> "The simple graph has brought more information to the data analyst’s mind than any other device."---John Tukey
Visualization makes data decipherable. Have you ever tried to study a table of raw data? Raw data is difficult to comprehend. You can examine values one at a time, but you cannot attend to many values at once. The data overloads your attention span, which makes it hard to spot patterns in the data. See this for yourself; can you spot the striking relationship between $X$ and $Y$ in the table below?
In contrast, visualized data is easy to understand. Once you plot your data, you can see the relationships between data points---instantly. For example, the graph below shows the same data as above. Here, the relationship between the points is obvious.
This chapter will teach you how to visualize your data with R and the `ggplot2` package. R contains several systems for making graphs, but the `ggplot2` system is one of the most beautiful and most versatile. `ggplot2` implements the *grammar of graphics*, a coherent system for describing and building graphs. With `ggplot2`, you can do more faster by learning one system and applying it in many places.
In *Section 1*, you will learn how to make scatterplots, the most popular type of data visualization. Along the way, you will learn to add information to your plots with color, size, shape, and facets; and how to change the "type" of your plot with _geoms_ .
*Section 2* shows how to build bar charts. Here you will learn how to plot summaries of your data with _stats_ and how to control the placement of objects with with _positions_. You'll also see how to change the _coordinate system_ of your graph.
*Section 3* draws on examples in the first two sections to teach the _gramar of graphics_, a versatile system for describing---and building---any plot.
Try to answer the question with a precise hypothesis: What does the relationship between engine size and fuel efficieny look like? Is it positive? Negative? Linear? Nonlinear? Strong? Weak?
You can test your hypothesis with the `mpg` data set in the `ggplot2` package. The data set contains observations collected by the EPA on 38 models of car. Among the variables in `mpg` are `displ`, a car's engine size in litres, and `hwy`, a car's fuel efficiency on the highway in miles per gallon (mpg). A car with a low fuel efficiency consumes more fuel than a car with a high fuel efficiency when they travel the same distance.
*Tip*: If you have trouble loading `mpg`, its help page, or any of the functions in this chapter, you may need to load the `ggplot2` package with the command
The code below plots the `displ` variable of `mpg` against the `hwy` variable. Open an R session and run the code. Does the graph confirm or refute your hypothesis?
You can immediately see that there is a negative relationship between engine size (`displ`) and fuel efficiency (`hwy`). In other words, cars with big engines have a worse fuel efficiency. But the graph shows us something else as well.
One group of points seems to fall outside the linear trend. These cars have a higher mileage than you might expect. Can you tell why? Before we examine this phenomenon, let's review the code that made our graph.
With `ggplot2`, you begin every plot with the function `ggplot()`. `ggplot()` doesn't create a plot by itself; instead it initializes a new plot that you can add layers to.
You complete your graph by adding one or more layers to `ggplot()`. Here, the function `geom_point()` adds a layer of points to the plot, which creates a scatterplot. `ggplot2` comes with 37 different `geom_` functions that you can use with `ggplot()`. Each function creates a different type of layer, and each function takes a mapping argument.
The mapping argument explains where your points should go. You must always set mapping to a call to `aes()`. The `x` and `y` arguments of `aes()` explain which variables to map to the x and y axes of the graph. `ggplot()` will look for those variables in your data set, `mpg`.
You can use this code as a template to make any graph with `ggplot2`. To make a graph, replace the bracketed sections in the code below with a new data set, a new geom, or a new set of mappings. You can also add functions and arguments to the template that do not appear here.
Let's hypothesize that the cars are hybrids. One way to test this hypothesis is to look at the `class` value for each car. The `class` variable of the `mpg` data set classifies cars into groups such as compact, midsize, and suv. If the outlying points are hybrids, they should be classified as compact, or perhaps subcompact, cars (keep in mind that this data was collected before hybrid trucks and suvs became popular).
There are two ways to add a third value, like `class`, to a two dimensional scatterplot. You can map the value to a new _aesthetic_ or you can divide the plot into _facets_.
An aesthetic is a visual property of the points in your plot. Aesthetics include things like the size, the shape, or the color of your points. You can display a point (like the one below) in different ways by changing its aesthetic properties.
