Matching for Causal Inference
matchit is the main function of MatchIt and performs pairing, subset selection, and subclassification with the aim of creating treatment and control groups balanced on included covariates. MatchIt implements the suggestions of Ho, Imai, King, and Stuart (2007) for improving parametric statistical models by preprocessing data with nonparametric matching methods. MatchIt implements a wide range of sophisticated matching methods, making it possible to greatly reduce the dependence of causal inferences on hard-to-justify, but commonly made, statistical modeling assumptions. The software also easily fits into existing research practices since, after preprocessing with MatchIt, researchers can use whatever parametric model they would have used without MatchIt, but produce inferences with substantially more robustness and less sensitivity to modeling assumptions.
This page documents the overall use of matchit, but for specifics of how matchit works with individual matching methods, see the individual pages linked in the Details section below.
matchit(formula, data = NULL, method = "nearest",
distance = "glm", link = "logit",
distance.options = list(), estimand = "ATT",
exact = NULL, mahvars = NULL, discard = "none",
reestimate = FALSE, s.weights = NULL,
replace = FALSE, m.order = NULL,
caliper = NULL, std.caliper = TRUE, ratio = 1,
verbose = FALSE, ...)
## S3 method for class 'matchit'
print(x, ...)formula |
a two-sided |
data |
a data frame containing the variables named in |
method |
the matching method to be used. The allowed methods are |
distance |
the distance measure to be used. Can be either a string containing the name of a distance measure or a vector of already-computed distance measures. The distance measures should be values whose pairwise difference is the distance between two units, e.g., propensity scores for propensity score matching. See |
link |
when |
distance.options |
a named list containing additional arguments supplied to the function that estimates the distance measure as determined by the argument to |
estimand |
a string containing the name of the target estimand desired. Can be one of |
exact |
for methods that allow it, for which variables exact matching should take place. Can be specified as a string containing the names of variables in |
mahvars |
for methods that allow it, on which variables Mahalanobis distance matching should take place when a distance measure other than |
discard |
a string containing a method for discarding units outside a region of common support. When a propensity score is estimated or supplied to |
reestimate |
if |
s.weights |
an optional numeric vector of sampling weights to be incorporated into propensity score models and balance statistics. Can also be specified as a string containing the name of variable in |
replace |
for methods that allow it, whether matching should be done with replacement ( |
m.order |
for methods that allow it, the order that the matching takes place. Allowable options depend on the matching method but include |
caliper |
for methods that allow it, the width(s) of the caliper(s) to use in matching. Should be a numeric vector with each value named according to the variable to which the caliper applies. To apply to the distance measure, the value should be unnamed. See the individual methods pages for information on whether and how this argument is used. The default is |
std.caliper |
|
ratio |
for methods that allow it, how many control units should be matched to each treated unit in k:1 matching. Should be a single integer value. See the individual methods pages for information on whether and how this argument is used. The default is 1 for 1:1 matching. |
verbose |
|
... |
additional arguments passed to the functions used in the matching process. See the individual methods pages for information on what additional arguments are allowed for each method. Ignored for |
x |
a |
Details for the various matching methods can be found at the following help pages:
method_nearest for nearest neighbor matching
method_optimal for optimal pair matching
method_full for optimal full matching
method_genetic for genetic matching
method_cem for coarsened exact matching
method_exact for exact matching
method_subclass for subclassification
The pages contain information on what the method does, which of the arguments above are allowed with them and how they are interpreted, and what additional arguments can be supplied to further tune the method. Note that the default method with no arguments supplied other than formula and data is 1:1 nearest neighbor matching without replacement on a propensity score estimated using a logistic regression of the treatment on the covariates. This is not the same default offered by other matching programs, such as those in Matching, teffects in Stata, or PROC PSMATCH in SAS, so care should be taken if trying to replicate the results of those programs.
