MatchIt (version 4.1.0)

distance: Propensity scores and other distance measures

Description

Several matching methods require or can involve the distance between treated and control units. Options include the Mahalanobis distance, propensity score distance, or distance between user-supplied values. Propensity scores are also used for common support via the discard options and for defined calipers. This page documents the options that can be supplied to the distance argument to matchit.

There are two ways to specify the distance argument: 1) as the string "mahalanobis", 2) as a string containing the name of a method for estimating propensity scores, or 3) as a vector of values whose pairwise differences define the distance between units.

When distance is specified as one of the allowed strings (described below) other than "mahalanobis", a propensity score is estimated using the variables in formula and the method corresponding to the given argument. This propensity score can be used to compute the distance between units as the absolute difference between the propensity scores of pairs of units. In this respect, the propensity score is more like a "position" measure than a distance measure, since it is the pairwise difference that form the distance rather than the propensity scores themselves. Still, this naming convention is used to reflect their primary purpose without committing to the status of the estimated values as propensity scores, since transformations of the scores are allowed and user-supplied values that are not propensity scores can also be supplied (detailed below). Propensity scores can also be used to create calipers and common support restrictions, whether or not they are used in the actual distance measure used in the matching, if any.

In addition to the distance argument, two other arguments can be specified that relate to the estimation and manipulation of the propensity scores. The link argument allows for different links to be used in models that require them such as generalized linear models, for which the logit and probit links are allowed, among others. In addition to specifying the link, the link argument can be used to specify whether the propensity score or the linearized version of the propensity score should be used; by specifying link = "linear.{link}", the linearized version will be used.

The distance.options argument can also be specified, which should be a list of values passed to the propensity score-estimating function, for example, to choose specific options or tuning parameters for the estimation method. If formula, data, or verbose are not supplied to distance.options, the corresponding arguments from matchit will be automatically supplied. See the Examples for demonstrations of the uses of link and distance.options. When s.weights is supplied in the call to matchit, it will automatically be passed to the propensity score-estimating function as the weights argument unless otherwise described below.

Allowable options

Below are the allowed options for distance:

"glm"

The propensity scores are estimated using a generalized linear model (e.g., logistic regression). The formula supplied to matchit is passed directly to glm, and predict.glm is used to compute the propensity scores. The link argument can be specified as a link function supplied to binomial, e.g., "logit", which is the default. When link is prepended by "linear.", the linear predictor is used instead of the predicted probabilities. distance = "glm" with link = "logit" (logistic regression) is the default in matchit.

"gam"

The propensity scores are estimated using a generalized additive model. The formula supplied to matchit is passed directly to mgcv::gam, and mgcv::predict.gam is used to compute the propensity scores. The link argument can be specified as a link function supplied to binomial, e.g., "logit", which is the default. When link is prepended by "linear.", the linear predictor is used instead of the predicted probabilities. Note that unless the smoothing functions s, te, ti, or t2 are used in formula, a generalized additive model is identical to a generalized linear model and will estimate the same propensity scores as glm. See the documentation for mgcv::gam, mgcv::formula.gam, and mgcv::gam.models for more information on how to specify these models. Also note that the formula returned in the matchit output object will be a simplified version of the supplied formula with smoothing terms removed (but all named variables present).

"rpart"

The propensity scores are estimated using a classification tree. The formula supplied to matchit is passed directly to rpart::rpart, and rpart::predict.rpart is used to compute the propensity scores. The link argument is ignored, and predicted probabilities are always returned as the distance measure.

"randomforest"

The propensity scores are estimated using a random forest. The formula supplied to matchit is passed directly to randomForest::randomForest, and randomForest::predict.randomForest is used to compute the propensity scores. The link argument is ignored, and predicted probabilities are always returned as the distance measure. When s.weights is supplied to matchit, it will not be passed to randomForest because randomForest does not accept weights.

"nnet"

The propensity scores are estimated using a single-hidden-layer neural network. The formula supplied to matchit is passed directly to nnet::nnet, and fitted is used to compute the propensity scores. The link argument is ignored, and predicted probabilities are always returned as the distance measure. An argument to size must be supplied to distance.options when using method = "nnet".

