In gnattino/polymatching: A Matching Algorithm for Designs with Multiple Groups

knitr::opts_chunk$set(echo = TRUE, 
                      message = FALSE, 
                      warning = FALSE)

##############################################
# Hide generation of dataset and matched set #
##############################################

#Set seed for reproducibility of results
set.seed(123)

#Group sizes
n_A <- 50
n_B <- 750
n_C <- n_D <- 1000

#Generate variables separately for each group
dat_A <- data.frame(X_1 = rnorm(n_A, mean = 0,  sd = 1), 
                    X_2 = rnorm(n_A, mean = 5,  sd = 1), 
                    X_3 = rnorm(n_A, mean = -5,  sd = 1), 
                    Z = factor(rbinom(n_A, size = 1, prob = .5)),
                    W = factor(apply(rmultinom(n_A, size = 1, prob = c(.25, .25, .25, .25)) == 1, 
                                     MARGIN = 2, 
                                     FUN = which)),
                    G = "A",
                    stringsAsFactors = FALSE)

dat_B <- data.frame(X_1 = rnorm(n_B, mean = 0,  sd = 1), 
                   X_2 = rnorm(n_B, mean = 5,  sd = 1), 
                   X_3 = rnorm(n_B, mean = -5,  sd = 1), 
                   Z = factor(rbinom(n_B, size = 1, prob = .5)),
                   W = factor(apply(rmultinom(n_A, size = 1, prob = c(.25, .25, .25, .25)) == 1, 
                                     MARGIN = 2, 
                                     FUN = which)),
                   G = "B",
                   stringsAsFactors = FALSE)

dat_C <- data.frame(X_1 = rnorm(n_C, mean = -0.5,  sd = 1), 
                   X_2 = rnorm(n_C, mean = 4.5,  sd = 1), 
                   X_3 = rnorm(n_C, mean = -4.5,  sd = 1), 
                   Z = factor(rbinom(n_C, size = 1, prob = .2)),
                   W = factor(apply(rmultinom(n_A, size = 1, prob = c(.1, .2, .3, .4)) == 1, 
                                     MARGIN = 2, 
                                     FUN = which)),
                   G = "C",
                   stringsAsFactors = FALSE)

dat_D <- data.frame(X_1 = rnorm(n_D, mean = 0.5,  sd = 1), 
                   X_2 = rnorm(n_D, mean = 5.5,  sd = 1), 
                   X_3 = rnorm(n_D, mean = -5.5,  sd = 1), 
                   Z = factor(rbinom(n_D, size = 1, prob = .8)),
                   W = factor(apply(rmultinom(n_A, size = 1, prob = c(.4, .3, .2, .1)) == 1, 
                                     MARGIN = 2, 
                                     FUN = which)),
                   G = "D",
                   stringsAsFactors = FALSE)

dat <- rbind(dat_A, dat_B, dat_C, dat_D)

library(polymatching)
result_match_1 <- polymatch(G ~ X_1 + X_2 + X_3, 
                        data = dat,
                        distance = "euclidean")
dat$match_id_1 <- result_match_1$match_id


result_match_3 <- polymatch(G ~ X_1 + X_2 + X_3, 
                        data = dat,
                        distance = "euclidean",
                        exactMatch = ~ Z + W)
dat$match_id_3 <- result_match_3$match_id

Evaluating the balance in matched samples

The package polymatching implements also functions to assess the balance in the variables of interest after matching. Consider the matched samples generated in the Polymatching tab. The following code can be used to assess the balance in all of the five variables of the dataset for the first matched set.

tabBalance_1 <- balance(G ~ X_1 + X_2 + X_3 + Z + W,
                        match_id = dat$match_id_1,
                        data = dat)
knitr::kable(head(tabBalance_1, n = 12), digits = 3) 

The table provides the standardized mean differences (SMDs) comparing each pair of groups, before and after matching, in terms of all of the listed variables. For continuous variables, the table also provides the ratio of the variances before and after matching. SMDs less than 10% are generally considered as negligible differences. The table above show that between-group differences have much decreased after matching for all variables that were taken into account in the matching step ($X_1$, $X_2$ and $X_3$). The balance in $Z$ and $W$, which were not taken into account to generate the first matched sample, is very poor. Plots to graphically show the same outputs can be produced with the following code.

plot_1 <- plotBalance(tabBalance_1, 
                      boxplots = FALSE,
                      ratioVariances = TRUE)

The plots of SMDs and the ratios of variances are distinct elements of the output.

#Standardized mean differences
plot_1$plotStdzDiff

#Ratio of variances
plot_1$plotRatioVars

Notably, when considering the balance of the matched set where the variables $Z$ and $W$ were exactly matched, it is possible to observe a perfect balance in the variables $Z$ and $W$ and a worse balance in the other variables.

tabBalance_3 <- balance(G ~ X_1 + X_2 + X_3 + Z + W,
                        match_id = dat$match_id_3,
                        data = dat)
plot_2 <- plotBalance(tabBalance_3, 
                      boxplots = FALSE,
                      ratioVariances = TRUE)

#Standardized mean differences
plot_2$plotStdzDiff

gnattino/polymatching documentation built on Feb. 9, 2025, 1:23 a.m.