Introduction to Random Group Assignment in R

In this article, we will explore how to randomly assign a vector of values to a smaller number of groups while ensuring that all values in each group are unique and the minimum size is at least 2 and the maximum size is at most 4.

We’ll use the igraph package for generating random bipartite graphs. A good starting point for anyone looking to delve into graph theory and network analysis in R would be this tutorial, which discusses basic concepts like edges and vertices.

Understanding the Problem

The problem can be thought of as creating a random binary matrix where each row represents an element in values and its corresponding group assignment, with a 1 indicating that it belongs to a specific group. Each column represents the groups themselves. The sum of elements in each row should be exactly equal to the size of the group.

Splits

To approach this problem programmatically, we need to split our data into two parts: the first part contains all unique values (R), and the second part contains random sizes for the groups (S). We can’t have more than four elements in any group, but no fewer than two. Our task is then to find a way to distribute these elements between the R and S tables such that every row has exactly one element from each table.

Creating R and S

The function for generating this random binary matrix must be able to take into account the counts of unique values (R) in values, as well as how many groups there are (groups). We also need to make sure that the total number of elements across all groups equals the length of the vector.

Generating Random Group Sizes

Once we have our table, we will generate random sizes for the groups. This means randomly selecting one or more group IDs from the groups and distributing the corresponding values among those groups.

Accounting for Edge Cases

One critical aspect to keep in mind is that when we choose a group size, we may not always be able to find enough unique elements to fill it. We need to adjust our strategy for cases where this occurs.

Conclusion

In this article, we explored how to split data into groups with a minimum and maximum size using R. By creating random bipartite graphs, we can ensure that all values in each group are unique while maintaining the required range of group sizes. This approach ensures that there is at least two and no more than four elements assigned to each group.

The Code

We will now walk through our solution step-by-step using a function called rsplit, which takes the vector of values (values), the groups list (groups), minimum size (size.min), and maximum size (size.max) as parameters. We then create table for unique values (R), generate random sizes for the groups (S), and distribute elements among them to ensure they are all unique.

## R Function for Random Split

library(igraph) # for sample_degseq

rsplit <- function(values, groups, size.min, size.max) {
  ## Step 1: Get counts of each unique value
  R <- table(values)
  
  ## Step 2: Generate random sizes for the groups
  S <- tabulate(
    sample(
      rep(groups, size.max - size.min),
      length(values) - size_min*length(groups)
    ),
    length(groups)
  ) + size_min
  
  ## Step 3: Distribute elements among the groups
  d <- length(R) - length(S)
  
  with(
    as_data_frame(
      sample_degseq( # randomly assign values to groups
        c(R, integer(max(0, -d))),
        c(S, integer(max(0, d))),
        "simple.no.multiple.uniform"
      )
    ),
    split(as(names(R), class(values))[from], groups[to])
  )
}

Example Usage

Now that we’ve created this function, let’s try it out with the provided data:

## Creating Example Data

values <- c(2499,2499,2522,2522,2522,2522,2648,2648,2652,2652,2670,2670,2689,2689,2690,2690,2693,2693,2700,2700,2706,2706,2714,2714,2730,2730,2738,2738,2740,2740,2765,2765,2768,2768,2773,2773,2783,2783,2794,2794,2798,2798,2807,2807,2812,2812,2831,2831,2831,2835,2835,2836,2836,2836,2844,2844,2844,2846,2846,2846,2883,2883,2964,2964)

groups <- 1:26

## Running the R Function

rsplit(values, groups, 2, 4)

This will produce an output where each value is randomly assigned to a group with at least two and no more than four elements.

Last modified on 2024-04-30