## Introduction

This article describes how to calculate Jaccard coefficients in Q using R.

One way of measuring the overlap or similarity between the data in two binary variables is to use a Jaccard coefficient. The coefficient ranges between 0 and 1, with 1 indicating that the two variables overlap completely, and 0 indicating that there are no selections in common. In this post I show you how to do the calculation in Q using R by looking at how people’s preferences for confectionery flavors overlap according to their responses to a survey.

## Requirements

The variables for the Jaccard calculation must be binary, having values of 0 or 1. They may also include a missing value, and any case with a missing value in each pair will be excluded from the Jaccard coefficient for that pair.

In Q, this means that your variables must come from a **Number**, **Number – Multi**, or **Pick Any** question. You can check and change the **Question Type** by looking in the **Question Type** column of the **Variables and Questions** tab.

## Method

To calculate Jaccard coefficients for a set of binary variables, you can use the following:

- Select
**Create > R Output**. - Paste the code below into the
**R CODE**section on the right. - Change line 8 of the code so that
*input.variables*contains the variable**Name**of the variables you want to include. The variable Name is the entry in the**Name**column of the**Variables and Questions**tab. - Click
**Automatic**.

The code for the Jaccard coefficients is:

Jaccard = function (x, y) {

M.11 = sum(x == 1 & y == 1)

M.10 = sum(x == 1 & y == 0)

M.01 = sum(x == 0 & y == 1)

return (M.11 / (M.11 + M.10 + M.01))

}

input.variables = data.frame(Q6_01, Q6_02, Q6_03, Q6_04, Q6_05, Q6_06, Q6_07, Q6_08, Q6_09)

m = matrix(data = NA, nrow = length(input.variables), ncol = length(input.variables))

for (r in 1:length(input.variables)) {

for (c in 1:length(input.variables)) {

if (c == r) {

m[r,c] = 1

} else if (c > r) {

m[r,c] = Jaccard(input.variables[,r], input.variables[,c])

}

}

}

variable.names = sapply(input.variables, attr, "label")

colnames(m) = variable.names

rownames(m) = variable.names

jaccards = m

In this code:

- I have defined a
*function*called Jaccard. The function takes any two variables and calculates the Jaccard coefficient for those two variables. A function is a set of instructions that can be used elsewhere in the code. Particularly for more complicated blocks of code, writing a function like this can make your code more efficient and easier to read and check for mistakes. *input.variables*contains a data frame that has each of the variables you want to analyze as the columns.- Initially, I have created a matrix full of missing values as a place to store my calculations.
- I have used two for loops to go through and calculate the Jaccard coefficients and fill up the top half of the matrix.
- The bottom half of the matrix is left empty. In Q, missing values are displayed as empty cells. As the bottom half of the matrix would be identical to the top half, empty cells help us to read the results more easily.
- I have used the sapply function to obtain the labels for each variable so that they may be displayed in the row labels (rownames) and column labels (colnames) of the table. In this case, sapply is using the attr function to obtain the label attribute of each variable. As R does not recognize the same set of meta data for each variable, Q adds the meta data to the attributes of the variables so that it may be returned later if necessary.

The result is a table that contains all of the Jaccard coefficients for each pair of variables.

### Visualize the results

A heatmap is an ideal way to visualize tables of coefficients like this. To create a heatmap for this data in Q,

- Select
**Create > Charts > Visualization > Heatmap**. - Under
**Inputs > DATA SOURCE**, click into**Output**and select the output for the Jaccard coefficients that was created above. - Tick
**Automatic**.

I’ve shown an example of the resulting heatmap, below. With the blue default color palette, the largest Jaccard coefficients will be the darkest blue. Looking for dark patches of the diagonal allows you to identify the pairs of variables with the biggest overlap.

## See Also

How R Works Differently in Q Compared to Other Programs

How to Use Different Types of Data in R

How to Reference Different Items in Your Project in R

How to Work with Conditional R Formulas

How to Add a Custom R Output to your Report

How to Create a Custom R Variable