Is it possible to use a multinomial outcome after a propensity score matching?

Question

I would like to use a propensity score matching (PSM) to evaluate the effect of a treatment T on an outcome Y.

In most of the papers that I have read, the outcome is continuous: health expenditures, income, etc. However, my outcome is multinomial since it corresponds to political parties for which people vote. I can order my outcome so that higher values correspond to a greater openness to a certain policy for example. However, I don't know if it is possible to use a PSM when the outcome is not continuous but multinomial.

In Stata 13 manual (p.34), it is said:

The outcome models can be continuous, binary, count, or nonnegative. The treatment model can be binary, or it can be multinomial, allowing for multivalued treatments.

Do you know if multinomial variables are accepted as outcome?

• If not, could you explain why count variables are accepted and multinomial variables are not?

• If it is accepted, do you know if it is covered by some R packages?

Answer 1

There are two varying philosophies when it comes to propensity score matching, which I outline here. In short, one philosophy sees matching as part of the estimation process with its own variance component associated with it, while another philosophy sees matching as nonparametric preprocessing of the data does not need to be taken into account when computing the uncertainty of the estimates. The teffects function in Stata uses the former approach, while the MatchIt package in R uses the second approach.

The second approach allows you to use the variance estimators that normally accompany an analysis on data that hasn't been matched. The advantage of this is that any analysis can take place in the matched dataset, including regression, structural equation model, mixed-effects modeling, etc. So, in the matched dataset, you can just perform multinomial regression just as you would in a dataset that hadn't been matched. This can be accomplished however you like to do it; there are a few packages to do this in R and some functions in Stata. The variance estimation doesn't include the variability due to the matching procedure itself. Some argue that one should account for the paired nature of the data by using a variance estimator that accounts for that, and this is straightforward in both R and Stata by employing cluster-robust standard errors with pair membership as the cluster.