Introduction to vtree

Exploring subsets of data using variable trees

Nick Barrowman, 03-Oct-2021, Version 5.4.6

Introduction

vtree is a flexible tool for calculating and displaying variable trees — diagrams that show information about nested subsets of a data frame. vtree can be used to:

  1. explore a data set interactively

  2. produce customized figures for reports and publications.

Note, however, that vtree is not designed to build or display decision trees.

Given a data frame and simple specifications, vtree will produce a variable tree and automatically label it with counts, percentages, and other summaries.

The sections below introduce variable trees and provide an overview of the features of vtree. Or you can skip ahead and start using the vtree function.

Two examples

Subsets play an important role in almost any data analysis. Imagine a data set of countries that includes variables named population, continent, and landlocked. Suppose we wish to examine subsets of the data set based on the continent variable. Within each of these subsets, we could examine nested subsets based on the population variable, for example, countries with populations under 30 million and over 30 million. We might continue to a third nesting based on the landlocked variable.

Nested subsets are at the heart of questions like the following: Among African countries with a population over 30 million, what percentage are landlocked? The variable tree below provides the answer:

                              

By default, vtree uses the colorful display above (to help distinguish variables and values), but if you prefer a more sedate version, you can specify a single fill color (or simply white):

                              

Even in simple situations like this, it can be a chore to keep track of nested subsets and calculate the corresponding percentages. The denominator used to calculate percentages may also depend on whether the variables have any missing values, as discussed later. Finally, as the number of variables increases, the magnitude of the task balloons, because the number of nested subsets grows exponentially. vtree provides a general solution to the problem of calculating nested subsets and displaying information about them.

Nested subsets arise in all kinds of situations. Consider, for example, flow diagrams for clinical studies, such as the following CONSORT-style diagram, produced by vtree.

                                                  

Both the structure of this variable tree and the numbers shown were automatically determined. When manual calculation and transcription are instead used to populate diagrams like this, mistakes are likely. And although the errors that make it into published articles are often minor, they can sometimes be disastrous. One motivation for developing vtree was to make flow diagrams reproducible. The ability to reproducibly generate variable trees also means that when a data set is updated, a revised tree can be automatically produced.

At the end of this vignette, there is a collection of examples of variable trees using R datasets that you can try.

Basic features of a variable tree

The examples that follow use a data set called FakeData which represents 46 fictitious patients. We’ll start by using just two variables, although variable trees are especially useful with three or more variables. The variable tree below depicts subsets defined by Sex (M or F) nested within subsets defined by disease Severity (Mild, Moderate, Severe, or NA).

A variable tree consists of nodes connected by arrows. At the top of the diagram above, the root node of the tree contains all 46 patients. The rest of the nodes are arranged in successive layers, where each layer corresponds to a specific variable. Note that this highlights one difference between variable trees and some other kinds of trees: each layer of a variable tree corresponds to just one variable. (In a decision tree, by contrast, different branches can have different sequences of variable splits.)

Continuing with the variable tree above, the nodes immediately below the root represent values of Severity and are referred to as the children of the root node. In this case, Severity was missing (NA) for 6 patients, and there is a node for these patients. Inside each of the nodes, the number of patients is displayed and—except for in the missing value node—the corresponding percentage is also shown. Note that, by default, vtree displays “valid” percentages, i.e. the denominator used to calculate the percentage is the total number of non-missing values, 40.

The final layer of the tree corresponds to values of Sex. These nodes represent males and females within subsets defined by each value of Severity. In each of these nodes the percentage is calculated in terms of the number of patients in its parent node.

Like any node, a missing-value node can have children. For example, of the 6 patients for whom Severity is missing, 3 are female and 3 are male. By default, vtree displays the full missing-value structure of the specified variables.

Also by default, vtree automatically assigns a color palette to the nodes of each variable. Severity has been assigned red hues (lightest for Mild, darkest for Severe), while Sex has been assigned blue hues (light blue for females, dark blue for males). The node representing missing values of Severity is colored white to draw attention to it.

Variable trees compared to contingency tables

A tree with two variables is similar to a two-way contingency table. In the example above, Sex is shown within levels of Severity. This corresponds to the following contingency table, where the percentages within each column add to 100%. These are called column percentages.

  Mild Moderate Severe NA
F 11 (58%) 11 (69%) 2 (40%) 3 (50%)
M 8 (42%) 5 (31%) 3 (60%) 3 (50%)

Likewise, a tree with Severity shown within levels of Sex corresponds to a contingency table with row percentages.

While the contingency table above is more compact than the corresponding variable tree, some people find the variable tree more intuitive. When three or more variables are of interest, multi-way contingency tables are often used. These are typically displayed using several two-way tables, but as the number of variables increases, these become increasingly difficult to interpret. Variable trees, on the other hand, have the same simple structure regardless of the number of variables.

Note that contingency tables are not always more compact than variable trees. When most cells of a large contingency table are empty (in which case the table is said to be sparse), the corresponding variable tree may be more compact since empty nodes are not shown.

