method_genetic: Genetic Matching

In MatchIt: Nonparametric Preprocessing for Parametric Causal Inference

Genetic Matching

Description

In matchit(), setting method = "genetic" performs genetic matching. Genetic matching is a form of nearest neighbor matching where distances are computed as the generalized Mahalanobis distance, which is a generalization of the Mahalanobis distance with a scaling factor for each covariate that represents the importance of that covariate to the distance. A genetic algorithm is used to select the scaling factors. The scaling factors are chosen as those which maximize a criterion related to covariate balance, which can be chosen, but which by default is the smallest p-value in covariate balance tests among the covariates. This method relies on and is a wrapper for \pkgfunMatchingGenMatch and \pkgfunMatchingMatch, which use \pkgfunrgenoudgenoud to perform the optimization using the genetic algorithm.

This page details the allowable arguments with method = "genetic". See matchit() for an explanation of what each argument means in a general context and how it can be specified.

Below is how matchit() is used for genetic matching:

matchit(formula,
        data = NULL,
        method = "genetic",
        distance = "glm",
        link = "logit",
        distance.options = list(),
        estimand = "ATT",
        exact = NULL,
        mahvars = NULL,
        antiexact = NULL,
        discard = "none",
        reestimate = FALSE,
        s.weights = NULL,
        replace = FALSE,
        m.order = NULL,
        caliper = NULL,
        ratio = 1,
        verbose = FALSE,
        ...) 

Arguments

formula	a two-sided formula object containing the treatment and covariates to be used in creating the distance measure used in the matching. This formula will be supplied to the functions that estimate the distance measure and is used to determine the covariates whose balance is to be optimized.
data	a data frame containing the variables named in formula. If not found in data, the variables will be sought in the environment.
method	set here to "genetic".
distance	the distance measure to be used. See distance for allowable options. When set to a method of estimating propensity scores or a numeric vector of distance values, the distance measure is included with the covariates in formula to be supplied to the generalized Mahalanobis distance matrix unless mahvars is specified. Otherwise, only the covariates in formula are supplied to the generalized Mahalanobis distance matrix to have their scaling factors chosen. distance cannot be supplied as a distance matrix. Supplying any method of computing a distance matrix (e.g., "mahalanobis") has the same effect of omitting propensity score but does not affect how the distance between units is computed otherwise.
link	when distance is specified as a method of estimating propensity scores, an additional argument controlling the link function used in estimating the distance measure. See distance for allowable options with each option.
distance.options	a named list containing additional arguments supplied to the function that estimates the distance measure as determined by the argument to distance.
estimand	a string containing the desired estimand. Allowable options include "ATT" and "ATC". See Details.
exact	for which variables exact matching should take place.
mahvars	when a distance corresponds to a propensity score (e.g., for caliper matching or to discard units for common support), which covariates should be supplied to the generalized Mahalanobis distance matrix for matching. If unspecified, all variables in formula will be supplied to the distance matrix. Use mahvars to only supply a subset. Even if mahvars is specified, balance will be optimized on all covariates in formula. See Details.
antiexact	for which variables ant-exact matching should take place. Anti-exact matching is processed using the restrict argument to Matching::GenMatch() and Matching::Match().
discard	a string containing a method for discarding units outside a region of common support. Only allowed when distance corresponds to a propensity score.
reestimate	if discard is not "none", whether to re-estimate the propensity score in the remaining sample prior to matching.
s.weights	the variable containing sampling weights to be incorporated into propensity score models and balance statistics. These are also supplied to GenMatch() for use in computing the balance t-test p-values in the process of matching.
replace	whether matching should be done with replacement.
m.order	the order that the matching takes place. Allowable options include "largest", where matching takes place in descending order of distance measures; "smallest", where matching takes place in ascending order of distance measures; "random", where matching takes place in a random order; and "data" where matching takes place based on the order of units in the data. When m.order = "random", results may differ across different runs of the same code unless a seed is set and specified with set.seed(). The default of NULL corresponds to "largest" when a propensity score is estimated or supplied as a vector and "data" otherwise.
caliper	the width(s) of the caliper(s) used for caliper matching. See Details and Examples.
std.caliper	logical; when calipers are specified, whether they are in standard deviation units (TRUE) or raw units (FALSE).
ratio	how many control units should be matched to each treated unit for k:1 matching. Should be a single integer value.
verbose	logical; whether information about the matching process should be printed to the console. When TRUE, output from GenMatch() with print.level = 2 will be displayed. Default is FALSE for no printing other than warnings.
...	additional arguments passed to \pkgfunMatchingGenMatch. Potentially useful options include pop.size, max.generations, and fit.func. If pop.size is not specified, a warning from Matching will be thrown reminding you to change it. Note that the ties and CommonSupport arguments are set to FALSE and cannot be changed. If distance.tolerance is not specified, it is set to 0, whereas the default in Matching is 1e-5.

