3, 2022 at 11:44
• Yeah, good point - it wasn't meant to be notation at all but it ended up resembling R notation. I'll edit to plain text as I'm still learning how to use mathematical notation here. Dec 3, 2022 at 12:12