minDiff is an R-package that can be used to assign elements to a specified number of groups and minimize differences between created groups.
Note that this package is no longer maintained, but there is a
successor package that is under active developement:
anticlust. The
anticlust package builds on the theory of cluster analysis to
create sets of elements that are as similar as possible.
Install the devtools package first via install.packages("devtools").
To install the minDiff package, type in your R console
devtools::install_github("m-Py/minDiff")
Load the package via
library("minDiff")
To reproduce the following example, install the "MASS" package that contains the data set that is used.
library("MASS")
data(survey) # load data set
head(survey, n=10) # look at the data
The survey data set contains some demographic information on a student
sample. Imagine you wish to assign students to three different
dormitories and want to create a similar groups of students in each
house. As a first step, we might want to match average student age.
To do so, we pass our data set to the function create_groups and
specify which variable should be made equal in how many sets.
equal <- create_groups(survey, criteria_scale = "Age",
sets_n = 3, repetitions = 100)
By passing the column Age to the argument criteria_scale we inform
create_groups that age is a continuous variable, for which we want to
minimize the differences between groups. create_groups returns a
data.frame that is saved into the object equal. equal is actually
the same as the input data survey, but it has one additional column:
newSet - this is the group assignment variable that was created.
Let's have a look at this:
> table(equal$newSet)
1 2 3
79 79 79
The survey data set has 237 entries, which can be assigned to three
groups of equal size. If the data set had not been a multiplier of the
group number, create_groups would have created groups that are of
similar size.
Let's see how successful we were in creating groups of age:
> tapply(equal$Age, equal$newSet, mean)
1 2 3
20.35449 20.57806 20.19099
Not so bad! But how did it work? In the function call above, we
specified another parameter, repetitions=100 (which is also the
default value if we do not specify a value for repetition). This means
that the function randomly assigned all cases (i.e. students) to three
groups 100 times, and returned the most equal group assignment. In the
default case, what is considered most equal is the assignment that has
the minimum difference in group means; but we can specify different
criteria if we want to (see below). By varying the parameter
repetitions we can increase our chances of creating equal groups. If
we conduct 10,000 repetitions (which is still very fast if we only
consider one variable), the groups will be very similar with regards to
age. Note that it is possible to pass a data set that has been optimized
previously; in this case, the program does not start all over, but only
tries find more similar groups than the previous best assignment:
equal <- create_groups(equal, criteria_scale = "Age",
sets_n = 3, repetitions = 10000)
> tapply(equal$Age, equal$newSet, mean)
1 2 3
20.37028 20.38194 20.37133
Nice! How well your groups can match of course depends on the input data.
We can pass more than one criterion to create_groups. Let's imagine we
also want students to be of equal heights in all dormitories:
equal <- create_groups(survey, criteria_scale = c("Age", "Height"),
sets_n = 3, repetitions = 10000)
> tapply(equal$Age, equal$newSet, mean)
1 2 3
20.37877 20.35233 20.39244
> tapply(equal$Height, equal$newSet, mean, na.rm=TRUE)
1 2 3
172.5658 172.3694 172.2292
Note that there were missing values in the variable
survey$Height. This is given out as a warning by create_groups, but
it will still return a result (and simply disregards the missing value
in the variable height).
We may not only wish to minimize differences with regards to age or height, but we might want to create equal gender ratios in all dormitories. Let's check in what ratios our previous group assignment resulted:
> table(equal$newSet, equal$Sex)
Female Male
1 36 43
2 38 41
3 44 34
We can see that gender ratios are very different between
dormitories. create_groups offers the possibility to consider
categorical variables when creating groups. These are passed via the
criteria_nominal parameter. Let's try this out:
equal <- create_groups(survey, criteria_scale = "Age",
criteria_nominal = "Sex", tolerance_nominal = 2,
sets_n = 3, repetitions = 100)
By specifying the parameter tolerance_nominal = 2, we tell
create_groups that we tolerate deviations between dormitories in the
frequency of female and male students of no more than 2. Did that work?
> table(equal$newSet, equal$Sex)
Female Male
1 40 39
2 38 40
3 40 39
Note that in this case, we could decrease our tolerance for deviations
to 1, but it is impossible to assign the same number of female and male
students to all dormitories in this case. If a tolerance value is passed
that cannot be met using the present data and the number of repetitions
that were conducted, create_groups will not return an assignment.
It is possible to pass two categorical criteria create_groups(). There
is no limit for scale criteria, but only two categorical variables can
be passed.
Here is an example where we want to create dormitories that are similar with regard to smoker status and gender ratio:
equal <- create_groups(survey, criteria_scale = c("Age", "Height"),
criteria_nominal = c("Sex", "Smoke"),
tolerance_nominal = c(2, 3, Inf), sets_n = 3,
repetitions=100)
> table(equal$newSet, equal$Sex)
Female Male
1 39 40
2 40 38
3 39 40
> table(equal$newSet, equal$Smoke)
Heavy Never Occas Regul
1 4 63 6 6
2 4 62 6 6
3 3 64 7 5
Note that the parameter tolerance_nominal expects a vector of length 3
if two categorical variables are passed to criteria_nominal. These
values indicate tolerances for deviations in the first, the second and
the combined categorical levels. In doubt, use large tolerance values
when starting to optimize your groups and see how well the function is
running. In the upper case I was not interested to assign an equal
number of smoking females and males to each dormitories and considered
both categorical variables independently from each other. So, I set the
tolerance for deviations in the combined groups to infinity.
I could be interested not only in equalizing mean age between groups,
but also the standard deviation of ages to achieve similar distributions
of age between dormitories. This is possible by passing another function
to the equalize parameter.
equal <- create_groups(survey, criteria_scale = "Age",
criteria_nominal = "Smoke",
tolerance_nominal = 2,
sets_n = 3, repetitions = 500,
equalize = list(mean, sd))
> tapply(equal$Age, equal$newSet, mean)
1 2 3
20.21943 20.41986 20.48425
> tapply(equal$Age, equal$newSet, sd)
1 2 3
6.599697 6.995727 5.855852
So far, we tried to minimize differences between groups using repeated
random assignments of students to groups. create_groups also offers
the possibility to compute the exact best assignment (with regard to the
specified criteria). You can compute the best assignment by setting the
parameter exact to TRUE (it defaults to FALSE). In this case, all
possible assignments will be tested sequentially. As the number of
assignments growths exponentially with the number of items to be
assigned, this option is not feasible for large data sets.
This code produces the best assignment of the first 20 students to two groups. A total of 184,756 assignments is conducted (fun fact: the number of all possible assignments of students to three groups is 4.16 * 10^110).
surv <- head(survey, n = 20)
equal <- create_groups(surv, criteria_scale = "Age", exact = TRUE,
sets_n = 2)
> tapply(equal$Age, equal$newSet, mean)
1 2
20.3248 20.3168
This ran 48 in seconds on my computer.
To be written.
Any feedback or reports on bugs is greatly appreciated; just open an issue or write an email to martin.papenberg at uni-duesseldorf.de.
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