Treatment of this dummy variable

[Solomon Lin]

Hi,

I have these two dummy variables and a continuous variable in my dataset and I was wondering how I should include them in my model?

dad10: A dummy variable = 1 if the individual lived with their dad when they were 10.

dadwork10: A dummy variable = 1 if the individual's dad worked when they were 10. This is set to 0 if they didn't know, which often happens if they didn't live with dad, so this variable should always be used along with dad10.

dadeduc: The number of years of education the individual's dad has. This is set to 0 if they didn't know, which often happens if they didn't live with dad, so this variable should always be used along with dad10.

I don't understand what the comment "this variable should always be used along with dad10" means. Does it simply mean that if I want to use those variables (dadwork10 and/or dadeduc), I have to include dad10? (Without necessarily having to interact them).

Or does it mean that I have to interact dad10 and those two variables if I want to use them?
For example, does it mean I should have:

reg Y dad10 dad10*dadwork10 dad10*dadeduc

Does it make sense to have these variables (dadwork10 and/or dadeduc) without interacting them with dad10?

[Carole J. Wilson]

You just need to have them as additive elements: Any of the following would be fine:
Y= alpha + dad10
Y= alpha + dad10+ dadwork10
Y= alpha + dad10 + dadeduc
Y= alpha + dad10 + dadwork10 + dadeduc


If you have the regression:
Y= alpha + dadwork10
The constant (alpha) is the value of y when dadwork10 is 0 which can mean that they didn't live with the dad or they didn't know

But, if you have
Y= alpha + dad10 + dadwork10
If they are both zero, then you know that the dadwork10 is 0 because they didn't live with the dad. If dad10 is 1 and dadwork10 is zero, you now it is because they didn't know

Likewise, if dad10 is in with dadeduc, you'll know if dadeduc is zero because they don't know or because they don't live with dad.

[Solomon Lin]

Thank you very much for the detailed explanation!