You can convey information about your data by mapping the aesthetics in your plot to the variables in your data set. For example, we can map the colors of our points to the `class` variable. Then the color of each point will reveal its class affiliation.
`ggplot2` will automatically assign a unique level of the aesthetic (here a unique color) to each unique value of the variable. `ggplot2` will also add a legend that explains which levels correspond to which values.
The colors reveal that many of the unusual points are two seater cars. These don't sound like hybrids. In fact, they sound like sports cars---and that's what the points are. Sports cars have large engines like suvs and pickup trucks, but small bodies like midsize and compact cars, which improves their gas mileage. In hindsight, these cars were unlikely to be hybrids since they have such large engines.
Color is one of the most popular aesthetics to use in a scatterplot, but we could have mapped `class` to the size aesthetic in the same way. In this case, the exact size of each point reveals its class affiliation.
Or we could have mapped `class` to the _alpha_, or transparency, of the points. Now the transparency of each point corresponds with its class affiliation.
In each case, we set the name of the aesthetic to the variable to display and we do this within the `aes()` function. The syntax highlights a useful insight because we also set `x` and `y` to variables within `aes()`: the x location and the y location of a point are also aesthetics, visual properties that you can map to variables to display information about the data.
Once you set an aesthetic, `ggplot2` takes care of the rest. It selects a pleasing set of values to use for the aesthetic and it constructs a legend that explains the mapping. For x and y aesthetics, `ggplot2` does not create a legend, but it creates an axis line with tick marks and a label. The axis line acts in the same way as a legend; it explains the mapping between locations and values.
See the help page for `geom_point()` (`?geom_point`) to learn which aesthetics are available to use in a scatterplot. See the help page for the `mpg` data set (`?mpg`) to learn which variables are in the data set.
Have you experimented with aesthetics? Great! Here are some things that you may have noticed.
A continuous variable can contain an infinite number of values that can be put in order, like numbers or date-times. If your variable is continuous, `ggplot2` will treat it in a special way. `ggplot2` will
`ggplot2` will not use the shape aesthetic to display continuous information. Why? Because the human eye cannot easily interpolate between shapes. Can you tell whether a shape is three-quarters of the way between a triangle and a circle? how about five-eights of the way?
A discrete variable can only contain a finite (or countably infinite) set of values. Character strings and boolean values are examples of discrete data. `ggplot2` will treat your variable as discrete if it is not a numeric, integer, or recognizable date-time structure.
* use a set of colors that span the hues of the rainbow. The exact colors will depend on how many hues appear in your graph. `ggplot2` selects the colors in a way that ensures that one color does not visually dominate the others.
If your data requires more than six unique shapes, `ggplot2` will print a warning message and only display the first six shapes. You may have noticed this in the graph above (and below), `ggplot2` did not display the suv values, which were the seventh unique class.
Facets provide a second way to add a variables to a two dimensional graph. When you facet a graph, you divide your data into subgroups and then plot a separate graph, or _facet_, for each subgroup.
The graphs below show what a faceted graph looks like. They also show how you can build a faceted graph with `facet_grid()`. I'm not going to tell you how `facet_grid()` works---well at least not yet. That would be too easy. Instead, I would like you to try to induce the syntax of `facet_grid()` from the code below. Consider:
To facet your graph, add `facet_grid()` to your code. The first argument of `facet_grid()` is always a formula, two variable names separated by a `~`.
`facet_grid()` will use the first variable in the formula to split the graph into rows. Each row will contain data points that have the same value of the variable.
`facet_grid()` will use the second variable in the formula to split the graph into columns. Each column will contain data points that have the same value of the second variable.
This syntax mirrors the rows first, columns second convention of R.
If you prefer to facet your plot on only one dimension, add a `.` to your formula as a place holder. If you place a `.` before the `~`, `facet_grid()` will not facet on the rows dimension. If you place a `.` after the `~`, `facet_grid()` will not facet on the columns dimension.
Facets let you quickly compare subgroups by glancing down rows and across columns. Each facet will use the same limits on the x and y axes, but you can change this behavior across rows or columns by adding a scales argument. Set scales to one of
What if you want to facet on a variable that has too many values to display nicely?
