# NOT RUN {
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.
# Suppose that the effect of homeworks on math score is unconfounded conditional on X
# and unobserved school features (we assume this only for illustrative purpouse).
# Let us consider the following variables:
X<-schools$ses # or X<-as.matrix(schools[,c("ses","white","public")])
Y<-schools$math
Tr<-ifelse(schools$homework>1,1,0)
Group<-schools$schid
# When Group is missing or there is only one Group CMatch returns
# the output of the Match function with a warning.
# Let us assume that the effect of homeworks (Tr) on math score (Y)
# is unconfounded conditional on X and other unobserved school features.
# Several strategies to handle unobserved group characteristics
# are described in Arpino & Cannas, 2016 (see References).
# Multivariate Matching on covariates in X
# default parameters: one-to-one matching on X with replacement with a caliper of 0.25
### Matching within schools
mw<-CMatch(type="within",Y=Y, Tr=Tr, X=X, Group=Group, caliper=0.1)
# compare balance before and after matching
bmw <- CMatchBalance(Tr~X,data=schools,match.out=mw)
# calculate proportion of matched observations
(mw$orig.treated.nobs-mw$ndrops)/mw$orig.treated.nobs
# check number of drops by school
mw$orig.dropped.nobs.by.group
# examine output
mw # complete list of results
summary(mw) # basic statistics
### Match preferentially within school
# i.e. first match within schools
# then (try to) match remaining units between schools
mpw <- CMatch(type="pwithin",Y=schools$math, Tr=Tr, X=schools$ses,
Group=schools$schid, caliper=0.1)
# examine covariate balance
bmpw<- CMatchBalance(Tr~ses,data=schools,match.out=mpw)
# equivalent to MatchBalance(...) with mpw coerced to class "Match"
# proportion of matched observations
(mpw$orig.treated.nobs-mpw$ndrops) / mpw$orig.treated.nobs
# check drops by school
mpw$orig.dropped.nobs.by.group.after.pref.within
# proportion of matched observations after match-within only
(mpw$orig.treated.nobs-sum(mpw$orig.dropped.nobs.by.group.after.within)) / mpw$orig.treated.nobs
# see complete output
mpw
# or use summary method for main results
summary(mpw)
#### Propensity score matching
# estimate the ps model
mod <- glm(Tr~ses+parented+public+sex+race+urban,
family=binomial(link="logit"),data=schools)
eps <- fitted(mod)
# eg 1: within school propensity score matching
psmw <- CMatch(type="within",Y=schools$math, Tr=Tr, X=eps,
Group=schools$schid, caliper=0.1)
# equivalent to direct call at MatchW(Y=schools$math, Tr=Tr, X=eps,
# Group=schools$schid, caliper=0.1)
# eg 2: preferential within school propensity score matching
psmw <- CMatch(type="pwithin",Y=schools$math, Tr=Tr, X=eps, Group=schools$schid, caliper=0.1)
# Other strategies for controlling unobserved cluster covariates
# via different specifications of propensity score (see Arpino and Mealli):
# eg 3: propensity score matching using ps estimated from a logit model with dummies for hospitals
mod <- glm(Tr ~ ses + parented + public + sex + race + urban
+schid - 1,family=binomial(link="logit"),data=schools)
eps <- fitted(mod)
dpsm <- CMatch(type="within",Y=schools$math, Tr=Tr, X=eps, Group=NULL, caliper=0.1)
# this is equivalent to run Match with X=eps
# eg4: propensity score matching using ps estimated from multilevel logit model
# (random intercept at the hospital level)
require(lme4)
mod<-glmer(Tr ~ ses + parented + public + sex + race + urban + (1 | schid),
family=binomial(link="logit"), data=schools)
eps <- fitted(mod)
mpsm<-CMatch(type="within",Y=schools$math, Tr=Tr, X=eps, Group=NULL, caliper=0.1)
# this is equivalent to run Match with X=eps
# }
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