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To begin, we will create some plotting code. This code will take a vector of covariate values, and generate a rugplot along with histograms for the covariate values of each group/batch.
plot.covars <- function(Xs, Ts, title="", xlabel="Covariate",
ylabel="Density") {
data.frame(Batch=factor(Ts, levels=c(0, 1)), Covariate=Xs) %>%
ggplot(aes(x=Covariate, group=Batch, color=Batch)) +
geom_rug() +
geom_histogram(aes(fill=Batch), binwidth=0.1, position="identity",
alpha=0.5) +
labs(title=title, x=xlabel, y=ylabel) +
scale_x_continuous(limits=c(-1, 1)) +
scale_color_manual(values=c(`0`="#bb0000", `1`="#0000bb"),
name="Group/Batch") +
scale_fill_manual(values=c(`0`="#bb0000", `1`="#0000bb"),
name="Group/Batch") +
theme_bw()
}generate some simulated data which is imbalanced, and some code to plot the covariates for the simulated data along with kernel density estimates of the covariates:
sim.low <- cb.sims.sim_linear(n=n, unbalancedness=2)
plot.covars(sim.low$Xs, sim.low$Ts, title="Sample covariate values")
#> Warning: Removed 4 rows containing missing values (`geom_bar()`).
Note particularly that there are many samples in group/batch \(0\) with covariate values much smaller than the smallest attained by samples in group/batch \(1\), and there are many samples in group/batch \(1\) with covariate values much larger than the largest attained by samples in group/batch \(2\).
Conceptually, vector matching can be thought of as a form of “propensity trimming”; that is, it will remove samples from a given group/batch which are dissimilar from one (or more) other groups/batches on the basis of their propensity scores. This is a relatively coarse approach to balancing covariates across the groups/batches:
vm.retained <- cb.align.vm_trim(sim.low$Ts, sim.low$Xs)
plot.covars(sim.low$Xs[vm.retained], sim.low$Ts[vm.retained],
title="Sample covariate values (after VM)")
#> Warning: Removed 4 rows containing missing values (`geom_bar()`).
Note that the covariate values attained by the two groups are now overlapping; that is, there are no longer covariates in individual groups/batches that are larger/smaller than the largest/smallest attained by the other group/batch.
Conceptually, \(K\)-way matching can be thought of as a way to directly include/exclude samples from across the groups/batches until the covariate distributions per group/batch are approximately rendered equal. This is a relatively restrictive approach to aligning covariates across the groups/batches:
kway.retained <- cb.align.kway_match(sim.low$Ts, data.frame(Covar=sim.low$Xs),
match.form="Covar")
plot.covars(sim.low$Xs[kway.retained], sim.low$Ts[kway.retained],
title="Sample covariate values (after K-way matching)")
#> Warning: Removed 4 rows containing missing values (`geom_bar()`).
In this case, we can see that the empirical covariate values retained after \(K\)-way matching are almost identical across the two groups.
Typically, vector matching will tend to retain more samples for subsequent analysis than k-way matching. This may be undesirable if subsequent inference/estimation techniques are known to be sensitive to unequal empirical covariate distributions.
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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