How to Calculate Jaccard Coefficients in Displayr Using R

Jaccard coefficients, also known as Jaccard indexes or Jaccard similarities, are measures of the similarity or overlap between a pair of binary variables. In Displayr, this can be calculated for variables in your data easily by using Anything > Advanced Analysis > Regression > Driver Analysis and selecting Data > Output > Jaccard Coefficient. However, you can also calculate them using R, which is what this article focuses on.

Requirements

A Data Set with variables appropriate for a Linear Regression analysis.

Method

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

1. Select Calculation > Custom Code from the toolbar.
2. Place the custom calculation on the page.
3. Paste the code below into the R Code editor.
4. Change line 8 of the code so that input.variables contains the variable Name of the variables you want to include. The variable Name can be found by hovering over the variable in the Data Sources tree, or by selecting the variable and looking under General > Name.

The code for the Jaccard coefficients is:

#create a function to calculate jaccard coefficient between binary variables
#note for each pair of variables, any case with a missing value for that pair should be excluded from the coefficient for that pair 
#the function only does comparisons between complete cases, that is cases that do not have any blank values in any of the variables
Jaccard = function (x, y) {
     complete = complete.cases(x,y)
     x = x[complete]
     y = y[complete]
     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))
}

#CHANGE the variables inside the data.frame() to those you want to include by using the variable name
input.variables = data.frame(Q6_01, Q6_02, Q6_03, Q6_04, Q6_05, Q6_06, Q6_07, Q6_08, Q6_09)

#Create an empty matrix of missing values to write results to
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])
          }
     }
}

#pull off the variable labels to use as the row and column headers
variable.names = sapply(input.variables, attr, "label")
colnames(m) = variable.names
rownames(m) = variable.names

#return the final table and name it jaccards
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.
• In case of missing values, the Sum function excludes any case with a missing value for that pair from the coefficient for that pair. 
• input.variables contains a data frame that has each of the variables you want to analyze as the columns. Use the reference Name of the variables for this, otherwise, see Code edits for variable sets below.
• 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 Displayr, 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 metadata for each variable, Displayr adds the metadata 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.

Code edits for variable sets

If you are working with a lot of variables and would rather reference them using the variable set name, use the code below.

#create a function to calculate jaccard coefficient between binary variables
#note for each pair of variables, any case with a missing value for that pair should be excluded from the coefficient for that pair 
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))
}

#CHANGE the variables inside the data.frame() to those you want to include by using the variable name
input.variables = data.frame(`Percieved proportion of time`, `Unaided Awareness`, check.names=F)
input.variables=input.variables[,names(input.variables) != "NET"]

#Create an empty matrix of missing values to write results to
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])
}
}
}

#pull off the variable names to use as the row and column headers
variable.names = names(input.variables)
colnames(m) = variable.names
rownames(m) = variable.names

#return the final table and name it jaccards
jaccards = m

Visualize the results

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

1. From the toolbar, click Visualization > Heatmaps > Heatmap.
2. Click onto the page to add the visualization.
3. From the object inspector go to Data > Data Source > Data, and select the output for the Jaccard coefficients that was created above.
4. Click Calculate.

You'll get a result that looks like the following. With the blue default color palette, the largest Jaccard coefficients will be the darkest blue. Looking for dark patches of the diagonal of the table allows you to locate the pairs of products that have the biggest overlap according to the Jaccard index. In this case, we see strong overlaps between iPhone, iPod, and iPad owners in the top left, and between Samsung owners and people who own non-Mac computers over to the right.

Next

How to Run a Linear Regression in Displayr