Interaction effect in probit/logit significant?

[Tristan De Blick]

Dear Listers,

My dependent variable is binary, so is one of my two independent variables. The other Ind Var is ordinal, ranging from 1 to 10.
Both independent variables have a significant impact when I run a probit/logit/ or even OLS.
Now, I'm interested in the interaction effect.

For this, I currently compare the average marginal effect of X2 when my binary independent variable, X1, either takes the value of 0 or the value of 1.

probit Y X1##X2, vce(cluster id) robust
margins, dydx (c.X2) at (X1=(0 1))

I do find a different average marginal effect. However, both effects are significant and are in the same direction (in this case, positive).
I would like now to say more about the difference, whether the difference is significant.

This can not be done through 'inteff', as I get the error factor-variable and time-series operators not allowed and I

I have browsed through the list, read multiple papers such as https://journals.sagepub.com/doi/pdf...867X1201200209 (Richard Williams, 2012), https://www3.nd.edu/~rwilliam/stats/Margins01.pdf (Richard Williams, 2020), and earlier work on LDV techniques by Bowen & Wiersema or Norton, Wang & Ai.
Yet, it seems as if this problem has not been solved/addressed yet?

Thank you for any insight!

[Clyde Schechter]

Well, before you puzzle over how to use -margins-, you need to set up the probit correctly. In factor variable notation, any variable mentioned in an interaction term is presumed to be discrete unless it is prefixed with c. So -probit- is estimating your model on the assumption that both X1 and X2 are discrete. For X2 to be treated as continuous you need X1##c.x2.

I'm actually surprised you got any results form -margins- at all, because there is no c.X2 in your probit model.

Anyway, once you go back and fix all that, to see what the difference between the marginal effects are, you can run -margins X1, dydx(X2) pwcompare-. (Note that in the -margins- command you do not have to specify c. or i. with variables, because -margins- follows what was done in the preceding estimation command.)

[Tristan De Blick]

I indeed use i. and c. but forgot to mention this. Thank you for providing me with the solution nonetheless, it works!