MatchPW: Preferential Within-cluster Matching

In CMatching: Matching Algorithms for Causal Inference with Clustered Data

Preferential Within-cluster Matching

Description

This function implements preferential within-cluster matching. In other words, units that do not match within clusters (as defined by the Group variable) can match between cluster in the second step.

Usage

MatchPW(Y = NULL, Tr, X, Group = NULL, estimand = "ATT", M = 1,
 exact = NULL, caliper = 0.25, replace = TRUE, ties = TRUE, weights = NULL, ...)

Arguments

Y	A vector containing the outcome of interest.
Tr	A vector indicating the treated and control units.
X	A matrix of covariates we wish to match on. This matrix should contain all confounders or the propensity score or a combination of both.
Group	A vector describing the clustering structure (typically the cluster ID). This can be any numeric vector of the same length of Tr and X containing integer numbers in ascending order otherwise an error message will be returned. Default is NULL, however if Group is missing, NULL or contains only one value the output of the Match function is returned with a warning.
estimand	The causal estimand desired, one of "ATE", "ATT" and "ATC", which stand for Average Treatment Effect, Average Treatment effect on the Treated and on the Controls, respectively. Default is "ATT".
M	The number of matches which are sought for each unit. Default is 1 ("one-to-one matching").
exact	An indicator for whether exact matching on the variables contained in X is desired. Default is FALSE. This option has precedence over the caliper option.
caliper	A maximum allowed distance for matching units. Units for which no match was found within caliper distance are discarded. Default is 0.25. The caliper is interpreted in standard deviation units of the unclustered data for each variable. For example, if caliper=0.25 all matches at distance bigger than 0.25 times the standard deviation for any of the variables in X are discarded. The caliper is used for both within and between clusters matching.
replace	Default is TRUE. From version 2.3 this parameter can be set to FALSE. Assuming ATT this means that controls matched within cannot be matched between (i.e. in the second step). However note that, even when replace is set to FALSE, controls can be re-used during match between.
ties	An indicator for dealing with multiple matches. If more than M matches are found for each unit the additional matches are a) wholly retained with equal weights if ties=TRUE; b) a random one is chosen if ties=FALSE. Default is TRUE.
weights	A vector of observation specific weights.
...	Please note that all additional arguments of the Match function are not used.

Details

The function performs preferential within-cluster matching in the clusters defined by the variable Group. In the first phase matching within clusters is performed (see MatchW) and in the second the unmatched treated (or controls if estimand="ATC") are matched with all controls (treated) units. This can be helpful to avoid dropping many units in small clusters.

Value

index.control	The index of control observations in the matched dataset.
index.treated	The index of control observations in the matched dataset.
index.dropped	The index of dropped observations due to the exact or caliper option. Note that these observations are treated if estimand is "ATT", controls if "ATC".
est	The causal estimate. This is provided only if Y is not null. If estimand is "ATT" it is the (weighted) mean of Y in matched treated minus the (weighted) mean of Y in matched controls. Equivalently it is the weighted average of the within-cluster ATTs, with weights given by cluster sizes in the matched dataset.
se	A model-based standard error for the causal estimand. This is a cluster robust estimator of the standard error for the linear model: y ~ constant+Tr, run on the matched dataset (see cluster.vcov for details on how this estimator is obtained).
mdata	A list containing the matched datasets produced by MatchPW. Three datasets are included in this list: Y, Tr and X. The matched dataset for Group can be recovered by rbind(Group[index.treated],Group[index.control]).
orig.treated.nobs.by.group	The original number of treated observations by group in the dataset.
orig.control.nobs.by.group	The original number of control observations by group in the dataset.
orig.dropped.nobs.by.group	The number of dropped observations by group after within cluster matching.
orig.dropped.nobs.by.group.after.pref.within	The number of dropped observations by group after preferential within group matching.
orig.nobs	The original number of observations in the dataset.
orig.wnobs	The original number of weighted observations in the dataset.
orig.treated.nobs	The original number of treated observations in the dataset.
orig.control.nobs	The original number of control observations in the dataset.
wnobs	the number of weighted observations in the matched dataset.
caliper	The caliper used.
intcaliper	The internal caliper used.
exact	The value of the exact argument.
ndrops.matches	The number of matches dropped either because of the caliper or exact option.
estimand	The estimand required.

Note

The function returns an object of class CMatch. The CMatchBalance function can be used to examine the covariate balance before and after matching. See the examples below.

Author(s)

Massimo Cannas <[e-mail]>

References

Sekhon, Jasjeet S. 2011. Multivariate and Propensity Score Matching Software with Automated Balance Optimization. Journal of Statistical Software, 42(7): 1-52. http://www.jstatsoft.org/v42/i07/

Arpino, B., and Cannas, M. (2016) Propensity score matching with clustered data. An application to the estimation of the impact of caesarean section on the Apgar score. Statistics in Medicine, 35: 2074-2091 doi: 10.1002/sim.6880.

See Also

See also Match, MatchBalance,cluster.vcov

Examples

data(schools)
	
# Kreft and De Leeuw, Introducing Multilevel Modeling, Sage (1988).   
# The data set is the subsample of NELS-88 data consisting of 10 handpicked schools 
# from the 1003 schools in the full data set.

X<-schools$ses  # (socio economic status) 
Y<-schools$math #(mathematics score)
Tr<-ifelse(schools$homework > 1, 1 ,0)
Group<-schools$schid #(school ID)
# Note that when Group is missing, NULL or there is only one Group, 
# MatchPW returns the same output of the Match function (with a warning).


# Matching math scores between group of students. X are confounders.


### Match preferentially within-school 
# first match students within schools
# then tries to match remaining students between schools
 mpw <- MatchPW(Y=schools$math, Tr=Tr, X=schools$ses, Group=schools$schid, caliper=0.1)


# examine covariate balance
  bmpw<- CMatchBalance(Tr~ses,data=schools,match.out=mpw)

# proportion of matched observations
  (mpw$orig.treated.nobs-mpw$ndrops) / mpw$orig.treated.nobs 
# check drops by school
  mpw$orig.ndrops.by.group  
  
# estimate the math score difference (default is ATT)
  mpw$estimand

# complete results
   mpw
# or use summary method for main results
   summary(mpw) 


#### Propensity score matching

# estimate the propensity score (eps)

mod <- glm(Tr~ses+parented+public+sex+race+urban,
family=binomial(link="logit"),data=schools)
eps <- fitted(mod)

# eg 1: preferential within-school propensity score matching
MatchPW(Y=schools$math, Tr=Tr, X=eps, Group=schools$schid, caliper=0.1)

# eg 2: standard propensity score matching using eps
# from a logit model with dummies for schools

mod <- glm(Tr ~ ses + parented + public + sex + race + urban 
+schid - 1,family=binomial(link="logit"),data=schools)
eps <- fitted(mod)

MatchPW(Y=schools$math, Tr=Tr, X=eps, caliper=0.1)

# eg3: standard propensity score matching using ps estimated from 
# multilevel logit model (random intercept at the school level)

require(lme4)
mod<-glmer(Tr ~ ses + parented + public + sex + race + urban + (1|schid),
family=binomial(link="logit"), data=schools)
eps <- fitted(mod)

MatchPW(Y=schools$math, Tr=Tr, X=eps, Group=NULL, caliper=0.1)

 

CMatching documentation built on April 12, 2025, 2:04 a.m.