For example, if we facet on `class`, `ggplot2` must display narrow subplots to fit each subplot into the same column. This makes it diffcult to compare x values with precision.
The results of `facet_wrap()` can be easier to study than the results of `facet_grid()`. However, `facet_wrap()` can only facet by one variable at a time.
You can add new data to your scatterplot with aesthetics and facets, but how can you summarize the data that is already there, for example with a trend line?
But the plots are not identical. Each uses a different _geom_, or geometrical object, to represent the data. The first plot uses a set of points to represent the data. The second plot uses a single, smoothed line.
`ggplot2` comes with 37 `geom_` functions that you can use to to visualize your data. Each function will represent the data with a different type of geom, like a bar, a line, a boxplot, a histogram, etc. You select the type of plot you wish to make by calling the geom_ function that draws the geom you have in mind.
Each `geom_` function takes a `mapping` argument. However, the aesthetics that you pass to the argument will change from geom to geom. For example, you can set the shape of points, but it would not make sense to set the shape of a line.
To see which aesthetics your geom uses, visit its help page. To see a list of all available geoms, open the `ggplot2` package help page with `help(package = ggplot2)`.
By default, `geom_smooth()` draws a single smoothed line for the entire data set. To draw a separate line for each group of points, set the group aesthetic to a grouping variable or expression.
`ggplot2` will automatically infer a group aesthetic when you map an aesthetic of a monolithic geom to a discrete variable. Below `ggplot2` infers a group aesthetic from the `linetype = drv` aesthetic. It is useful to combine group aesthetics with secondary aesthetics because `ggplot2` cannot build a legend for a group aesthetic.
This system lets you build sophisticated graphs geom by geom. You can add as many geoms as you like to a single plot call. `ggplot2` will place each new geom on top of the preceeding geom.
You can create a set of global mappings that apply to all geoms by passing a mapping argument to `ggplot()`. For example, we can eliminate the duplication of `mapping = aes(x = displ, y = hwy)` in our previous code by using global mappings:
The smooth line above is a single line with a single color. This does not occur if you add the color aesthetic to the global mappings. Smooth will draw a different colored line for each class of cars.
A bar chart is a graph that uses the bar geom. Bar charts are the most commonly used type of plot after scatterplots.
The chart below displays the total number of diamonds in the `diamonds` data set, grouped by `cut`. The `diamonds` data set comes in `ggplot2` and contains information about 53940 diamonds, including the `price`, `carat`, `color`, `clarity`, and `cut` of each diamond.
```{r}
ggplot(data = diamonds) +
geom_bar(mapping = aes(x = cut))
```
The graph shows that more diamonds are available with high quality cuts than low quality cuts.
A bar has different visual properties than a point, which can create some surprises. For example, how would you create this simple chart? If you have an R session open, give it a try.
Bar charts are interesting because they reveal something subtle about common types of plots.
### Stats
Consider our basic bar chart.
```{r}
ggplot(data = diamonds) +
geom_bar(mapping = aes(x = cut))
```
On the x axis it displays `cut`, a variable in the `diamonds` data set. On the y axis, it displays count. But where does count come from? Count is not a variable in the diamonds data set:
```{r}
head(diamonds)
```
And we didn't tell `ggplot2` in our plot call where to find count values.
```{r eval = FALSE}
ggplot(data = diamonds) +
geom_bar(mapping = aes(x = cut))
```
What is going on here?
Some plots, like scatterplots, plot the raw values in your data set. Other types of graphs, like bar charts and smooth lines, do not plot raw values at all. These graphs apply an algorithm to the data and then plot the results of the algorithm. Consider how many graphs do this.
* **bar charts** and **histograms** bin the data and then plot bin counts
* **smooth lines** apply a model to the data and then plot the model line
* **boxplots** calculate the first, second, and third quartiles of a data set and then plot those summary statistics (among others)
* and so on.
`ggplot2` calls these algorithms _stats_, which is short for statistical transformation. Each geom in `ggplot2` is paired with a stat; although for some geoms, like points, the stat is the identity transformation, i.e. no transformation.
When you use a geom, `ggplot2` automatically applies the geom's stat algorithm in the background. You don't need to worry about the details or even think much about stats.
