The PSMATCH Procedure

Matching Statistics

The PSMATCH procedure provides the following types of statistic on which to match observations in the treated group with observations in the control group (you specify the statistic with the STAT= option in the MATCH statement):

the difference in the logit of the propensity score (STAT=LPS; this is the default)
the Mahalanobis distance between sets of continuous variables (STAT=MAH)
the difference in the propensity score (STAT=PS)

Let and be the propensity scores of the ith treated unit and the jth control unit, respectively. When you specify STAT=PS, matching is based on the absolute difference,

When you specify STAT=LPS, matching is based on the absolute difference,

where and are the logits of the propensity scores.

When you specify STAT=MAH, two different distances can be used as the Mahalanobis distance in matching (as specified in the SQRT= suboption of the STAT=MAH option):

(SQRT=YES; this is the default)
(SQRT=NO)

where is the set of variables of the ith treated unit, is the set of variables of the jth control unit, and is the covariance matrix of .

Note that the SQRT= option does not affect the results for greedy nearest neighbor matching and matching with replacement; it affects only the results for optimal matching.

Three different covariance matrices can be used to compute the Mahalanobis distance (as specified in the COV= suboption of the STAT=MAH option):

the covariance matrix that is based on observations in the control group (COV=CONTROL; this is the default)
the pooled covariance matrix that is based on observations in the treated and control groups (COV=POOLED)
the identity matrix (COV=IDENTITY) that yields the Euclidean distance.

Note that you can also include the propensity score and the logit of propensity in the Mahalanobis distance. For example, when you specify STAT=MAH(PS VAR=(X1 X2 X3) / COV=POOLED), the PSMATCH procedure computes the Mahalanobis distance between observations in the treated and control groups by using the propensity score and variables X1, X2, and X3. The covariance matrix is the pooled covariance matrix of the treated and control groups.