When method = NULL, no matching will occur, but any propensity score estimation and common support restriction will. This can be a simple way to estimate the propensity score for use in future matching specifications without having to reestimate it each time. The matchit output with no matching can be supplied to summary to examine balance prior to matching on any of the included covariates and on the propensity score if specified. All arguments other than distance, discard, and reestimate will be ignored.
See the distance argument for details on the several ways to specify the distance and link arguments to estimate propensity scores and create distance measures.
When the treatment variable is not a 0/1 variable, it will be coerced to one and returned as such in the matchit output (see section Value, below). The following rules are used: 1) if 0 is one of the values, it will be considered the control and the other value the treated; otherwise, 2) if the variable is a factor, levels(treat)[1] will be considered control and the other variable the treated; otherwise, 3) sort(unique(treat))[1] will be considered control and the other value the treated. It is safest to ensure the treatment variable is a 0/1 variable.
The discard option implements a common support restriction. It can only be used when a distance measure is estimated or supplied, i.e., when distance is specified as something other than "mahalanobis", and is ignored for some matching methods. When specified as "treated", treated units whose distance measure is outside the range of distance measures of the control units will be discarded. When specified as "control", control units whose distance measure is outside the range of distance measures of the treated units will be discarded. When specified as "both", treated and controls units whose distance measure is outside the intersection of the range of distance measures of the treated units and the range of distance measures of the control units will be discarded. When reestimate = TRUE and distance corresponds to a propensity score-estimating function, the propensity scores are re-estimated in the remaining units prior to being used for matching or calipers.
Caution should be used when interpreting effects estimated with various values of estimand. Setting estimand = "ATT" doesn't necessarily mean the average treatment effect in the treated is being estimated; it just means that for matching methods, treated units will be untouched and given weights of 1 and control units will be matched to them (and the opposite for estimand = "ATC"). If a caliper is supplied or treated units are removed for common support or some other reason (e.g., lacking matches when using exact matching), the actual estimand targeted is not the ATT but the treatment effect in the matched sample. The argument to estimand simply triggers which units are matched to which, and for stratification-based methods (exact matching, CEM, full matching, and subclassification), determines the formula used to compute the stratification weights.
Matching weights are computed in one of two ways depending on whether matching was done with replacement or not.
For matching without replacement, each unit is assigned to a subclass, which represents the pair they are a part of (in the case of k:1 matching) or the stratum they belong to (in the case of exact matching, coarsened exact matching, full matching, or subclassification). The formula for computing the weights depends on the argument supplied to estimand. A new stratum "propensity score" (p) is computed as the proportion of units in each stratum that are in the treated group, and all units in that stratum are assigned that propensity score. Weights are then computed using the standard formulas for inverse probability weights: for the ATT, weights are 1 for the treated units and p/(1-p) for the control units; for the ATC, weights are (1-p)/p for the treated units and 1 for the control units; for the ATE, weights are 1/p for the treated units and 1/(1-p) for the control units.
For matching with replacement, units are not assigned to unique strata. For the ATT, each treated unit gets a weight of 1. Each control unit is weighted as the sum of the inverse of the number of control units matched to the same treated unit across its matches. For example, if a control unit was matched to a treated unit that had two other control units matched to it, and that same control was matched to a treated unit that had one other control unit matched to it, the control unit in question would get a weight of 1/3 + 1/2 = 5/6. For the ATC, the same is true with the treated and control labels switched. The weights are computed using the match.matrix component of the matchit output object.
In each treatment group, weights are divided by the mean of the nonzero weights in that treatment group to make the weights sum to the number of units in that treatment group. If sampling weights are included through the s.weights argument, they will be included in the matchit output object but not incorporated into the matching weights. match.data, which extracts the matched set from a matchit object, combines the matching weights and sampling weights.