However, you can change or fine tune a geom's default stat to create interesting and useful plots.
To learn which stat a geom uses, visit the geom's help page. For example, the `?geom_bar` help page shows that `geom_bar()` uses the `stat_bin()` stat by default. To learn about the stat, visit the stat's help page.
To change a geom's stat, set the `stat` argument to the name of a stat in `ggplot2`. You can find a list of these stats by running `help(package = "ggplot2")`. Each stat is represented by a function that begins with `stat_`. The name of the stat is the portion of the function name that appears after `stat_`.
Many combinations of geoms and stats will create incompatible results. However, one useful non-default combination is to pair `geom_bar()` with `stat_identity()`. This combination let's you map the height of each bar to the value of a variable.
```{r}
demo <- data.frame(
a = c(1,2,3),
b = c(20, 30, 40)
)
ggplot(data = demo) +
geom_bar(aes(x = a, y = b), stat = "identity")
```
#### ..variables..
Many stats in `ggplot2` create more data than they display. For example, the `?stat_bin` help page explains that `stat_bin()` uses your raw data to create a new data frame with four columns: `count`, `density`, `ncount`, `ndensity`.
`geom_bar()` maps one of these columns, the `count` column to the y axis of your plot. You can map any of the three remaining columns to your y axis as well. To do this, map the y aesthetic to the stat column name, and surround the column name with a pair of dots, `..`.
```{r}
ggplot(data = diamonds) +
geom_bar(mapping = aes(x = cut, y = ..density..))
```
Note that to do this, you will need to
1. Determine which stat your geom uses
2. Determine which variables the stat creates from its help page
3. Surround the variable name with `..`
Also note that this procedure will not make sense in as many cases as you suppose. Usually stat columns exist for a very narrow purpose. For example, it does not make sense to use `..density..` in a bar chart of discrete values, but `..density..` is a useful alternative to `..count..` when you use a histogram geom (histograms rely on the same stat as bar charts).
geom_histogram(mapping = aes(x = carat, y = ..density..))
```
### Parameters
Two of the graphs in the last section used the `width` argument. `width` is a _parameter_ of the `geom_bar()` function, a piece of information that `ggplot2` uses to build the geom.
Each overlays a smooth geom on a points geom, but each displays a different "type" of smooth line. In the first graph, `ggplot2` draws the result of a loess algorithm. In the second plot, `ggplot2` draws the result of a linear regression.
You can customize the output of `geom_smooth()` with its `method` argument. Set `method` to the name of a model function in R. `geom_smooth()` will display the result of modelling y on x with the function. In the graph above, we set `method = lm` to create the regression line. `lm()` is the R function that builds linear models.
`method` is a _parameter_ of the `geom_smooth()` function, a piece of information that `ggplot2` uses to build the geom. If you do not set the `method` parameter, `ggplot2` defaults to a loess model or a general additive model depending on how many points appear in the graph.
`se` is another parameter of `geom_smooth()`. You can set the `se` parameter of `geom_smooth()` to `FALSE` to prevent `ggplot2` from drawing the standard error band that appears around the smooth line, i.e.
Parameters are different than mappings because you do not set a parameter to a variable in the data set. `ggplot2` uses the value of a parameter directly. In contrast, to use a mapping, `ggplot2` must create a system of equivalencies between values of a variable and levels of an aesthetic.
##### Aesthetics as parameters
The distinction between parameters and mappings makes it easy to customize your graphs. Suppose you want to make a graph like the one below. How would you do it?
If you add `color = "blue"` to the mappings argument, you will get an unexpected result.
```{r}
ggplot(data = mpg) +
geom_point(mapping = aes(x = displ, y = hwy, color = "blue"))
```
`ggplot2` treats `color = "blue"` as a mapping. It assumes that "blue" is a value in the data space. It uses R's recycling rules to assign the single value "blue" to each row of data. Then it creates a mapping from the value "blue" in the data space to the pinkish color that we see in the visual space. It even creates a legend to let you know that the color pink represents the value "blue." The choice of pink is a coincidence; `ggplot2` defaults to pink whenever a single discrete value is mapped to the color aesthetic.
This is not what we want. We want to set the color to blue. In short, we want to treat the color of the points like a parameter and set it directly.
