Matching with Sampling Weights
Noah Greifer
2026-08-21
Source:vignettes/sampling-weights.Rmd
sampling-weights.RmdIntroduction
Sampling weights (also known as survey weights) frequently appear
when using large, representative datasets. They are required to ensure
any estimated quantities generalize to a target population defined by
the weights. Evidence suggests that sampling weights need to be
incorporated into a propensity score matching analysis to obtain valid
and unbiased estimates of the treatment effect in the sampling weighted
population (DuGoff et
al. 2014; Austin et al. 2016; Lenis et al. 2019). In this guide, we
demonstrate how to use sampling weights with MatchIt for
propensity score estimation, matching, balance assessment, and effect
estimation. Fortunately, doing so is not complicated, but some care must
be taken to ensure sampling weights are incorporated correctly. It is
assumed one has read the other vignettes explaining matching
(vignette("matching-methods")), balance assessment
(vignette("assessing-balance")), and effect estimation
(vignette("estimating-effects").
We will use the same simulated toy dataset used in
vignette("estimating-effects") except with the addition of
a sampling weights variable, SW, which is used to
generalize the sample to a specific target population with a
distribution of covariates different from that of the sample. Code to
generate the covariates, treatment, and outcome is at the bottom of
vignette("estimating-effects") and code to generate the
sampling weights is at the end of this document. We will consider the
effect of binary treatment A on continuous outcome
Y_C, adjusting for confounders
X1-X9.
head(d)## A X1 X2 X3 X4 X5 X6 X7 X8 X9 Y_C SW
## 1 0 0.1725 -1.4283 -0.4103 -2.36059 1 -1.1199 0.6398 -0.4840 -0.59385 -3.5907 1.675
## 2 0 -1.0959 0.8463 0.2456 -0.12333 1 -2.2687 -1.4491 -0.5514 -0.31439 -1.5481 1.411
## 3 0 0.1768 0.7905 -0.8436 0.82366 1 -0.2221 0.2971 -0.6966 -0.69516 6.0714 2.332
## 4 0 -0.4595 0.1726 1.9542 -0.62661 1 -0.4019 -0.8294 -0.5384 0.20729 2.4906 1.644
## 5 1 0.3563 -1.8121 0.8135 -0.67189 1 -0.8297 1.7297 -0.6439 -0.02648 -0.6687 2.722
## 6 0 -2.4313 -1.7984 -1.2940 0.04609 1 -1.2419 -1.1252 -1.8659 -0.56513 -9.8504 14.773Matching
Sampling weights can enter the matching specification in two ways: 1) in computing the distance measure (e.g., the propensity score) and 2) in computing matching weights from stratum membership.
When using sampling weights with propensity score matching, one has the option of including the sampling weights in the model used to estimate the propensity scores. Although evidence is mixed on whether this is required (Austin et al. 2016; Lenis et al. 2019), it can be a good idea. The choice should depend on whether including the sampling weights improves the quality of the matches. Specifications including and excluding sampling weights should be tried to determine which is preferred.
For stratification methods, including (coarsened) exact matching, full matching, and propensity score subclassification, sampling weights can also enter the calculation of the matching weights from stratum membership. Without sampling weights, matching weights are computed using the proportion of treated units in each stratum. With sampling weights, matching weights are computed using the weighted proportion of treated units in each stratum, weighted by the sampling weights. This does not affect pair matching methods, which compute matching weights from the match matrix rather than stratum membership.
To supply sampling weights to the propensity score-estimating
function and calculation of the matching weights in
matchit(), the sampling weights variable should be supplied
to the s.weights argument. It can be supplied either as a
numerical vector containing the sampling weights, or a string or
one-sided formula with the name of the sampling weights variable in the
supplied dataset. Below we demonstrate including sampling weights into
propensity scores estimated using logistic regression for generalized
full matching for the average treatment effect in the treated (ATT)
(note that all methods and steps apply the same way to all forms of
matching and all estimands).
mF_s <- matchit(A ~ X1 + X2 + X3 + X4 + X5 + SW +
X6 + X7 + X8 + X9, data = d,
method = "quick", distance = "glm",
estimand = "ATT", s.weights = ~SW)
mF_sNotice that the description of the matching specification when the
matchit object is printed includes lines indicating that
the sampling weights were included in the estimation of the propensity
score and that they are present in the matchit object. It
is stored in the s.weights component of the
matchit object. The matching weights (stored in the
weights component of the matchit object) were
computed incorporating the sampling weights with stratum membership, but
the matching weights alone are not ready for use in estimating the
treatment effect.
We’ll also perform full matching on a propensity score that does not
include the sampling weights in its estimation. Here we use the same
specification as was used in
vignette("estimating-effects").
mF <- matchit(A ~ X1 + X2 + X3 + X4 + X5 + SW +
X6 + X7 + X8 + X9, data = d,
method = "quick", distance = "glm",
estimand = "ATT")
mFNotice that there is no mention of sampling weights in the
description of the matching specification. However, to properly
incorporate sampling weights into the calculation of the matching
weights and to assess balance and estimate effects, we need the sampling
weights to be included in the matchit object, even if they
were not used at all in the matching. To do so, we use the function
add_s.weights(), which adds sampling weights to the
supplied matchit objects and recomputes the matching
weights.
mF <- add_s.weights(mF, ~SW)
mFNow when we print the matchit object, we can see lines
have been added identifying that sampling weights are present but they
were not used in the estimation of the propensity score used in the
matching.