When method is something other than "subclass", a matchit object with the following components:
match.matrix |
a matrix containing the matches. The rownames correspond to the treated units and the values in each row are the names (or indices) of the control units matched to each treated unit. When treated units are matched to different numbers of control units (e.g., with exact matching or matching with a caliper), empty spaces will be filled with |
subclass |
a factor containing matching pair/stratum membership for each unit. Unmatched units will have a value of |
weights |
a numeric vector of estimated matching weights. Unmatched and discarded units will have a weight of zero. |
model |
the fit object of the model used to estimate propensity scores when |
X |
a data frame of covariates mentioned in |
call |
the |
info |
information on the matching method and distance measures used. |
estimand |
the argument supplied to |
formula |
the |
treat |
a vector of treatment status converted to zeros (0) and ones (1) if not already in that format. |
distance |
a vector of distance values (i.e., propensity scores) when |
discarded |
a logical vector denoting whether each observation was discarded ( |
s.weights |
the vector of sampling weights supplied to the |
exact |
a one-sided formula containing the variables, if any, supplied to |
mahvars |
a one-sided formula containing the variables, if any, supplied to |
nn |
a matrix of the sample sizes of the treated and control groups before and after matching. See |
When method = "subclass", a matchit.subclass object with the same components as above except that match.matrix is excluded and two additional components, q.cut and qn, are included, containing a vector of the distance measure cutpoints used to define the subclasses and a matrix of the subclass sample sizes, respectively. See method_subclass for details.
Daniel Ho dho@law.stanford.edu; Kosuke Imai imai@harvard.edu; Gary King king@harvard.edu; Elizabeth Stuart estuart@jhsph.edu
Version 4.0.0 update by Noah Greifer noah.greifer@gmail.com
Ho, D. E., Imai, K., King, G., & Stuart, E. A. (2007). Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal Inference. Political Analysis, 15(3), 199–236. doi: 10.1093/pan/mpl013
Ho, D. E., Imai, K., King, G., & Stuart, E. A. (2011). MatchIt: Nonparametric Preprocessing for Parametric Causal Inference. Journal of Statistical Software, 42(8). doi: 10.18637/jss.v042.i08
summary.matchit for balance assessment after matching. plot.matchit for plots of covariate balance and propensity score overlap after matching.
vignette("MatchIt") for an introduction to matching with MatchIt; vignette("matching-methods") for descriptions of the variety of matching methods and options available; vignette("assessing-balance") for information on assessing the quality of a matching specification; vignette("estimating-effects") for instructions on how to estimate treatment effects after matching; and vignette("sampling-weights") for a guide to using MatchIt with sampling weights.
data("lalonde")
# Default: 1:1 NN PS matching w/o replacement
m.out1 <- matchit(treat ~ age + educ + race + nodegree +
married + re74 + re75, data = lalonde)
m.out1
summary(m.out1)
# 1:1 NN Mahalanobis distance matching w/ replacement and
# exact matching on married and race
m.out2 <- matchit(treat ~ age + educ + race + nodegree +
married + re74 + re75, data = lalonde,
distance = "mahalanobis", replace = TRUE,
exact = ~ married + race)
m.out2
summary(m.out2)
# 2:1 NN Mahalanobis distance matching within caliper defined
# by a probit pregression PS
m.out3 <- matchit(treat ~ age + educ + race + nodegree +
married + re74 + re75, data = lalonde,
distance = "glm", link = "probit",
mahvars = ~ age + educ + re74 + re75,
caliper = .1, ratio = 2)
m.out3
summary(m.out3)
# Optimal full PS matching for the ATE within calipers on
# PS, age, and educ
m.out4 <- matchit(treat ~ age + educ + race + nodegree +
married + re74 + re75, data = lalonde,
method = "full", estimand = "ATE",
caliper = c(.1, age = 2, educ = 1),
std.caliper = c(TRUE, FALSE, FALSE))
m.out4
summary(m.out4)
# Subclassification on a logistic PS with 10 subclasses after
# discarding controls outside common support of PS
s.out1 <- matchit(treat ~ age + educ + race + nodegree +
married + re74 + re75, data = lalonde,
method = "subclass", distance = "glm",
discard = "control", subclass = 10)
s.out1
summary(s.out1)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.