Inverse probability weighting (IPW) with positive and negative treatments? I am studying the effects of the government intervention which can take two directions and is usually represented as follows:

$Treat = \left\{\begin{matrix}
 & +1 (intervene), if state A\\ 
 &0 (do nothing), if all  is  ok \\ 
 & -1 (intervene  in opposite direction) if B
\end{matrix}\right.$

Is it possible to do in the IPW setting? The key is that A and B (1 and -1) are the opposite. They are not really ordered and representing them as 0, 1, 2 would not make sense. Treatment is actually a censored variable so most of the time it is zero and then when the combination of covariates is above a certain treshold it is +1, when it is below it is -1.
I would appreaciate if somebody can help. I run straight to the stata but I saw that probit does not allow for negative treatment values and that in the case of multiple treatments only logit is used (why?). Am I missing something theoretically or should I just use R?
 A: You are actually in a standard multi-category treatment scenario. The fact that treatment -1 is in the opposite direction as treatment 1 is a matter of the interpretation of the causal effect you estimate, not a matter of how the effects are estimated. So any literature you read on multi-category (nominal) treatments will apply here. Mccaffrey et al (2013; doi:10.1002/sim.5753) is a great resource. 
Essentially, you estimate a multinomial logit/probit model and compute the predicted probability of each treatment for each individual (so each individual will have three predicted probabilities). You need to ensure the treatment is modeled as a categorical variable. The IPW is the inverse of the probability of being in the treatment actually received. Then you can estimate a weighted regression or ANOVA to estimate the causal contrasts of interest (e.g., +1 vs 0, -1 vs. 0, +1 vs -1).
If you decide not to use Stata, the WeightIt package in R is well equipped to estimate IPWs for multi-category treatments.
