Charts for Three or More Variables

The methods that we covered in Chapters 6 and 7 provided an initial approach to exploring the associations between variables, but those methods were limited to two variables at a time. Outside of a basic laboratory experiment, however, there is often a need to look at several variables at once. The methods that we will discuss in this chapter will allow us to do just that; they will allow us to visualize the connections between three or more variables at a time. The following chapter, Chapter 9, will then present methods for describing those complex relationships statistically.

Before we begin, a note about terminology is in order. When an analysis addresses one variable at a time, it's called a univariate analysis. When an analysis addresses the associations between pairs of variables, it's called a bivariate analysis. It would make sense, then, that an analysis that addressed multiple variables would be called a multivariate analysis. However, the term “multivariate” is typically reserved for situations where you specifically have more than one outcome variable. Those kinds of statistics are much more complicated than what we are going to be doing, which is using more than one predictor variable with a single outcome variable. With this in mind, I will generally avoid the term “multivariate” for these procedures and instead discuss “multiple variables.”

Clustered bar chart for means

Our first chart will be a bar chart of means when there is more than one predictor variable. In this situation, a clustered bar chart is often the best choice. It is important to point out that many programs, such as Excel, PowerPoint, and similar programs, may offer to do three-dimensional charts with the bars laid out in a grid. Though there are situations where this would be a reasonable solution, they are rare. Three-dimensional charts are nearly always harder to read accurately than flat charts. For this same reason, adding a false thickness to the bars should be avoided. It simply complicates the charts without adding any usable information. Consequently, a side-by-side chart is typically a better choice as is easier to focus on the data and interpret it accurately.

For this exercise, we will use the warpbreaks data from R’s datasets package. This data set gives the number of breaks in yarn in a loom according to the kind of yarn used (recorded as A and B) and the level of tension in the loom (recorded as L, M, and H, for low, medium, and high).

The first step is to load the datasets package and the warpbreaks data.

Sample: sample_8_1.R

It would be convenient if these data could work directly with R’s barplot() function, like this: barplot(breaks ~ wool*tension, data = warpbreaks). Unfortunately, that will give an error message saying “'height' must be a vector or a matrix,” meaning that the variable containing the height for the bars—which should be the mean number of breaks in this example—must have a different format. We can get the data into the correct format by using a combination of the list() function, which identifies the type of wool and the level of tension as factors (i.e., categorical predictor variables), and tapply(), which applies a function—FUN = mean, in this case—to a ragged array, or an array that may contain empty cells. We can then save the restructured data into a new object called wbdata for “warpbreaks data.”

We can then use wbdata to create the bar plot.

Then we can add a legend using the interactive locator(1) function, which lets us choose a location by clicking the mouse on the plot.

The resulting chart is shown in Figure 32.

32. Grouped Bar Plot for Means

We can finish by cleaning up the workspace.

Scatter plots by groups

The clustered bar chart for means, which we looked at in the last section, is best used when you have two categorical predictor variables and a single quantitative outcome. If, instead, you have one categorical and one quantitative predictor for the quantitative outcome, then a grouped scatter plot can work well. This is simply a scatter plot in which the points are marked, usually by shape or color, according to the categorical variable. It is also possible to include separate fit lines such as linear regression lines or smoothers for each group.

For this example, we will use the iris data from R’s datasets package.

Sample: sample_8_2.R

We will look at the relationship between sepal length and sepal width for the three different species in the iris data.

The easiest way to make a grouped scatter plot in R is with the external car package that we also used for the modified bivariate scatter plot in Chapter 6.

We will use the scatterplot() function, which can also be called with abbreviated name sp(). The important difference between this code and the command for the bivariate scatter plot is the addition of the pipe operator, |, which is used here to separate a grouping variable or factor—Species, in this case—from the rest of the function.

The resulting chart is shown in Figure 33.

33. Scatter Plot by Group

The car package uses both colors and shapes to indicate group membership. By default, it also superimposes a linear regression line and a lowess smoother for each group, matched by color.

We can finish by unloading the packages and clearing the workspace.

Scatter plot matrices

The grouped scatter plot we created in the last section was able to show the relationship between two quantitative variables while indicating group membership on a third, categorical variable. While that chart was impressively information-dense, it did not include all of the variables in the data set. To get all four quantitative variables in a chart, we need to do a scatter plot matrix, which is simply a collection of bivariate scatter plots. There are a few different ways to do this: R’s default pairs() function, pairs() with a custom function, or the scatterplotMatrix() function from the car package. We will explore each approach, but first we need to load our data.

Sample: sample_8_3.R

The first approach we will use is R’s pairs() function. The only argument needed for this function is the name a data frame. However, because the fifth variable in iris is categorical—the species name—we will exclude it by using only the first four columns of data.

The resulting plot is shown in Figure 34.

34. Scatterplot Matrix with pairs()

This is a reasonable plot, but it is not information-dense: there is no indication of group membership, there are no fit lines, and the large cells with the variable names could be used for other purposes.

We can fix these problems in a few steps. The first step is to augment the names on the diagonal with histograms for each variable. We can create a custom function for this with the following code, which was adapted from the code in ?pairs in R’s built-in help. It creates a new function called panel.hist. This function will be saved to the workspace and can then be called when we run the pairs() function again.

We can then load the RColorBrewer package so we can select a palette to indicate group membership in the plots.

After creating the panel.hist function and loading the RColorBrewer package, we can run the pairs() function again with several options specified. The pairs() function has a wide array of options, allowing us to choose, for example, which function will be displayed on the diagonal, the upper panel, the lower panel, etc. (See ?pairs for more information.)

Also, the three species of iris are shown in different colors by calling the RColorBrewer palette Pastel1 in the col attribute and using the unclass() function to break the Species factor into a list of ones, twos, and threes.

The resulting chart is shown in Figure 35.

35. Scatter Plot Matrix with Custom Function

Figure 35 is an improvement over Figure 34, but it can still be improved. Most significantly, it is missing a legend to indicate group membership. It is also potentially troublesome to use a custom function with unknown compatibility issues. Instead, we can use the scatterplotMatrix() function from the car package. Also note in the code below the paste() function in the title attribute main. paste() puts separate strings together into a single string, which makes it possible to write a long title in the R command but keep the code from being too wide.

The previous command produces the chart shown in Figure 36.

36. Scatter Plot Matrix with the scatterplotMatrix() Function from the car Package

Figure 36 accomplishes several things at once:

• It shows the relationship between four quantitative variables and one categorical variable.
• It marks group membership with colors and shapes.
• It provides a legend to the group variable.
• It provides a linear regression line for each plot.
• It provides a smoother with confidence intervals for each plot.
• It provides kernel density estimators with rugplots for each variable.

These factors make Figure 36 the most information-dense chart we have created in this book. This chart also serves as an example of the extraordinary flexibility and power of R, especially with the help of any of the thousands of external packages.

We can finish by returning the palette to the default, unloading the packages, and clearing our workspace.