The PSMATCH Procedure

MATCH Statement

MATCH <options>;

The MATCH statement matches observations in the control group to observations in the treatment group. The MATCH statement is not allowed if a FREQ statement is specified, and the STRATA statement does not apply if a MATCH statement is specified.

Table 95.3 summarizes the options in the MATCH statement.

Table 95.3: MATCH Statement Options

Option	Description
CALIPER=	Specifies the caliper width requirement for matching
EXACT=	Requests exact matching for specified classification variables
METHOD=	Specifies the method for matching
STAT=	Specifies the statistic for comparing treated units and control units

The flowchart in Figure 95.13 displays the steps in the propensity score matching process.

Figure 95.13: Propensity Score Matching Options

You can specify the following options in the MATCH statement:

CALIPER <(caliper-options )> = r

specifies the caliper width requirement for matching, where r is either missing or greater than 0. The difference between the treated unit and its matching control unit must be less than or equal to r. If you specify CALIPER=., then the caliper requirement is ignored. By default, CALIPER=0.25 (Rosenbaum and Rubin 1985, p. 37). Austin (2011a) has shown that CALIPER=0.20 is optimal in many settings.

You can use the following two caliper-options to prescribe the caliper requirement:

MULT=ONE | STDDEV

specifies the multiplier for the specified caliper width r:

ONE: uses r for the caliper width.
STDDEV: uses r times the pooled estimate of the common standard deviation of the STAT= statistic, where this estimate is computed as the square root of the average of the variances in the treated and control groups.

By default, MULT=STDDEV.

STAT=LPS | PS

specifies the statistic in the caliper width specification that is used for determining the distance between two units. This suboption applies only if you specify the STAT=MAH option in the MATCH statement.

LPS: uses the logit of propensity score.
PS: uses the propensity score scale.

By default, STAT=LPS.

If you do not specify the STAT=MAH option in the MATCH statement, the STAT= option in the MATCH statement is used to select the statistic used in the caliper width specification.

EXACT=variable | (variables )

specifies classification variables that are to be matched exactly. That is, observations in each matched set must have the same values for these variables. The variables must be specified in the CLASS statement.

METHOD=method <(method-options )>

specifies the method for the matching. You can specify the following method and method-options. By default, METHOD=OPTIMAL.

METHOD=FULL (KMAX=kmax <full-options> )

requests optimal full matching. Each treated unit is matched with one or more control units, and each control unit (if matched) is matched with one or more treated units. If the specified total number of control units to be matched is less than the number of available control units, then constrained full matching is performed—that is, not all observations are matched.

You must specify the following suboption:

KMAX=kmax: specifies the maximum number of control units to be matched with each treated unit, where kmax 1.

You can also specify the following full-options:

KMAXTREATED=kmaxtrt KMAXTRT=kmaxtrt: specifies the maximum number of treated units for each control, where kmaxtrt 1. By default, KMAXTREATED=2.
KMEAN=kmean: specifies the average number of control units for each treated unit in the matched data set. If the resulting number of control units is greater than the number of control units in the support region, the number in the support region is used.
NCONTROL=m: specifies the total number of control units in the matched data set. If the number m is greater than the number of control units in the support region, the number in the support region is used.
PCTCONTROL=p: specifies the percentage of the total number of control units in the matched data set. If the resulting number of control units is greater than the total number of control units in the support region, the number in the support region is used.

If you do not specify any of the KMEAN=, NCONTROL=, and PCTCONTROL= options, KMEAN= (kmax + 1 / kmaxtrt) / 2 is used. If the resulting number of units computed from the KMEAN=, NCONTROL, or PCTCONTROL= option is less than the total number of control units, then not all control units are matched.

METHOD=GREEDY <(K=k ORDER=order-option )>

requests greedy nearest neighbor matching in which each treated unit is sequentially matched with the k nearest control units. Matching depends on the ordering of the treated units, which you can specify in the ORDER= suboption.

