29.1 MatchIt

Procedure typically involves (proposed by Noah Freifer using MatchIt)

  1. planning
  2. matching
  3. checking (balance)
  4. estimating the treatment effect
library(MatchIt)
data("lalonde")

examine treat on re78

  1. Planning

  • select type of effect to be estimated (e.g., mediation effect, conditional effect, marginal effect)

  • select the target population

  • select variables to match/balance (Austin 2011) (T. J. VanderWeele 2019)

  1. Check Initial Imbalance
# No matching; constructing a pre-match matchit object
m.out0 <- matchit(
    formula(treat ~ age + educ + race 
            + married + nodegree + re74 + re75, env = lalonde),
    data = data.frame(lalonde),
    method = NULL,
    # assess balance before matching
    distance = "glm" # logistic regression
)

# Checking balance prior to matching
summary(m.out0)
  1. Matching
# 1:1 NN PS matching w/o replacement
m.out1 <- matchit(treat ~ age + educ,
                  data = lalonde,
                  method = "nearest",
                  distance = "glm")
m.out1
#> A matchit object
#>  - method: 1:1 nearest neighbor matching without replacement
#>  - distance: Propensity score
#>              - estimated with logistic regression
#>  - number of obs.: 614 (original), 370 (matched)
#>  - target estimand: ATT
#>  - covariates: age, educ
  1. Check balance

Sometimes you have to make trade-off between balance and sample size.

# Checking balance after NN matching
summary(m.out1, un = FALSE)
#> 
#> Call:
#> matchit(formula = treat ~ age + educ, data = lalonde, method = "nearest", 
#>     distance = "glm")
#> 
#> Summary of Balance for Matched Data:
#>          Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
#> distance        0.3080        0.3077          0.0094     0.9963    0.0033
#> age            25.8162       25.8649         -0.0068     1.0300    0.0050
#> educ           10.3459       10.2865          0.0296     0.5886    0.0253
#>          eCDF Max Std. Pair Dist.
#> distance   0.0432          0.0146
#> age        0.0162          0.0597
#> educ       0.1189          0.8146
#> 
#> Sample Sizes:
#>           Control Treated
#> All           429     185
#> Matched       185     185
#> Unmatched     244       0
#> Discarded       0       0

# examine visually
plot(m.out1, type = "jitter", interactive = FALSE)


plot(
    m.out1,
    type = "qq",
    interactive = FALSE,
    which.xs = c("age")
)

Try Full Match (i.e., every treated matches with one control, and every control with one treated).

# Full matching on a probit PS
m.out2 <- matchit(treat ~ age + educ, 
                  data = lalonde,
                  method = "full", 
                  distance = "glm", 
                  link = "probit")
m.out2
#> A matchit object
#>  - method: Optimal full matching
#>  - distance: Propensity score
#>              - estimated with probit regression
#>  - number of obs.: 614 (original), 614 (matched)
#>  - target estimand: ATT
#>  - covariates: age, educ

Checking balance again

# Checking balance after full matching
summary(m.out2, un = FALSE)
#> 
#> Call:
#> matchit(formula = treat ~ age + educ, data = lalonde, method = "full", 
#>     distance = "glm", link = "probit")
#> 
#> Summary of Balance for Matched Data:
#>          Means Treated Means Control Std. Mean Diff. Var. Ratio eCDF Mean
#> distance        0.3082        0.3081          0.0023     0.9815    0.0028
#> age            25.8162       25.8035          0.0018     0.9825    0.0062
#> educ           10.3459       10.2315          0.0569     0.4390    0.0481
#>          eCDF Max Std. Pair Dist.
#> distance   0.0270          0.0382
#> age        0.0249          0.1110
#> educ       0.1300          0.9805
#> 
#> Sample Sizes:
#>               Control Treated
#> All            429.       185
#> Matched (ESS)  145.23     185
#> Matched        429.       185
#> Unmatched        0.         0
#> Discarded        0.         0

plot(summary(m.out2))

Exact Matching

# Full matching on a probit PS
m.out3 <-
    matchit(
        treat ~ age + educ,
        data = lalonde,
        method = "exact"
    )
m.out3
#> A matchit object
#>  - method: Exact matching
#>  - number of obs.: 614 (original), 332 (matched)
#>  - target estimand: ATT
#>  - covariates: age, educ

