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Do exact matching variables need to be included when estimating effects after matching with the MatchIt package? Take the following example (adapted from the MatchIt vignette on estimating effects after matching):

library(MatchIt)
library(marginaleffects)

Generate toy dataset


gen_X <- function(n) {
  X <- matrix(rnorm(9 * n), nrow = n, ncol = 9)
  X[,5] <- as.numeric(X[,5] < .5)
  X
}


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)
}


gen_Y_B <- function(A, X) {
  LP_B <- -2 + log(2.4)A + log(2)X[,1] + log(2)X[,2] + log(2)X[,3] + log(1.5)X[,4] + log(2.4)X[,5] + log(1.5)*X[,6]
  P_B <- plogis(LP_B)
  rbinom(length(A), 1, P_B)
}


set.seed(123)


n <- 2000
X <- gen_X(n)
A <- gen_A(X)
Y_B <- gen_Y_B(A, X)
stratum <- sample(rep(1:10, each = n/10))


d <- data.frame(A, X, Y_B, stratum)


rm(list=setdiff(ls(), "d"))


Create matchit object


mF <- matchit(A ~ X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 + X9, 
              data = d,
              method = "quick", 
              distance = "glm", 
              link = "logit",
              exact = ~stratum)


Extract matched data


md <- match.data(mF)

Is the following estimation of the regression model and computation of effects correct? If so, why doesn't the stratum variable need to be included?


#Logistic regression model with covariates
fit <- glm(Y_B ~ A * (X1 + X2 + X3 + X4 + X5 + X6 + X7 + X8 + X9),
           data = md, 
           weights = weights,
           family = quasibinomial())

#Compute effects; RR and confidence interval
avg_comparisons(fit,
                variables = "A",
                vcov = ~subclass,
                newdata = subset(md, A == 1),
                wts = "weights",
                comparison = "lnratioavg",
                transform = "exp")
```
nicholas
  • 103
  • And how do you model the within-matched-sets correlations? Matching is pretty arbitrary, loses a lot of statistical efficiency, and results in an unclear path to statistical inference because of the lack of principled final modeling strategies. – Frank Harrell Oct 24 '23 at 16:10

1 Answers1

4

Including covariates in the outcome model is optional. If you can't afford to include every covariate and its interaction with treatment in the model, you can just include the ones that are most predictive of the outcome (based on theory, not statistical significance or model selection). The fact that you did exact matching on the variable does not affect this. Exact matching on a covariate just affects which subclass each unit is a member of, but otherwise is just a regular constraint on matching to improve balance that doesn't affect how the outcome model is estimated.

To respond to Frank's comment, it is well established that a cluster-robust standard error is sufficient to account for the matching in an outcome model. The form of matching OP is doing (generalized full matching with method = "quickmatch") uses all units, is deterministic, and is not order-dependent, so doesn't share some of the problems with 1:1 matching (discarding too many units and order-dependent). All this form of matching does is down-weight control units in the tails far from the treated units. The benefit of matching over a pure outcome model strategy is that you can assess the degree to which covariate imbalance might bias the resulting effect estimate (whereas with regression, all you can do is trust that the model accounts for all associations between the covariates and treatment).

Noah
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