"cbps"

The propensity scores are estimated using the covariate balancing propensity score (CBPS) algorithm, which is a form of logistic regression where balance constraints are incorporated to a generalized method of moments estimation of of the model coefficients. The formula supplied to matchit is passed directly to CBPS::CBPS, and fitted is used to compute the propensity scores. The link argument can be specified as "linear" to use the linear predictor instead of the predicted probabilities. No other links are allowed. The estimand argument supplied to matchit will be used to select the appropriate estimand for use in defining the balance constraints, so no argument needs to be supplied to ATT in CBPS.

"bart"

The propensity scores are estimated using Bayesian additive regression trees (BART). The formula supplied to matchit is passed directly to dbarts::bart2, and dbarts::fitted is used to compute the propensity scores. The link argument can be specified as "linear" to use the linear predictor instead of the predicted probabilities. When s.weights is supplied to matchit, it will not be passed to bart2 because the weights argument in bart2 does not correspond to sampling weights.

"mahalanobis"

No propensity scores are estimated. Rather than using the propensity score difference as the distance between units, the Mahalanobis distance is used instead. See mahalanobis for details on how it is computed. The Mahalanobis distance is always computed using all the variables in formula. With this specification, calipers and common support restrictions cannot be used and the distance component of the output object will be empty because no propensity scores are estimated. The link and distance.options arguments are ignored. See individual methods pages for whether the Mahalanobis distance is allowed and how it is used. Sometimes this setting is just a placeholder to indicate that no propensity score is to be estimated (e.g., with method = "genetic"). To perform Mahalanobis distance matching and estimate propensity scores to be used for a purpose other than matching, the mahvars argument should be used along with a different specification to distance. See the individual matching method pages for details on how to use mahvars.

distance can also be supplied as a numeric vector whose values will be taken to function like propensity scores; their pairwise difference will define the distance between units. This might be beneficial to supply propensity scores computed outside matchit or to resupply matchit with propensity scores estimated before without having to recompute them. When distance is a supplied as a numeric vector, link and distance.options are ignored.

Outputs

When specifying an argument to distance that estimates a propensity score, the output of the function called to estimate the propensity score (e.g., the glm object when distance = "glm") will be included in the matchit output object in the model component. When distance is anything other than "mahalanobis", the estimated or supplied distance measures will be included in the matchit output object in the distance component.

Examples

# NOT RUN {
data("lalonde")
# Linearized probit regression PS:
m.out1 <- matchit(treat ~ age + educ + race + married +
                    nodegree + re74 + re75, data = lalonde,
                  distance = "glm", link = "linear.probit")
# }
# NOT RUN {
# GAM logistic PS with smoothing splines (s()):
m.out2 <- matchit(treat ~ s(age) + s(educ) + race + married +
                    nodegree + re74 + re75, data = lalonde,
                  distance = "gam")
summary(m.out2$model)
# }
# NOT RUN {
# CBPS for ATC matching w/replacement, using the just-
# identified version of CBPS (setting method = "exact"):
m.out3 <- matchit(treat ~ age + educ + race + married +
                    nodegree + re74 + re75, data = lalonde,
                  distance = "cbps", estimand = "ATC",
                  distance.options = list(method = "exact"),
                  replace = TRUE)
# }
# NOT RUN {
# Mahalanobis distance matching - no PS estimated
m.out4 <- matchit(treat ~ age + educ + race + married +
                    nodegree + re74 + re75, data = lalonde,
                  distance = "mahalanobis")

m.out4$distance #NULL

# Mahalanobis distance matching with PS estimated
# for use in a caliper; matching done on mahvars
m.out5 <- matchit(treat ~ age + educ + race + married +
                    nodegree + re74 + re75, data = lalonde,
                  distance = "glm", caliper = .1,
                  mahvars = ~ age + educ + race + married +
                                nodegree + re74 + re75)

summary(m.out5)

# User-supplied propensity scores
p.score <- fitted(glm(treat ~ age + educ + race + married +
                        nodegree + re74 + re75, data = lalonde,
                      family = binomial))

m.out6 <- matchit(treat ~ age + educ + race + married +
                    nodegree + re74 + re75, data = lalonde,
                  distance = p.score)
# }