Details

In genetic matching, covariates play three roles: 1) as the variables on which balance is optimized, 2) as the variables in the generalized Mahalanobis distance between units, and 3) in estimating the propensity score. Variables supplied to formula are always used for role (1), as the variables on which balance is optimized. When distance corresponds to a propensity score, the covariates are also used to estimate the propensity score (unless it is supplied). When mahvars is specified, the named variables will form the covariates that go into the distance matrix. Otherwise, the variables in formula along with the propensity score will go into the distance matrix. This leads to three ways to use distance and mahvars to perform the matching:

1. When distance corresponds to a propensity score and mahvars is not specified, the covariates in formula along with the propensity score are used to form the generalized Mahalanobis distance matrix. This is the default and most typical use of method = "genetic" in matchit().

2. When distance corresponds to a propensity score and mahvars is specified, the covariates in mahvars are used to form the generalized Mahalanobis distance matrix. The covariates in formula are used to estimate the propensity score and have their balance optimized by the genetic algorithm. The propensity score is not included in the generalized Mahalanobis distance matrix.

3. When distance is a method of computing a distance matrix (e.g.,"mahalanobis"), no propensity score is estimated, and the covariates in formula are used to form the generalized Mahalanobis distance matrix. Which specific method is supplied has no bearing on how the distance matrix is computed; it simply serves as a signal to omit estimation of a propensity score.

When a caliper is specified, any variables mentioned in caliper, possibly including the propensity score, will be added to the matching variables used to form the generalized Mahalanobis distance matrix. This is because Matching doesn't allow for the separation of caliper variables and matching variables in genetic matching.

Estimand

The estimand argument controls whether control units are selected to be matched with treated units (estimand = "ATT") or treated units are selected to be matched with control units (estimand = "ATC"). The "focal" group (e.g., the treated units for the ATT) is typically made to be the smaller treatment group, and a warning will be thrown if it is not set that way unless replace = TRUE. Setting estimand = "ATC" is equivalent to swapping all treated and control labels for the treatment variable. When estimand = "ATC", the default m.order is "smallest", and the match.matrix component of the output will have the names of the control units as the rownames and be filled with the names of the matched treated units (opposite to when estimand = "ATT"). Note that the argument supplied to estimand doesn't necessarily correspond to the estimand actually targeted; it is merely a switch to trigger which treatment group is considered "focal". Note that while GenMatch() and Match() support the ATE as an estimand, matchit() only supports the ATT and ATC for genetic matching.

Outputs

All outputs described in matchit() are returned with method = "genetic". When replace = TRUE, the subclass component is omitted. When include.obj = TRUE in the call to matchit(), the output of the call to \pkgfunMatchingGenMatch will be included in the output.

References

In a manuscript, be sure to cite the following papers if using matchit() with method = "genetic":

Diamond, A., & Sekhon, J. S. (2013). Genetic matching for estimating causal effects: A general multivariate matching method for achieving balance in observational studies. Review of Economics and Statistics, 95(3), 932–945. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1162/REST_a_00318")}

Sekhon, J. S. (2011). Multivariate and Propensity Score Matching Software with Automated Balance Optimization: The Matching package for R. Journal of Statistical Software, 42(1), 1–52. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v042.i07")}

For example, a sentence might read:

Genetic matching was performed using the MatchIt package (Ho, Imai, King, & Stuart, 2011) in R, which calls functions from the Matching package (Diamond & Sekhon, 2013; Sekhon, 2011).

See Also

matchit() for a detailed explanation of the inputs and outputs of a call to matchit().

\pkgfun

MatchingGenMatch and \pkgfunMatchingMatch, which do the work.

Examples

data("lalonde")

# 1:1 genetic matching with PS as a covariate
m.out1 <- matchit(treat ~ age + educ + race + nodegree +
                    married + re74 + re75, data = lalonde,
                  method = "genetic",
                  pop.size = 10) #use much larger pop.size
m.out1
summary(m.out1)

# 2:1 genetic matching with replacement without PS
m.out2 <- matchit(treat ~ age + educ + race + nodegree +
                    married + re74 + re75, data = lalonde,
                  method = "genetic", replace = TRUE,
                  ratio = 2, distance = "mahalanobis",
                  pop.size = 10) #use much larger pop.size
m.out2
summary(m.out2, un = FALSE)

# 1:1 genetic matching on just age, educ, re74, and re75
# within calipers on PS and educ; other variables are
# used to estimate PS
m.out3 <- matchit(treat ~ age + educ + race + nodegree +
                    married + re74 + re75, data = lalonde,
                  method = "genetic",
                  mahvars = ~ age + educ + re74 + re75,
                  caliper = c(.05, educ = 2),
                  std.caliper = c(TRUE, FALSE),
                  pop.size = 10) #use much larger pop.size
m.out3
summary(m.out3, un = FALSE)

MatchIt documentation built on Oct. 13, 2023, 9:08 a.m.