You can specify the following suboptions:

K=k

specifies the number of matching control units, where k > 0, for each treated unit. PROC PSMATCH performs k separate loops of matching for treated units. In each loop, the nearest control unit is sequentially matched to each treated unit. By default, K=1 (one control unit for each treated unit).

ORDER=ASCENDING | DESCENDING | RANDOM <(SEED=number)>

specifies the ordering of treated units that are used to find the matching control units. You can specify one of the following values:

ASCENDING: orders the treated units in ascending order of the propensity score.
DESCENDING: orders the treated units in descending order of the propensity score.
RANDOM <(SEED=number)>: orders the treated units in random order of the propensity score. The SEED= suboption specifies a positive integer to start the pseudorandom number generator. If the SEED= option is not specified, the value is generated from reading the time of day from the computer’s clock.

By default, ORDER=DESCENDING.

METHOD=OPTIMAL <(K=k )>

requests optimal fixed ratio matching. The K=k suboption specifies the number of matching control units, where k > 0, for each treated unit. By default, K=1 (one control unit is matched with each treated unit).

METHOD=REPLACE <(K=k )>

requests a fixed number k of unique matching control units for each treated unit, where the matched control units are selected with replacement. This means that each control unit can be matched to more than one treated unit, but it can only be matched once to the same treated unit. The K=k suboption specifies the number of matching control units, where k > 0, for each treated unit. By default, K=1 (one control unit is matched with each treated unit).

METHOD=VARRATIO (KMAX=kmax <varratio-options> )

requests optimal variable ratio matching. Each treated unit is matched with one or more control units.

You must specify the following suboption:

KMAX=kmax: specifies the maximum number of control units matched with each treated unit, where kmax 1.

You can also specify the following varratio-options:

KMEAN=kmean: specifies the average number of control units for each treated unit in the matched data set. If the resulting number of control units is greater than the total number of control units in the support region, the number in the support region is used.
KMIN=kmin: specifies the minimum number of control units to be matched with each treated unit. By default, KMIN=1.
NCONTROL=m: specifies the total number of control units in the matched data set. If the number m is greater than the total number of control units in the support region, the number in the support region is used.
PCTCONTROL=p: specifies the percentage of total control units in the matched data set. If the resulting number of control units is greater than the total number of control units in the support region, the number in the support region is used.

If you do not specify any of the KMEAN=, NCONTROL=, and PCTCONTROL= options, then KMEAN= (kmin + kmax) / 2 is used.

STAT=statistic

specifies the statistic to be compared when treated units are matched to control units. You can specify the following statistics:

LPS

specifies matching that minimizes the difference between the logits of the propensity scores for the two units.

PS

specifies matching that minimizes the difference between the propensity scores for the two units.

MAH (var-options </ mah-options> )

specifies matching that minimizes the Mahalanobis distance between the two units.

You use the following var-options to select at least one variable for computing the Mahalanobis distance:

LPS: includes the logit of the propensity score.
PS: includes the propensity score.
VAR=(var-list): includes variables in the specified var-list. These variables must be continuous variables in the input data set.

You can also specify the following mah-options:

COV=CONTROL | IDENTITY | POOLED

specifies the type of covariance matrix in the Mahalanobis distance:

CONTROL: uses the covariance matrix that is computed from observations in the control group.
IDENTITY: uses the identity matrix, and the resulting distance is the Euclidean distance.
POOLED: uses the pooled covariance matrix that is computed from observations in the treated group and observations in the control group.

By default, COV=CONTROL.

SQRT=YES | NO

specifies whether to apply the square root to the Mahalanobis distance in the difference computation. This mah-option does not affect matching results for greedy nearest neighbor matching and matching with replacement. It affects only results for optimal matching that minimizes the total absolute difference.

YES: uses the square root of the Mahalanobis distance as the difference between treated and control units.
NO: uses the Mahalanobis distance as the difference between treated and control units.

By default, SQRT=YES.