Interpreting Interaction Terms in Tobit regression

[Mimika Saha]

Dear Statalist Users,

I am using Tobit model for my thesis and have a query regarding the interpretation of the interaction term.

I have two types of interactions: continuos*continuous and continuous*dummy

Could you please kindly guide me on how to interpret the coefficients for the interaction term from a Tobit regression?

Thank you for your time in advance.

Regards,

Mimika Saha

[Charlie Joyez]

Running a Tobit model (linear but bounded model) doesn't change the way you interpret interaction terms, so basically, you do the same interpretation than with an OLS model.

The web is full of resources for you, e.g.:
https://www.princeton.edu/~otorres/Regression101.pdf
Start looking from page 36.

Best,
Charlie

[Mimika Saha]

Dear Charlie,

Thank you very much for your response.

Regards,

Mimika

[Maarten Buis]

That is only true if you are interested in the latent dependent variable. Sometimes that makes sense, but sometimes we want to interpret the results in terms of the actual dependent variable or the dependent variable when it is not 0. So it depends on what Mimika wants.

[Mimika Saha]

Dear Maarten,

Noted. Thank you for your response.

[Minhaj uddin]

Dear @ Maarten

That is only true if you are interested in the latent dependent variable. Sometimes that makes sense, but sometimes we want to interpret the results in terms of the actual dependent variable or the dependent variable when it is not 0. So it depends on what Mimika wants.

Could you please explain how we can interpret the results in terms of the actual dependent variable?

Thank you!

[Maarten Buis]

Minhaj uddin : here is an example:

webuse gpa, clear
tobit gpa2 hsgpa pincome program, ll
margins , at(hsgpa=3 program=0 pincome=(0.5(0.2)6.8)) predict(ystar(2,.))
marginsplot

[Minhaj uddin]

So, by predicting the marginal effect, I understand now. Thank you so much!

[Minhaj uddin]

Sir, correct me if I am wrong. In case our objective is not to predict the marginal effect on the actual variable but rather to test the impact of IDV on DV and the direction of the impact (like positive and significant), then in that case we can directly interpret the coefficient.

Can we apply the same interpretation to the interaction coefficient, or compare the coefficients from the two Tobit models? Say, if one Tobit model gives an ROA coefficient of 0.05 (sig.) and another gives 0.09 (sig.), can we say that ROA has a higher impact on DV in model 2 than 1?