29.7 Genetic Matching

• GM uses iterative checking process of propensity scores, which combines propensity scores and Mahalanobis distance.

• GM is arguably “superior” method than nearest neighbor or full matching in imbalanced data

• Use a genetic search algorithm to find weights for each covariate such that we have optimal balance.

• Implementation

  • could use with replacement

  • balance can be based on

    • paired \(t\)-tests (dichotomous variables)

    • Kolmogorov-Smirnov (multinomial and continuous)

Packages

Matching

library(Matching)
data(lalonde)
attach(lalonde)

#The covariates we want to match on
X = cbind(age, educ, black, hisp, married, nodegr, u74, u75, re75, re74)

#The covariates we want to obtain balance on
BalanceMat <-
    cbind(age,
          educ,
          black,
          hisp,
          married,
          nodegr,
          u74,
          u75,
          re75,
          re74,
          I(re74 * re75))

#
#Let's call GenMatch() to find the optimal weight to give each
#covariate in 'X' so as we have achieved balance on the covariates in
#'BalanceMat'. This is only an example so we want GenMatch to be quick
#so the population size has been set to be only 16 via the 'pop.size'
#option. This is *WAY* too small for actual problems.
#For details see http://sekhon.berkeley.edu/papers/MatchingJSS.pdf.
#
genout <-
    GenMatch(
        Tr = treat,
        X = X,
        BalanceMatrix = BalanceMat,
        estimand = "ATE",
        M = 1,
        pop.size = 16,
        max.generations = 10,
        wait.generations = 1
    )

#The outcome variable
Y=re78/1000

#
# Now that GenMatch() has found the optimal weights, let's estimate
# our causal effect of interest using those weights
#
mout <-
    Match(
        Y = Y,
        Tr = treat,
        X = X,
        estimand = "ATE",
        Weight.matrix = genout
    )
summary(mout)

#                        
#Let's determine if balance has actually been obtained on the variables of interest
#                        
mb <-
    MatchBalance(
        treat ~ age + educ + black + hisp + married + nodegr 
        + u74 + u75 + re75 + re74 + I(re74 * re75),
        match.out = mout,
        nboots = 500
    )