Matching

author: “Vincent Arel-Bundock”

This chapter introduces how to use marginaleffects to estimate treatment effects after pre-processing a dataset to achieve better covariate balance. The presentation is very short. Readers who seek a more comprehensive understanding and application of these methods should refer to Noah Greifer’s excellent and detailed work on the topic and to the MatchIt package vignettes and website

The procedure we highlight can be broken down into three steps:

  1. Use MatchIt to pre-process the data and achieve better covariate balance
  2. Fit a regression model to the outcome of interest
  3. Use marginaleffects and G-Computation to estimate a quantity of interest, such as the Average treatment effect on the treated (ATT)

To begin, we load libraries and the data from the classic Lalonde experiment:

library("MatchIt")
library("marginaleffects")
data("lalonde", package = "MatchIt")

head(lalonde)
     treat age educ   race married nodegree re74 re75       re78
NSW1     1  37   11  black       1        1    0    0  9930.0460
NSW2     1  22    9 hispan       0        1    0    0  3595.8940
NSW3     1  30   12  black       0        0    0    0 24909.4500
NSW4     1  27   11  black       0        1    0    0  7506.1460
NSW5     1  33    8  black       0        1    0    0   289.7899
NSW6     1  22    9  black       0        1    0    0  4056.4940

We are interested in the treatment effect of the treat variable on the re78 outcome. The treat variable is a binary variable indicating whether the individual received job training. The re78 variable is the individual’s earnings in 1978.

Matching

The first step is to pre-process the dataset to achieve better covariate balance. To do this, we use the MatchIt::matchit() function and a 1-to-1 nearest neighbor matching with replacement on the Mahaloanobis distance. This function supports many other matching methods, see ?matchit.

dat <- matchit(
    treat ~ age + educ + race + married + nodegree + re74 + re75, 
    data = lalonde, distance = "mahalanobis",
    replace = FALSE)
dat <- match.data(dat)

Fitting

Now, we estimate a linear regression model with interactions between the treatment and covariates. Note that we use the weights argument to use the weights supplied by our matching method:

fit <- lm(
    re78 ~ treat * (age + educ + race + married + nodegree),
    data = dat,
    weights = weights)

Quantity of interest

Finally, we use the avg_comparisons() function of the marginaleffects package to estimate the ATT and its standard error. In effect, this function applies G-Computation to estimate the quantity of interest. We use the following arguments:

  • variables="treat" indicates that we are interested in the effect of the treat variable.
  • newdata=subset(dat, treat == 1) indicates that we want to estimate the effect for the treated individuals only (i.e., the ATT).
  • wts="weights" indicates that we want to use the weights supplied by the matching method.
avg_comparisons(
    fit,
    variables = "treat",
    newdata = subset(dat, treat == 1),
    vcov = ~subclass,
    wts = "weights")

  Term Contrast Estimate Std. Error    z Pr(>|z|)   S 2.5 % 97.5 %
 treat    1 - 0     1228        851 1.44    0.149 2.7  -439   2895

Columns: term, contrast, estimate, std.error, statistic, p.value, s.value, conf.low, conf.high 
Type:  response 

Learn more

The MatchIt vignette titled “Estimating Effects After Matching” describes many more options, including different measures of uncertainty (bootstrap, clustering, etc.), different estimands (ATE, etc.), and different strategies for adjustment.