Using PROC MIXED to estimate PSM treatment effects that vary at school level

[whs278]

I have a question about Propensity Score Matching (PSM) and PROC MIXED.

I have dataset of treatment students matched to control students.  I want to see if the treatment varies by school by allowing the treatment effect to vary by school.  I believe I can do  with the statement RANDOM TREATMENT / SUBJECT = SCHOOL.  However, at the same time I feel like I still need to control for the PSM process and the fact that each treatment student is matched to a similar control student.  My understanding of PSM without replacement is that it mimics paired experiment (almost as if the treatment and the control students are twins).  I tried doing this with a Random INT / subject = ID statement (where ID is an indicator for each treatment/control student pair), but this seems to take up a lot of memory.  However, if I add a REPEATED / SUBJECT = ID statement in addition to the RANDOM TREATMENT / SUBJECT = SCHOOL statement, the model seems to work.  

I just want to know if this model is valid?  I posted the code below.

PROC MIXED DATA = PSM_DATA METHOD = REML COVTEST ORDER = DATA ;
			    CLASS SCHOOL ID;
			    MODEL HSGRADG12 = TREATMENT / DDFM = BW  SOLUTION NOINT ;
				REPEATED / SUBJECT=ID TYPE=UN;
			    RANDOM TREATMENT / SUBJECT = SCHOOL TYPE = UN SOLUTION G GCORR;

RUN;  
 
 

[MichaelL_SAS · Accepted solution]

>>My understanding of PSM without replacement is that it mimics paired experiment (almost as if the treatment and the control students are twins).

Note, that this is not necessarily true. For a discussion on this, one excellent source is this commentary paper written by Elizabeth Stuart: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.477.4683&rep=rep1&type=pdf

In particular, from the discussion in the “Matched-Pair Analyses” section:

There are at least two reasons to believe that analyses of matched data do not need to account for the paired nature of the data. First, the theory behind propensity scores does not imply that any individual pairs will have similar covariate values—in fact, two individuals with the same propensity score may have very different values of the covariates. The theory of propensity scores says only that within groups of individuals with similar propensity scores, the distributions of the covariates that went into the propensity score will be similar. If matched-pair analyses will be done, arguably balance checks should also be done accounting for the matched pairs. Second, the theory underlying matching methods developed by Rubin and Thomas [9, 12] and Rubin and Stuart [13] does not rely on matched pairs—just matched samples.

[whs278]

Thank, this paper was exactly what I was looking for!