Features of vtree

vtree is designed to be quick and easy to use, so that it is convenient for data exploration, but also flexible enough that it can be used to prepare publication-ready figures. To generate a basic variable tree, it is only necessary to specify a data frame and some variable names. However extra features extend this basic functionality to provide:

In many cases, you may wish to generate several different variable trees to investigate a collection of variables in a data frame. For example, it is often useful to change the order of variables, prune parts of the tree, etc.

Technical overview

vtree is built on open-source software: in particular Richard Iannone’s DiagrammeR package, which provides an interface to the Graphviz software using the htmlwidgets framework. Additionally, vtree makes use of the Shiny package, and the svg-pan-zoom JavaScript library.

A formal description of variable trees follows.

The root node of the variable tree represents the entire data frame. The root node has a child for each observed value of the first variable that was specified. Each of these child nodes represents a subset of the data frame with a specific value of the variable, and is labeled with the number of observations in the subset and the corresponding percentage of the number of observations in the entire data frame. The nth layer below the root of the variable tree corresponds to the nth variable specified. Apart from the root node, each node in the variable tree represents the subset of its parent defined by a specific observed value of the variable at that layer of the tree, and is labeled with the number of observations in that subset and the corresponding percentage of the number of observations in its parent node.

Note that a node always represents at least one observation. And unlike a contingency table, which can have empty cells, a variable tree has no empty nodes.

The vtree function

Consider a data frame named df, which includes discrete variables v1 and v2. Suppose we wish to produce a variable tree showing subsets based on values of v1 as well as subsets of those subsets based on values of v2. The variable tree can be displayed using the following command:

vtree(df,"v1 v2")

Alternatively, you may wish to assign the output of vtree to an object:

simple_tree <- vtree(df,"v1 v2")

Then it can be displayed later using:

simple_tree

Suppose vtree is called without a list of variables:

vtree(df)

In this case, only the root node is shown, representing the entire data frame. Although a tree with just one node might not seem very useful, we’ll see later that summary information about the whole data frame can be displayed there.

The vtree function has numerous optional parameters. For example, by default vtree produces a horizontal tree (that is, a tree that grows from left to right). To generate a vertical tree, specify horiz=FALSE.

Mini tutorial

This section introduces some basic features of the vtree function.

To display a variable tree for a single variable, say Severity, use the following command:

vtree(FakeData,"Severity")

                                             

By default, next to each layer of the tree, a variable name is shown. In the example above, “Severity” is shown below the corresponding nodes. (For a vertical tree, “Severity” would be shown to the left of the nodes.) If you specify showvarnames=FALSE, no variable names will be shown.

vtree can also be used with dplyr. For example, to rename the Severity variable as HowBad, we can pipe the data frame into the rename function in dplyr, and then pipe the result into vtree:

library(dplyr)
FakeData %>% rename("HowBad"=Severity) %>% vtree("HowBad")

Note that vtree also has a built-in way of renaming variables, which is an alternative to using dplyr.

Large variable trees can be difficult to display in a readable way. One approach that helps is to display the count and percentage on the same line in each node. For example, in the tree above, the label for the Moderate node is on two lines, like this:

                                                                 Moderate
                                                                 16 (40%)

Specifying sameline=TRUE results in single-line labels, like this:

                                                                 Moderate, 16 (40%)

Percentages

By default, vtree shows “valid percentages”, i.e. percentages calculated using the total number of non-missing values as denominator. In the case of Severity, there are 6 missing values, so the denominator is 46 - 6, or 40. There are 19 Mild cases, and 19/40 = 0.475 so the percentage shown is 48%. No percentage is shown in the NA node since missing values are not included in the denominator.

If you prefer the denominator to represent the complete set of observations (including any missing values), specify vp=FALSE. A percentage will be shown in each of the nodes, including any NA nodes.

If you don’t wish to see percentages, specify showpct=FALSE, and if you don’t wish to see counts, specify showcount=FALSE.

Displaying a legend and hiding node labels

To display a legend, specify showlegend=TRUE. Next to each variable name are “legend nodes” representing the values of that variable and colored accordingly. For each variable, the legend nodes are grouped within a light gray box. Each legend node also contains a count (with a percentage) for the value represented by that node in the whole data frame. This is known as the marginal count (and percentage).

When the legend is shown, labels in the nodes of the variable tree are redundant, since the colors of the nodes identify the values of the variables (although the labels may aid readability). If you prefer, you can hide the node labels, by specifying shownodelabels=FALSE:

vtree(FakeData,"Severity Sex",showlegend=TRUE,shownodelabels=FALSE)

                                             

Since Severity is the first variable in the tree, it is not nested within another variable. Therefore the marginal counts and percentages for Severity shown in the legend nodes are identical to those displayed in the nodes of the variable tree. In contrast, for Sex, the marginal counts and percentages are different from what is shown in the nodes of the variable tree for Sex since they are nested within levels of Severity.

