Causal Inference With a Nominal Treatment I am working with a treatment that has three nominal (I suppose these could be considered ordered) values:
0 = no mediation,
1 = failed mediation,
2 = successful mediation,
For the purposes of the project I am working on, "failed mediation" is the treatment of interest. In particular, I am interested in whether failed mediation attempts cause warring actors to pursue violence and abandon diplomacy over the course of a conflict.
However, I am concerned how this will work in practice. For example, if I approached this using matching, I would match cases of failed mediation with...? This is where it gets confusing for me. Would I create a new binary treatment variable (1 = failed mediation, 0 = else)? If so, do I run any risk with lumping cases of "no mediation" and "successful mediation" together in the control group? If so, it feels like I am creating a control group that contains substantively different information as it relates to treatment.
Alternatively, I could drop cases of "no mediation" and have "successful mediation" serve as the control group, but I feel like this creates a selection bias issue.

One way of turning your research idea into a hypothesis is that Violence(SM) > Violence(NM) > Violence(FM) or perhaps Violence(SM) > Violence(FM) > Effect(NM).
The first says that SM helps, NM leads to violence, and FM is worse than no mediation. The second says that FM is between SM and NM, but both cause violence to increase. You can define effects relative to the NM experience. These aren't the only options, just those that spring to my mind.
There aren't any nearest neighbor and propensity score matching estimators with multivalued treatments.
A good approach is:
Cattaneo, M. D. 2010. Efficient semiparametric estimation of multivalued treatment effects under ignorability. Journal of Econometrics 155: 138–154.
He has older Stata and forthcoming R code here, with examples and replications files.
Stata has a slew of newer parametric multivalued TE estimators (teffects ra, teffects ipw, teffects ipwra, and teffects aipw). These use regression adjustment, inverse-probability weighting, inverse-probability-weighted regression adjustment, and augmented inverse-probability weighting. All assume ignorability conditional on observed covariates. There are also a few other community-contributed commands that are mentioned in the documentation.
There could well be other implementations and approaches that I am not aware of. I don't have deep expertise with these models.
