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?