Note that not all methods can involve sampling weights in the
estimation. Some propensity score estimation methods, like
randomForest and bart (as presently
implemented), cannot incorporate sampling weights; one alternative is to
include the sampling weights as a predictor in the propensity score
model. Sampling weights should still be supplied to
matchit() even when using these methods to avoid having to
use add_s.weights().
Assessing Balance
Now we need to decide which matching specification is the best to use
for effect estimation. We do this by selecting the one that yields the
best balance without sacrificing remaining effective sample size.
Because the sampling weights are incorporated into the
matchit object, the balance assessment tools in
plot.matchit() and summary.matchit()
incorporate them into their output.
We’ll use summary() to examine balance on the two
matching specifications. With sampling weights included, the balance
statistics for the unmatched data are weighted by the sampling weights.
The balance statistics for the matched data are weighted by the product
of the sampling weights and the matching weights. It is the product of
these weights that will be used in estimating the treatment effect.
Below we use summary() to display balance for the two
matching specifications. No additional arguments to
summary() are required for it to use the sampling weights;
as long as they are in the matchit object (either due to
being supplied with the s.weights argument in the call to
matchit() or to being added afterward by
add_s.weights()), they will be correctly incorporated into
the balance statistics.
#Balance before matching and for the SW propensity score full matching
summary(mF_s)
#Balance for the non-SW propensity score full matching
summary(mF, un = FALSE)The results of the two matching specifications are similar. Balance
appears to be slightly better when using the sampling weight-estimated
propensity scores than when using the unweighted propensity scores.
However, the effective sample size for the control group is larger when
using the unweighted propensity scores. Neither propensity score
specification achieves excellent balance, and more fiddling with the
matching specification (e.g., by changing the method of estimating
propensity scores, the type of matching, or the options used with the
matching) might yield a better matched set. For the purposes of this
analysis, we will move forward with the matching that used the sampling
weight-estimated propensity scores (mF_s) because of its
superior balance. Some of the remaining imbalance may be eliminated by
adjusting for the covariates in the outcome model.
Note that had we not added sampling weights to mF (the
matching specification that did not include the sampling weights), our
balance assessment would be inaccurate because the balance statistics
would not include the sampling weights. In this case, in fact, assessing
balance on mF without incorporating the sampling weights
would have yielded radically different results and a different
conclusion. It is critical to incorporate sampling weights into the
matchit object using add_s.weights() even if
they are not included in the propensity score estimation.
Estimating the Effect
Estimating the treatment effect after matching is straightforward
when using sampling weights. Effects are estimated in the same way as
when sampling weights are excluded, except that the matching weights
must be multiplied by the sampling weights for use in the outcome model
to yield accurate, generalizable estimates. match_data()
and get_matches() do this automatically, so the weights
produced by these functions already are a product of the matching
weights and the sampling weights. Note this will only be true if
sampling weights are incorporated into the matchit object.
With avg_comparisons(), only the sampling weights should be
included when estimating the treatment effect.
Below we estimate the effect of A on Y_C in
the matched and sampling weighted sample, adjusting for the covariates
to improve precision and decrease bias.
md_F_s <- match_data(mF_s)
fit <- lm(Y_C ~ A * (X1 + X2 + X3 + X4 + X5 +
X6 + X7 + X8 + X9),
data = md_F_s, weights = weights)
library("marginaleffects")
avg_comparisons(fit,
variables = "A",
vcov = ~subclass,
newdata = subset(A == 1),
wts = "SW")Note that match_data() and get_weights()
have the option include.s.weights, which, when set to
FALSE, makes it so the returned weights do not incorporate
the sampling weights and are simply the matching weights. Because one
might to forget to multiply the two sets of weights together, it is
easier to just use the default of include.s.weights = TRUE
and ignore the sampling weights in the outcome model (because they are
already included in the returned weights).
Code to Generate Data used in Examples
#Generatng data similar to Austin (2009) for demonstrating
#treatment effect estimation with sampling weights
gen_X <- function(n) {
X <- matrix(rnorm(9 * n), nrow = n, ncol = 9)
X[,5] <- as.numeric(X[,5] < .5)
X
}
#~20% treated
gen_A <- function(X) {
LP_A <- - 1.2 + log(2)*X[,1] - log(1.5)*X[,2] + log(2)*X[,4] - log(2.4)*X[,5] +
log(2)*X[,7] - log(1.5)*X[,8]
P_A <- plogis(LP_A)
rbinom(nrow(X), 1, P_A)
}
# Continuous outcome
gen_Y_C <- function(A, X) {
2*A + 2*X[,1] + 2*X[,2] + 2*X[,3] + 1*X[,4] + 2*X[,5] + 1*X[,6] + rnorm(length(A), 0, 5)
}
#Conditional:
# MD: 2
#Marginal:
# MD: 2
gen_SW <- function(X) {
e <- rbinom(nrow(X), 1, .3)
1/plogis(log(1.4)*X[,2] + log(.7)*X[,4] + log(.9)*X[,6] + log(1.5)*X[,8] + log(.9)*e +
-log(.5)*e*X[,2] + log(.6)*e*X[,4])
}
set.seed(19599)
n <- 2000
X <- gen_X(n)
A <- gen_A(X)
SW <- gen_SW(X)
Y_C <- gen_Y_C(A, X)
d <- data.frame(A, X, Y_C, SW)