To set an aesthetic as if it were a parameter, set it _outside_ of the `mapping` argument. This will place it outside of the `aes()` function as well.
```{r}
ggplot(data = mpg) +
geom_point(mapping = aes(x = displ, y = hwy), color = "blue")
```
`ggplot2` will treat assignments that appear in the `aes()` call of the mapping argument as mappings. It will treat assignments that appear outside of the mappign argument as parameters.
As with aesthetics, different geoms respond to different parameters. How do you know which parameters to use with a geom? You can always treat a geom's aesthetics as parameters. You can also spot additional parameters by identifying a geom's stat.
### Stats
How does `ggplot2` know where to place the line in our smooth plot?
The y values of the line do not appear in our data set, nor did we give the y values to `ggplot2`. `ggplot2` calculated they y values by applying an algorithm to the data. In this case, `ggplot2` applied a smoothing algorithm to the data.
Many types of graphs plot information that does not appear in the raw data. To do this, the graph first applies an algorithm to the raw data and then plots the results. For example, a boxplot calculates the first, second, and third quartiles of a data set and then plots those summary statistics (among others). A histogram bins the raw data and then counts how many points fall into each bin. It plots those counts on the y axis.
`ggplot2` calls these algorithms _stats_, which is short for statistical transformation. Stats are handled automatically in `ggplot2`. Not every geom uses a stat; but when one does, `ggplot2` will apply the stat in the background.
You can fine tune how a geom implements a stat by passing the geom parameters for the stat to use. To discover which stat a geom uses, visit the geom's help page.
For example, the `?geom_smooth` help page shows that `geom_smooth()` uses the `stat_smooth()` stat by default. If you then open the `?stat_smooth` help page, you will see that `stat_smooth()` takes the arguments `method` and `se` among others. With `ggplot2`, you can supply arguments to the stat called by a geom, by passing the arguments as parameters to the geom.
***
In general practice, you do not need to worry much about stats. Usually one geom will be closely associated with one stat, and `ggplot2` will implement the stat by default. However, stats are an integral part of the `ggplot2` package that you are welcome to modify. To learn more about `ggplot2`'s stat system, see [ggplot2: Elegant Graphics for Data Analysis](http://www.amazon.com/dp/0387981403/ref=cm_sw_su_dp?tag=ggplot2-20).
### Position
What if you didn't want a stacked bar chart? What if you wanted the chart below? Could you make it?
However, the position of the bars within the two charts is different. In the stacked bar chart, `ggplot2` stacked the bars on top of each other if they had the same cut. In the second plot, `ggplot2` placed the bars beside each other if they had the same cut.
You can control this behavior by adding a _position adjustment_ to your call. A position adjustment tells `ggplot2` what to do when two or more objects overlap.
To set a position adjustment, set the `position` argument of your geom function to one of `"identity"`, `"stack"`, `"dodge"`, `"fill"`, or `"jitter"`.
#### Position = "identity"
For many geoms, the default position value is "identity". When `position = "identity"`, `ggplot2` will place each object exactly where it falls in the context of the graph.
This would make little sense for our bar chart. Each bar would start at `y = 0` and would appear directly above the `cut` value that it describes. Since there are seven bars for each value of `cut`, many bars would overlap. The plot will look suspiciously like a stacked bar chart, but the stacked heights will be inaccurate, as each bar actually extends to `y = 0`. Some bars would not appear at all because they would be completely overlapped by other bars.
geom_bar(mapping = aes(x = cut, fill = clarity), position = "identity") +
ggtitle('Position = "identity"')
```
#### Position = "stack"
To avoid confusion, `ggplot2` uses a default "stack" position adjustment for bar charts. When `position = "stack"` `ggplot2` places overlapping objects directly _above_ one another.
Here each bar begins exactly where the bar below it ends.
```{r}
ggplot(data = diamonds) +
geom_bar(mapping = aes(x = cut, fill = clarity), position = "stack") +
ggtitle('Position = "stack"')
```
#### Position = "dodge"
When `position = "dodge"`, `ggplot2` places overlapping objects directly _beside_ one another. This is how I created the graph at the start of the section.