Text wrapping

By default, vtree wraps text onto the next line whenever a space occurs after at least 20 characters. This can be adjusted, for example, to 15 characters, by specifying splitwidth=15. To disable line splitting, specify splitwidth=Inf (Inf means infinity, i.e. “do not split”.)

The vsplitwidth parameter is similarly used to control text wrapping in variable names. This is helpful with long variable names, which may be truncated unless wrapping is used. In this case text wrapping occurs not only at spaces, but also at any of the following characters:

. - + _ = / (

For example if vsplitwidth=5, a variable name like First_Emergency_Visit would be split into

                                                                 First_
                                                                 Emergency_
                                                                 Visit

This concludes the mini-tutorial. vtree has many more features, described in the following sections.

Pruning

This section shows how to remove branches from a variable tree.

When a variable tree gets too big, or you are only interested in certain parts of the tree, it may be useful to remove some nodes along with their descendants. This is known as pruning. For convenience, there are several different ways to prune a tree, described below.

The prune parameter

Here’s a variable tree we’ve already seen in various forms:

vtree(FakeData,"Severity Sex")

                                        

Suppose you don’t want the tree to show branches for individuals whose disease is Mild or Moderate. Specifying prune=list(Severity=c("Mild","Moderate")) removes those nodes, and all of their descendants:

vtree(FakeData,"Severity Sex",prune=list(Severity=c("Mild","Moderate")))

                                        

In general, the argument of the prune parameter is a list with an element named for each variable you wish to prune. In the example above, the list has a single element, named Severity. In turn, that element is a vector c("Mild","Moderate") indicating the values of Severity to prune.

Caution: Once a variable tree has been pruned, it is no longer complete. This can sometimes be confusing since not all observations are represented at certain layers of the tree. For example in the tree above, only 11 observations are shown in the Severity nodes and their children.

The keep parameter

Sometimes it is more convenient to specify which nodes should be retained rather than which ones should be discarded. The keep parameter is used for this purpose, and can thus be considered the complement of the prune parameter. For example, to retain the Moderate Severity node:

vtree(FakeData,"Severity Sex",keep=list(Severity="Moderate"))

                                        

Note: In addition to the Moderate node, the missing value node has also been retained. In general, whenever valid percentages are used (which is the default), missing value nodes are retained when keep is used. This is because valid percentages are difficult to interpret without knowing the denominator, which requires knowing the number of missing values.

On the other hand, here’s what happens when vp=FALSE:

vtree(FakeData,"Severity Sex",keep=list(Severity="Moderate"),vp=FALSE)

                                        

The prunebelow parameter

As seen above, a disadvantage of pruning is that in the resulting tree, the counts shown in child nodes may not add up to the counts shown in their parent node.

An alternative is to prune below the specified nodes (i.e. to prune their descendants), so that the counts always add up. In the present example, this means that the Mild and Moderate nodes will be shown, but not their descendants. The prunebelow parameter is used to do this:

vtree(FakeData,"Severity Sex",prunebelow=list(Severity=c("Mild","Moderate")))

                                        

The follow parameter

The complement of prunebelow is follow. Instead of specifying which nodes should be pruned below, this allows you to specify which nodes should be “followed” (that is, not pruned below).

Targeted pruning

This section describes a more flexible way to prune variable trees. To explain this, first note that the prune, keep, prunebelow, and follow parameters specify pruning across all branches of the tree. For example, if you were pruning Severity nested within levels of Sex, the pruning would take place in both the M and F branches.

Sometimes, however, it is preferable to perform pruning only in specified branches of the tree. This is called targeted pruning, and the parameters tprune, tkeep, tprunebelow, and tfollow provide this functionality. However, their arguments have a more complex form than those of the corresponding prune, keep, prunebelow, and follow parameters because they specify the full path from the root of the tree all the way to the nodes to be pruned. For example to remove every Severity node except Moderate, but only for males, the following command can be used:

vtree(FakeData,"Sex Severity",tkeep=list(list(Sex="M",Severity="Moderate")))

                                        

Note that the argument of tkeep is a list of lists, one for each path through the tree. To keep both Moderate and Severe, specify tkeep=list(list(Sex="M",Severity=c("Moderate","Severe"))). Now suppose that, in addition to this, within females,you want to keep just Mild. Use the following specification to do this:

tkeep=list(list(Sex="M",Severity=c("Moderate","Severe")),list(Sex=F",Severity="Mild"))

The prunesmaller parameter

As a variable tree grows, it can become difficult to see the forest for the tree. For example, the following tree is hard to read, even when sameline=TRUE has been specified:

vtree(FakeData,"Severity Sex Age Category",sameline=TRUE)

                                                  

One solution is to prune nodes that contain small numbers of observations. For example if you want to only see nodes with at least 3 observations, you can specify prunesmaller=3, as in this example:

vtree(FakeData,"Severity Sex Age Category",sameline=TRUE,prunesmaller=3)