Subclassfication

m.out4 <- matchit(
    treat ~ age + educ, 
    data = lalonde,
    method = "subclass"
)
m.out4
#> A matchit object
#>  - method: Subclassification (6 subclasses)
#>  - distance: Propensity score
#>              - estimated with logistic regression
#>  - number of obs.: 614 (original), 614 (matched)
#>  - target estimand: ATT
#>  - covariates: age, educ

# Or you can use in conjunction with "nearest"
m.out4 <- matchit(
    treat ~ age + educ,
    data = lalonde,
    method = "nearest",
    option = "subclass"
)
m.out4
#> A matchit object
#>  - method: 1:1 nearest neighbor matching without replacement
#>  - distance: Propensity score
#>              - estimated with logistic regression
#>  - number of obs.: 614 (original), 370 (matched)
#>  - target estimand: ATT
#>  - covariates: age, educ

Optimal Matching

m.out5 <- matchit(
    treat ~ age + educ, 
    data = lalonde,
    method = "optimal",
    ratio = 2
)
m.out5
#> A matchit object
#>  - method: 2:1 optimal pair matching
#>  - distance: Propensity score
#>              - estimated with logistic regression
#>  - number of obs.: 614 (original), 555 (matched)
#>  - target estimand: ATT
#>  - covariates: age, educ

Genetic Matching

m.out6 <- matchit(
    treat ~ age + educ, 
    data = lalonde,
    method = "genetic"
)
m.out6
#> A matchit object
#>  - method: 1:1 genetic matching without replacement
#>  - distance: Propensity score
#>              - estimated with logistic regression
#>  - number of obs.: 614 (original), 370 (matched)
#>  - target estimand: ATT
#>  - covariates: age, educ
  1. Estimating the Treatment Effect
# get matched data
m.data1 <- match.data(m.out1)

head(m.data1)
#>      treat age educ   race married nodegree re74 re75       re78  distance
#> NSW1     1  37   11  black       1        1    0    0  9930.0460 0.2536942
#> NSW2     1  22    9 hispan       0        1    0    0  3595.8940 0.3245468
#> NSW3     1  30   12  black       0        0    0    0 24909.4500 0.2881139
#> NSW4     1  27   11  black       0        1    0    0  7506.1460 0.3016672
#> NSW5     1  33    8  black       0        1    0    0   289.7899 0.2683025
#> NSW6     1  22    9  black       0        1    0    0  4056.4940 0.3245468
#>      weights subclass
#> NSW1       1        1
#> NSW2       1       98
#> NSW3       1      109
#> NSW4       1      120
#> NSW5       1      131
#> NSW6       1      142
library("lmtest") #coeftest
library("sandwich") #vcovCL

# imbalance matched dataset
fit1 <- lm(re78 ~ treat + age + educ ,
           data = m.data1, 
           weights = weights)

coeftest(fit1, vcov. = vcovCL, cluster = ~subclass)
#> 
#> t test of coefficients:
#> 
#>              Estimate Std. Error t value Pr(>|t|)   
#> (Intercept)  -174.902   2445.013 -0.0715 0.943012   
#> treat       -1139.085    780.399 -1.4596 0.145253   
#> age           153.133     55.317  2.7683 0.005922 **
#> educ          358.577    163.860  2.1883 0.029278 * 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

treat coefficient = estimated ATT

# balance matched dataset 
m.data2 <- match.data(m.out2)

fit2 <- lm(re78 ~ treat + age + educ , 
           data = m.data2, weights = weights)

coeftest(fit2, vcov. = vcovCL, cluster = ~subclass)
#> 
#> t test of coefficients:
#> 
#>             Estimate Std. Error t value Pr(>|t|)  
#> (Intercept) 2151.952   3141.152  0.6851  0.49355  
#> treat       -725.184    703.297 -1.0311  0.30289  
#> age          120.260     53.933  2.2298  0.02612 *
#> educ         175.693    241.694  0.7269  0.46755  
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

When reporting, remember to mention

  1. the matching specification (method, and additional options)
  2. the distance measure (e.g., propensity score)
  3. other methods, and rationale for the final chosen method.
  4. balance statistics of the matched dataset.
  5. number of matched, unmatched, discarded
  6. estimation method for treatment effect.

References

Austin, Peter C. 2011. “Optimal Caliper Widths for Propensity-Score Matching When Estimating Differences in Means and Differences in Proportions in Observational Studies.” Pharmaceutical Statistics 10 (2): 150–61.
VanderWeele, Tyler J. 2019. “Principles of Confounder Selection.” European Journal of Epidemiology 34: 211–19.