When you specify the MATCH statement, the PSMATCH procedure matches observations in the control group to observations in the treatment group by using one of the methods that are described in the following subsections. You can request the method in the METHOD= option.
Greedy nearest neighbor matching, requested by the METHOD=GREEDY option, selects the control unit whose propensity score best matches the propensity score of each treated unit. Greedy nearest neighbor matching is done sequentially and without replacement.
The following criteria are available for greedy nearest neighbor matching:
the number of control units to be matched to each treated unit (you can specify this number in the K= suboption)
the order of propensity scores of treated units, which can be ascending, descending, or random (you can specify the order in the ORDER= suboption)
Replacement matching, requested by the METHOD=REPLACE option, selects with replacement the control unit whose propensity score is closest to the propensity score for each treated unit. You can specify the number of control units to be matched to each treated unit in the K= suboption.
Optimal matching selects all matches simultaneously and without replacement to minimize the total absolute difference in propensity score across all matches. You can request the following optimal matching methods:
fixed ratio matching, requested by the METHOD=OPTIMAL option, which matches a fixed number of control units to each treated unit
variable ratio matching, requested by the METHOD=VARRATIO option, which matches one or more control units to each treated unit
full matching, requested by the METHOD=FULL option, which matches each treated unit to one or more control units or matches each control unit to one or more treated units. By additionally specifying the KMEAN=, NCONTROL=, or PCTCONTROL= suboptions, you can request constrained full matching in which the number of matched control units is less than the total number of available controls.
As alternatives to matching on the propensity score, you can match on the logit of the propensity score or use the Mahalanobis distance to match on a set of variables (possibly including the PS or the LPS). All three of these methods minimize the total absolute difference across all matches in the matching metric, which is the total difference in the logit of the propensity score by default.
Table 8 lists the suboptions available for optimal matching. The symbol X indicates that the option applies for the specified method.
Table 8: Applicable Options for Optimal Matching
| KMEAN= | |||||||
|---|---|---|---|---|---|---|---|
| NCONTROL= | |||||||
| METHOD= | K= | KMIN= | KMAX= | KMAXTRT= | PCTCONTROL= | ||
| OPTIMAL | X | ||||||
| VARRATIO | X | X | X | ||||
| FULL | X | X | X |
K= specifies the number of control units to be matched to each treated unit.
KMIN= specifies the minimum number of control units to be matched to each treated unit.
KMAX= specifies the maximum number of control units to be matched to each treated unit.
KMAXTRT= specifies the maximum number of treated units to be matched to each matched control unit.
KMEAN= specifies the average number of control units to be matched to each treated unit.
NCONTROL= specifies the total number of control units to be matched.
PCTCONTROL= specifies the percentage of control units to be matched.
You can specify only one of the KMEAN=, NCONTROL=, and PCTCONTROL= options.