Omitting variables because of collinearity in interaction

[Thomas Hau]

Dear Stata users

I have a problem with omitting variables because of collinearity in my nbreg model. My dependent variable is a count variable measuring the number of terroristattacks in dyad-year. My main independent variable is a dummy, measuring wether or not the state intervened in that state that year.

I want to check for interactions, for example: is the effect of intervention on terrorism affected by the duration of the intervention, e.g. if you intervene in the country in a 10 years period, your more exposed to terrorism than if you intervene in 1 year. Duration is a continuous variable.

When I add the interaction in the regression command (nbreg attacks i.intervention##c.duration) it omits the duration variable because of collinearity. I have also tried to dummy code duration (0=no duration because of no intervention, 1=intervention and duration of to years, 2=intervention and duration to years and following) but the same happens.

Does anyone know how to solve this problem? All help is deeply appreciated. Attached below is how the duration variable variance on the intervention variable.

interventi | Intervention duration
on | 0 1 2 3 4 | Total
-----------+-------------------------------------------------------+----------
0 | 104,067 0 0 0 0 | 104,067
1 | 0 88 57 45 37 | 347
-----------+-------------------------------------------------------+----------
Total | 104,067 88 57 45 37 | 104,414


interventi | Intervention duration
on | 5 6 7 8 9 | Total
-----------+-------------------------------------------------------+----------
0 | 0 0 0 0 0 | 104,067
1 | 29 23 17 16 15 | 347
-----------+-------------------------------------------------------+----------
Total | 29 23 17 16 15 | 104,414


interventi | Intervention duration
on | 10 11 12 | Total
-----------+---------------------------------+----------
0 | 0 0 0 | 104,067
1 | 10 6 4 | 347
-----------+---------------------------------+----------
Total | 10 6 4 | 104,414

[Clyde Schechter]

Each country has the same value of intervention duration in all of its post-intervention observations, correct? If that is the case, then if you know which country you are talking about (the fixed effects) and you are in the post-intervention period, then you automatically know the intervention duration in that country, and there is no within-country variation. That's why it's being dropped.

But remember also that in the interaction model, the coefficient of duration is not really the effect of duration. It is the effect of duration conditional on intervention = 0. And, in truth, from what you describe it sounds like this would be a meaningless number even if you could get it: it would be the effect of an intervention's duration when there is no intervention in the first place! As long as the i.intervention#c.duration term itself is not being omitted, I don't think you have a problem here. It seems to me that it is perfectly appropriate that duration itself is omitted due to multicolinearity.

tldr; It ain't broke. Don't fix it.