MatchPW: 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, ...)

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.

Arguments

Y
Tr
X
Group
estimand
M
exact
caliper
replace
ties
weights
...: Please note that all additional arguments of the Match function are not used.

Author

tools:::Rd_package_maintainer("CMatching")

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.

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.

Examples

Run this code

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)

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