I am estimating a model where interaction terms play a role, and I am wondering which specification I should use, and how to interpret the results.

More specifically, I regress a binary variable, say Y, on a bunch of covariates, some continuous, some binary. Interaction between some binary covariates play a role.

I am mostly interested in the effect of one covariate, let's call it X, which I interact with other covariates, say Z:

$$Y = \beta_X \cdot X + \beta_Z \cdot Z + \beta_{XZ} X \cdot Z + u$$

With OLS, $\beta_X$ is not significant(ly different from 0), but $\beta_{XZ}$ is. With logit, it is the contrary.

I guess I should use logit, but I am not sure how to interpret $\beta_{XZ}$, given what I read on the topic: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3447245/ and https://stats.idre.ucla.edu/stata/seminars/deciphering-interactions-in-logistic-regression/.

Also, how to interpret the results? Has $X$ an effect by itself (as logit tends to show) or only when interacted (as seen with OLS)?


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