Matching on a quaternary variable R - r

Question

I am working with data set you can generate with the following code:
set.seed(922)
dat<-data.frame("y" = c(rnorm(500,20,2),rnorm(500, 40,2),rnorm(500,60,2),rnorm(500,80,2)),
"quaternary" = sample(LETTERS[1:4],2000,replace = T),
"binary" = sample(c("0","1"),2000,replace = T))
(Generating a 4-modal distribution was an arbitrary decision)
the four treatment groups ("A","B","C","D") are what is important.
I am trying to create a balanced matched sample based on the values of y in the data frame. I've used the "Matchit" package to build balanced samples based on a binary variable:
matchit(binary~y,data = dat)
but I'm not sure how I could build matches of a 4-level factor "quaternary" on the values of "y".
I'm not certain there's an elegant way to do it in the Matchit package, but I'm open to any suggestion on how I might stack the methodologies to get a good balanced sample. Any help would be awesome
EDIT:
OK so I think I'm close. You can leverage dplyr in a for loop. It's a bit inefficient, and I still have to think about the implications of using this to create a balanced sample, but it's getting closer...
first in the dat frame, you create four new variables populated with NAs:
dat$A_match<-NA
dat$B_match<-NA
dat$C_match<-NA
dat$D_match<-NA
The you use summarise function in dplyr to find the values.
require(dplyr) #haha. Hey that rhymes
for(i in 1:dim(dat)[1]){
dat_A_index<-dat%>%
mutate(y = ifelse(quaternary=="A",y,0),
abs = abs(dat[i,1]-y))%>%
summarise(A_index = which.min(abs))
dat$A_match[i]<-dat[dat_A_index$A_index,1]
rm(dat_A_index)
dat_B_index<-dat%>%
mutate(y = ifelse(quaternary=="B",y,0),
abs = abs(dat[i,1]-y))%>%
summarise(B_index = which.min(abs))
dat$B_match[i]<-dat[dat_B_index$B_index,1]
rm(dat_B_index)
dat_C_index<-dat%>%
mutate(y = ifelse(quaternary=="C",y,0),
abs = abs(dat[i,1]-y))%>%
summarise(C_index = which.min(abs))
dat$C_match[i]<-dat[dat_C_index$C_index,1]
rm(dat_C_index)
dat_D_index<-dat%>%
mutate(y = ifelse(quaternary=="D",y,0),
abs = abs(dat[i,1]-y))%>%
summarise(D_index = which.min(abs))
dat$D_match[i]<-dat[dat_D_index$D_index,1]
rm(dat_D_index)
}
I know it's clunky, but at least it's selecting the best match in each of the 4 categories for the given value of y. In a real world application, the final balanced sample should be no larger than smallest conditional n multiplied by 4. You also have to assume some outliers might have to be thrown out (maybe an F-test to set the last filtering rule?). At any rate, the vector, y, we generated already represent a balanced sample, but for a real-world application, this is not correct.

Answer 1

Remember that MatchIt only produces matched samples that are suitable for estimating the ATT (average treatment effect on the treated). Typically, MatchIt selects a group it considers the "treated", which is usually the treatment level labeled "1". It then matches to each treated unit one or more control units.
With multinomial treatments, you also need to decide which estimand you are interested in. If, again, you are interested in the ATT, you must select one group to be considered the "treated", and the other groups are considered "control" (I prefer to refer to them as "focal" and "non-focal"). Importantly, your treatment effect estimates will only generalize to a population similar in composition to that of the focal group.
If this is what you want, you need to select one group as focal, and then perform three separate matchit calls where each one matches units from one of the non-focal group to the units in the focal group. The focal group remains unchanged. Below is some code I might use to do this:
set.seed(922)
library(MatchIt)
dat<-data.frame("y" = c(rnorm(500,20,2),rnorm(500, 40,2),rnorm(500,60,2),rnorm(500,80,2)),
"quaternary" = sample(LETTERS[1:4],2000,replace = T, prob = c(.1, .3, .3, .3)),
"binary" = sample(c("0","1"),2000,replace = T))
focal <- "A"
dat$match.weights <- 1
for (lev in levels(dat$quaternary)) {
if (lev != focal) {
dat0 <- dat[dat$quaternary %in% c(focal, lev),]
dat0$treat <- as.numeric(dat0$quaternary == focal)
m.out <- matchit(treat ~ y, dat = dat0, replace = FALSE)
dat$match.weights[dat$quaternary == lev] <- m.out$weights[dat0$treat == 0]
}
}
library(cobalt)
bal.tab(quaternary ~ y, data = dat, weights = dat$match.weights,
method = "matching", focal = focal, un = TRUE)
#> Note: estimand and s.d.denom not specified; assuming ATT and treated.
#> Balance summary across all treatment pairs
#> Type Max.Diff.Un Max.Diff.Adj
#> y Contin. 0.1134 0.0009
#>
#> Sample sizes
#> B C D A
#> All 593 597 612 198
#> Matched 198 198 198 198
#> Unmatched 395 399 414 0
Created on 2018-10-13 by the reprex package (v0.2.1)
Note that if your focal group is not the smallest of the groups, you must match with replacement by setting replace = TRUE in matchit(). To ensure the focal group in this example was the smallest, I set the probabilities of the randomly sampled values of quaternary so that the probability of A was lowest.
If, on the other hand, you want the ATE, matching is probably not your best option. It would be hard to use MatchIt to produce a matched set for the ATE for a binary treatment, making it even harder to do so for multiple treatment groups. Instead, you might look into propensity score weighting, for which the weights are well defined with multinomial treatments. Below is some code to estimate the weights using the above data set to estimate either the ATT or the ATE:
library(WeightIt)
#Weighting for the ATT with A as focal:
w.out.att <- weightit(quaternary ~ y, data = dat, estimand = "ATT", focal = "A")
#> Using multinomial logit regression.
dat$w.att <- w.out.att$weights
#Weighting for the ATE:
w.out.ate <- weightit(quaternary ~ y, data = dat, estimand = "ATE")
#> Using multinomial logit regression.
dat$w.ate <- w.out.ate$weights
bal.tab(quaternary ~ y, data = dat, weights = c("w.att", "w.ate"),
method = "weighting", estimand = c("ATT", "ATE"), un = TRUE)
#> Balance summary across all treatment pairs
#> Type Max.Diff.Un Max.Diff.w.att Max.Diff.w.ate
#> y Contin. 0.1092 0.0055 0.0024
#>
#> Effective sample sizes
#> A B C D
#> All 198.000 593.000 597.000 612.000
#> w.att 198.000 591.139 593.474 604.162
#> w.ate 196.947 592.822 596.993 611.107
Created on 2018-10-13 by the reprex package (v0.2.1)
No matter what strategy you use, you can use the weights in a weighted regression of the outcome on the treated using the estimated matching weights or ATT or ATE weights.
[Disclosure: I'm the author of both the cobalt and WeightIt packages.]