Creating balanced groups based on three categorical variables - r

Question

I'm creating a group assignment for a college class (~180 students) I'm instructing. It's important that these groups be as heterogeneous as possible across three variables (field of study (FOS), sex, division:i.e., newer/older students).
FOS has 5 levels, sex has 2, division has 2. Given the project, I'd like to create about 8-9 groups. In other words, I'd like groups of approximately 6 with a "good" balance of different fields of study, males/females, and new and older students. I'd then simply post the names with the automated assignments.
The instructor before did it all by hand, but I've tried playing around with R to see if there's a more systematic way of doing this, but only came up with repeated (and clunky) sorting. I expect the 5 FOS levels to vary in size, so I recognize that it will not be a perfect solution. Interested in people's clever solutions. Here's a reproducible sample:
dat <- data.frame(
student = 1:180,
gender = factor(sample(LETTERS[1:2], 180, replace = T, prob = c(.52,.48)),
labels=c("female","male")),
division = factor(sample(LETTERS[1:2], 180, replace = T, prob = c(.6,.4)),
labels=c("lower","upper")),
field = factor(sample(LETTERS[1:5], 180, replace = T,
prob = c(.26,.21,.35,.07,.11)),
labels = c("humanities","natural science",
"social science","engineer","other")))
This was what I was playing with, but it's really increasing the randomness in assignment and not so much the balance as can be seen:
library(dplyr)
dat$rand <- sample(1:180,180)
dat1 <- arrange(dat, field, division, gender, rand)
dat1$grp <- 1:(nrow(dat1)/6) #issue if not divisible
Which does not result in adequate balance:
with(dat1, table(gender, grp)) #as a check
with(dat1, table(field, grp))
with(dat1, table(division, grp))

Answer 1

I know this is an old question, but I had a similar problem today and here's the solution I came up with. Basically you assign groups randomly then use either chi square test for categorical variables or ANOVA for continuous variables to test for group differences for each variable. You set a threshold for the p-value that you do not want to drop below. The code will reshuffle the groups until all p values are above that threshold. If it goes through 10,000 iterations without reaching a grouping solution, it will stop and suggest that you lower the threshold.
set.seed(905)
#let's say you have a continuous variable you would also like to keep steady across groups
dat$age <- sample(18:35, nrow(dat), replace = TRUE)
dat$group <- rep_len(1:20, length.out = nrow(dat)) #if you wanted to make 20 groups
dat$group <- as.factor(dat$group)
a <- 0.1; b <- 0.1; c <- 0.1; d <- 0.1
thresh <- 0.85 #Minimum threshold for p value
z <- 1
while (a < thresh | b < thresh |c < thresh |d < thresh) {
dat <- transform(dat, group = sample(group)) #shuffles the groups
x <- summary(aov(age ~ group, dat)) #ANOVA for continuous variables
a <- x[[1]]['group','Pr(>F)']
x <- summary(table(dat$group, dat$gender)) #Chi Sq for categorical variables
b <- x[['p.value']]
x <- summary(table(dat$group, dat$division))
c <- x[['p.value']]
x <- summary(table(dat$group, dat$field))
d <- x[['p.value']]
z <- z + 1
if (z > 10000) {
print('10,000 tries, no solution, reduce threshold')
break
}
}

Answer 2

With enough datapoints per combination of the variables, you should be able to do this:
dat <- groupdata2::fold(dat, k = 8,
cat_col = c("gender", "division", "field"))
with(dat, table(gender, .folds))
## .folds
## gender 1 2 3 4 5 6 7 8
## female 11 12 11 12 12 11 12 12
## male 10 11 11 11 11 11 11 11
with(dat, table(field, .folds))
## .folds
## field 1 2 3 4 5 6 7 8
## humanities 5 8 9 7 9 6 6 5
## natural science 2 3 4 6 3 9 2 4
## social science 9 7 6 8 5 6 9 6
## engineer 3 3 2 1 3 0 2 4
## other 2 2 1 1 3 1 4 4
with(dat, table(division, .folds))
## .folds
## division 1 2 3 4 5 6 7 8
## lower 11 15 13 14 10 13 11 15
## upper 10 8 9 9 13 9 12 8