# Propensity Score Matching in R with Multiple Treatments

I commonly estimate Average effect of Treatment on the Treated (ATT) via Propensity Score Matching for a particular business use case.

I'm currently using R, where I can carry this out with a package (library) called Matching (there are other libraries that do this as well, but Sekhon's Matching works fine for me).

It goes something like this:

glm1 <- glm(prog ~  X),family = binomial(link = "probit"), data = psm.df) #

rr1 <- Match(Y = Y, Tr = Tr, X = glm1\$fitted, estimand = "ATT", M = 1, ties = FALSE,
replace = TRUE, caliper = FALSE, exact = FALSE, version = "fast" )
summary(rr1)


However, the consumer of my analysis wants me to estimate not only a treatment effect, but also the lagged effect of treatment in a prior time period.

Could I make the treatment variable, Tr, a factor instead of dichotomous? If I defined it as:

Tr == 0 # No treatment in time t or t-1

Tr == 1 # Treatment in time t, but not t-1

Tr == 2 # Treatment in time t-1, but not t

Tr == 3 # Treatment in both time t-1 and t

Then how would that change the interpretation of the results? I need to be able to state the "percent lift" (or at least percentage point lift) from treatment on average, as well as with a lagged effect from prior treatment.

Should I define it as in the psuedo-code above and then run it again without the lagged treatment effect to produce those two number? Or just use the interpretation of the marginal effect of treatment and lagged treatment relative to no treatment from the factor variable specification? Or should I go a completely different route?

What's the best way to carry this out?

• I think you should do two different propensity score models instead. I'm not sure though, since it was somewhat unclear to me what you were looking for. – Adam Robinsson Dec 11 '14 at 15:00
• Depending on the available covariates, I think there will be problems justifying matching on your four groups (did you leave out treated both t-1 and t or is my conception of the problem incorrect?) – Affine Dec 11 '14 at 15:01
• @AdamRobinsson So you mean a PSM for treatment and a separate PSM for lagged treatment, right? @Affine Yes, one level dropped by default; the one represented by 0` unless otherwise specified – Hack-R Dec 11 '14 at 16:22
• I'm probably misunderstanding but you, generally, should not assign an indiviual to a group (e.g treated non treated) based on covariates assessed before or after treatment assignment. As far as I can see it, the reference group 'no treatment' could be compared to each group in a two-group prop score analysis; i.e do a separate analysis for each treatment arm. But someone might provide better advice on this. – Adam Robinsson Dec 11 '14 at 18:59