Interpreting interaction in probit with endogenous covariate

[Amanda McGowan]

Hi all,

My model is an ordered probit regression with an endogenous covariate. The dependent variable represents the adoption group based on the number of technologies the respondent adopted, and is either "Non-adopter", "Simple", or "Complex". The endogenous variable, train, is binary.

The model includes a gender by training interaction (female##train). Where male is indicated by female = 0 and female is female = 1.

eoprobit ordinal age labor i.migrant dvet dexten exp land i.memb i.school i.cbf i.input i.female i.district i.caste i.female##i.train, endogenous(train = villtrain age labor i.migrant dvet dexten exp land i.memb i.school i.cbf i.input i.female i.district i.caste,probit) vce(robust)

And I used margins to get Pr(ordinal)

margins female#train, post

I then created graphs for each response variable category.

Lastly, I used the same method found in Stata tip 134: Multiplicative and marginal interactive effects in nonlinear models by Dow, Norton, and Donahoe (2019) to obtain the marginal interaction effect which is the difference in differences of changes in female and train on the probability scale.

My interpretation of this is that as female changes from male (female = 0) to female (female = 1), the effect of training (0  1) —

• for Non-adopters increases (because of marginal interaction effect on probability scale)
• for Simple adopters increases
• for Complex adopters decreases

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My questions:

1) Is this a correct interpretation?
2) Does this mean that compared to when males who are trained, females who have training have an increased probability to be non-adopters and simple adopters and have an decreased probability of being complex adopter?

Hopefully I have posted this question correctly since I am new to Stata and Statalist. Any and all help is much appreciated .

Thank you all!

Amanda

[Fei Wang]

Amanda, nothing is wrong about your interpretation, but I would interpret the results in a more accessible way: Training is more likely to convert males from non-adaptors to complex technology adopters as compared with females. We can hardly say something about simple tech adoption as the effects of training on adopting simple tech seem insignificant for both males and females.

[Amanda McGowan]

Amanda, nothing is wrong about your interpretation, but I would interpret the results in a more accessible way: Training is more likely to convert males from non-adaptors to complex technology adopters as compared with females. We can hardly say something about simple tech adoption as the effects of training on adopting simple tech seem insignificant for both males and females.

Thank you Fei Wang for your response. I agree, your interpretation is more understandable. Thanks again!