```{r}
ggplot(data = diamonds) +
geom_bar(mapping = aes(x = cut, fill = clarity), position = "dodge") +
When `position = "fill"`, `ggplot2` uses all of the available space to display overlapping objects. Within that space, `ggplot2` scales each object in proportion to the other objects. `position = "fill"` is the most unusual of the position adjustments, but it creates an easy way to compare relative frequencies across groups.
Why does the plot appear to display only 126 points? There are 234 observations in the data set. Also, why do the points appear to be arranged on a grid?
The points appear in a grid because the `hwy` and `displ` measurements were rounded to the nearest integer and tenths values. As a result, many points overlap each other because they've been rounded to the same values of `hwy` and `displ`. This also explains why our graph appears to contain only 126 points. 108 points are hidden on top of other points located at the same value.
This arrangement can cause problems because it makes it hard to see where the mass of the data is. Is there one special combination of `hwy` and `displ` that contains 109 values? Or are the data points more or less equally spread throughout the graph?
You can avoid this overplotting problem by setting the position adjustment to "jitter". `position = "jitter"` adds a small amount of random noise to each point, as we see above. This spreads the points out because no two points are likely to receive the same amount of random noise.
```{r}
ggplot(data = mpg) +
geom_point(mapping = aes(x = displ, y = hwy), position = "jitter")
```
But isn't this, you know, bad? It *is* true that jittering your data will make it less accurate at the local level, but jittering may make your data _more_ accurate at the global level. By jittering your data, you can see where the mass of your data falls on an overplotted grid. Occasionally, jittering will reveal a pattern that was hidden within the grid.
`ggplot2` recognizes `position = "jitter"` as shorthand for `position = position_jitter()`. This is true for the other values of position as well:
* `position = "identity"` is shorthand for `position = position_identity()`
* `position = "stack"` is shorthand for `position = position_stack()`
* `position = "dodge"` is shorthand for `position = position_dodge()`
* `position = "fill"` is shorthand for `position = position_fill()`
You can use the explanded syntax to specify details of the position process. You can also use the expanded syntax to open a help page for each position process (which you will need to do if you wish to learn more).
You can make your bar charts even more versatile by changing the coordinate system of your plot. For example, you could flip the x and y axes of your plot, or you could plot your bar chart on polar coordinates, which creates a coxcomb plot.
To change the coordinate system of your plot, add a `coordinate_` function to your plot call. `ggplot2` comes with seven coordinate functions that each implement a different coordinate system.
`coord_cartesian()` generates a cartesian coordinate system for your plot. `ggplot2` adds a call to `coord_cartesian()` to your plot by default, but you can also manually add this call. Why would you want to do this?
You can set the `xlim` and `ylim` arguments of `coord_cartesian()` to zoom in on a region of your plot. Set each argument to a vector of length 2. `ggplot2` will use the first value as the minimum value on the x or y axis. It will use the second value as the maximum value.
However, `xlim()` and `ylim()` do not provide a true zoom. Instead, they plot the subset of data that appears within the limits. This may change the appearance of elements that rely on unseen data points, such as a smooth line.
`coord_fixed()` also generates a cartesian coordinate system for your plot. However, you can used `coord_fixed()` to set the visual ratio between units on the x axis and units on the y axis. To do this, set the `ratio` argument to the desired ratio in length between y units and x units, e.g.
Add `coord_polar()` to your plot to plot your data in polar coordinates. By default, `ggplot2` will map your y variable to $r$ and your x variable to $\theta$. Reverse this behavior with the argument `theta = "y"`.
You can also use the `start` argument to control where in the plot your data starts, from 0 to 12 (o'clock), and the `direction` argument to control the orientation of the plot (1 for clockwise, -1 for anti-clockwise).
Ignore `width = 1` for now. We will cover the argument in the section on parameters below.
***
*Tip*: `ggplot2` does not come with a pie chart geom, but you can make a pie chart by plotting a stacked bar chart in polar coordinates. To do this, ensure that:
* your x axis only has one value, e.g. `x = factor(1)`
Add `coord_trans()` to plot your data on cartesian coordinates that have been transformed in some way. To use `coord_trans()`, set the `xtrans` and/or `ytrans` argument to the name of a function that you would like to apply to the x and/or y values.
