Interpretation of the interaction terms of two categorical variables in Non Linear models

[Frank Newman]

Hi,

I have been searching online but cant find much. I need help in understanding the interpretations of coefficients in a Probit model once an interaction term between two categorical variables in included. Specifically variable s2 can take on values 0 1 2 3 4 5, whilst im2 is a dummy vaiable 0, 1.

Stata Command: probit a05_ i.s2 i.pe2 i.im2 age i.female i.degree i.im2#i.s2

Am i correct in thinking that in the stat output table, the main effects of s2 is the effect of 1 2 3 4 5 when im2=0 compared to the baseline of s2=0 when im=0

and then the main effects of im2 represents im2 when s2=0

and then the interaction terms represent the effects of each s2 value for when im2=1 in comparison to s2=0 when im2=1

Any help would be greatly appreciated.

[Clyde Schechter]

Exactly correct. To be a little more precise, the interaction terms represent the differences between the effects at each s2 value at im = 1 and the effects at the same s2 values at im = 0.

Added: Since even without interaction terms probit models are difficult to understand, and interaction terms, even without probit models are difficult to understand, I strongly suggest that you follow your -probit- with -margins im2#is2- to get the predicted probabilities of a05_ for each combination of im2 and is2. You might also want to look at -margins im2, dydx(s2)- which will give you the effect (as a probability difference) of each level of s2, separately by values of im2, and perhaps its opposite, -margins s2, dydx(im2)-.

[Frank Newman]

Great, thanks for the clarification, and the tips on margins.

In terms of the interpretation of margins im2, dydx(s2) as you mentioned I get the effects for each level of s2 for both values of im2 (0 and 1) - 1.s2 yields a value for im2 = 0 and im=1, am i correct in interpreting the coefficient of im2= 1 as the probability of getting a05_ =1 for 1.s2 (with im2=1) in comparison to 0.s2 (with im2=1); and for im2 = 0 its the probability of getting a05=1 for 1.s2 (with im2=0) in comparison to 0.s2 (with im2=0).

Whereas with margins s2, dydx(im2) i get one value for each level of s2 with im2=1 - such that the probabilities represent the probability of getting a05_1 are in comparison to the same level of s2 but with im=0

thanks again.

[Clyde Schechter]

These interpretations are correct!

[Frank Newman]

Thanks for your help.