So using the `Matching`

Package (Link to package here)

We can work through a modified `GenMatch`

example.

```
library(Matching)
data(lalonde)
#introduce an id vaiable
lalonde$ID <- 1:length(lalonde$age)
X = cbind(lalonde$age, lalonde$educ, lalonde$black, lalonde$hisp,
lalonde$married, lalonde$nodegr, lalonde$u74, lalonde$u75,
lalonde$re75, lalonde$re74)
BalanceMat <- cbind(lalonde$age, lalonde$educ, lalonde$black,
lalonde$hisp, lalonde$married, lalonde$nodegr,
lalonde$u74, lalonde$u75, lalonde$re75, lalonde$re74,
I(lalonde$re74*lalonde$re75))
genout <- GenMatch(Tr=lalonde$treat, X=X, BalanceMatrix=BalanceMat, estimand="ATE",
pop.size=16, max.generations=10, wait.generations=1)
mout <- Match(Y=NULL, Tr=lalonde$treat, X=X,
Weight.matrix=genout,
replace=TRUE, ties=FALSE)
# here we set ties FALSE so we only have 1-1 Matching
summary(mout)
#now lets create our "Matched dataset"
treated <- lalonde[mout$index.treated,]
# and introduce an indetity variable for each pair
treated$Pair_ID <- treated$ID
non.treated <- lalonde[mout$index.control,]
non.treated$Pair_ID <- treated$ID
matched.data <- rbind(treated, non.treated)
matched.data <- matched.data[order(matched.data$Pair_ID),]
#this outputs which of the non-treated ID was paired with the first person
matched.data$ID[matched.data$Pair_ID==1 & matched.data$treat==0]
```

We see that for the data, the **ID=1 is matched with ID=193**

Now lets introduce some randomisation into the order of the data and see if we get the same pairs

```
n <- 500
P1 <- rep(NA, n)
P2 <- rep(NA, n)
P3 <- rep(NA, n)
P4 <- rep(NA, n)
P5 <- rep(NA, n)
P6 <- rep(NA, n)
P7 <- rep(NA, n)
for (i in 1:n) {
lalonde <- lalonde[sample(1:nrow(lalonde)), ] # randomise order
genout <- GenMatch(Tr=lalonde$treat, X=X, BalanceMatrix=BalanceMat, estimand="ATE",
pop.size=16, max.generations=10, wait.generations=1)
mout <- Match(Y=NULL, Tr=lalonde$treat, X=X,
Weight.matrix=genout,
replace=TRUE, ties=FALSE)
summary(mout)
treated <- lalonde[mout$index.treated,]
treated$Pair_ID <- treated$ID
non.treated <- lalonde[mout$index.control,]
non.treated$Pair_ID <- treated$ID
matched.data <- rbind(treated, non.treated)
matched.data <- matched.data[order(matched.data$Pair_ID),]
P1[i] <- matched.data$ID[matched.data$Pair_ID==1 & matched.data$treat==0]
P2[i] <- matched.data$ID[matched.data$Pair_ID==2 & matched.data$treat==0]
P3[i] <- matched.data$ID[matched.data$Pair_ID==3 & matched.data$treat==0]
P4[i] <- matched.data$ID[matched.data$Pair_ID==4 & matched.data$treat==0]
P5[i] <- matched.data$ID[matched.data$Pair_ID==5 & matched.data$treat==0]
P6[i] <- matched.data$ID[matched.data$Pair_ID==6 & matched.data$treat==0]
P7[i] <- matched.data$ID[matched.data$Pair_ID==7 & matched.data$treat==0]
}
```

So the `loop`

will match the pairs 500 times and `P1`

will save the `treat==0`

case each time.

We then look at the which `P1`

appears the most, by:

```
plot(1:n, P1, main="P1")
```

OR

```
summary(as.factor(P1))
```

We see that no one `treat==0`

case is commonly paired. I would expect there to be a case (possibly =193??) that is commonly paired that does not depend on the order of the data. Therefore I think my loop is wrong. Can anybody point out where? Or when they run a loop, they find, independent of the order of the data, that similar cases are paired??