r4ds/visualize.Rmd

---
layout: default
title: Data Visualization
output: bookdown::html_chapter
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(cache = TRUE)
```

# Visualize Data

> "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? 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?

```{r data, echo=FALSE}
x <- rep(seq(0.2, 1.8, length = 5), 2) + runif(10, -0.15, 0.15)
X <- c(0.02, x, 1.94)
Y <- sqrt(1 - (X - 1)^2)
Y[1:6] <- -1 * Y[1:6]
Y <- Y - 1
order <- sample(1:10)
knitr::kable(round(data.frame(X = X[order], Y = Y[order]), 2))
```

Raw data is difficult to comprehend, but 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.

```{r echo=FALSE, dependson=data}
ggplot2::qplot(X, Y) + ggplot2::coord_fixed(ylim = c(-2.5, 2.5), xlim = c(-2.5, 2.5))
```

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.

## Outline

*Section 1* will get you started making graphs right away. You'll learn how to make several common types of plots, and how to use the `ggplot2` syntax.

*Section 2* will guide you through the geoms, stats, position adjustments, coordinate systems, and facetting schemes that you can use to make many different types of plots with `ggplot2`.  

*Section 3* will teach you the _layered grammar of graphics_, a versatile system for building multi-layered plots that underlies `ggplot2`.

*Section 4* will show you how to customize your plots with labels, legends, color schemes, and more.

## Prerequisites

To access the data sets and functions that we will use in this chapter, load the `ggplot2` package:

```{r echo = FALSE, message = FALSE, warning = FALSE}
library(ggplot2)
```

```{r eval = FALSE}
install.packages("ggplot2")
library(ggplot2)
```

## Basics

Before we look at any graphs, let's begin with a question to explore: Do cars with big engines use more fuel than cars with small engines? 

You probably have an intuitive answer, but try to make your answer precise: 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. 

To learn more about `mpg`, open its help page with the command `?mpg`.

***

*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

```{r eval=FALSE}
library(ggplot2)
```

You will need to reload the package each time you start a new R session.

***

### Scatterplots

The easiest way to understand the `mpg` data set is to visualize it, which means that it is time to make our first graph. To do this, open an R session and run the code below. The code plots the `displ` variable of `mpg` against the `hwy` variable. 

```{r}
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy))
```

Your result will look like the graph above. Does the graph confirm your hypothesis about fuel and engine size?

The graph shows a negative relationship between engine size (`displ`) and fuel efficiency (`hwy`). In other words, cars with big engines use more fuel. But the graph shows us something else as well. 

One group of points seems to fall outside of the linear trend. These cars have a higher mileage than you might expect. Can you tell why? Before we examine these cars, let's review the code that made our graph.

`r bookdown::embed_png("images/visualization-1.png", dpi = 150)`

#### Template

Our code is almost a template for making plots with `ggplot2`.

```{r eval=FALSE}
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy))
```

With `ggplot2`, you begin a 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. 

The first argument of `ggplot()` is the data set to use in the graph. So `ggplot(data = mpg)` initializes a graph that will use the `mpg` data set.

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 other `geom_` functions that you can use as well. Each function creates a different type of layer, and each function takes a mapping argument. We'll learn about all of the geom functions in Section 2.

The mapping argument of your geom function explains where your points should go. You must 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`.

This code suggests a template for making graphs with `ggplot2`. To make a graph, replace the bracketed sections in the code below with a new data set, a new geom function, or a new set of mappings.

```{r eval = FALSE}
ggplot(data = <DATA>) + 
  <GEOM_FUNCTION>(mapping = aes(<MAPPINGS>))
```

The next few subsections will introduce several arguments (and functions) that you can add to the template. Each argument will come with a new set of options---and likely a new set of questions. Hold those questions for now. We will catalogue your options in Section 2. Use this section to become familiar with the `ggplot2` syntax. Once you do, the low level details of `ggplot2` will be easier to understand.

#### Aesthetic Mappings

> "The greatest value of a picture is when it forces us to notice what we never expected to see."---John Tukey

Our plot above revealed a group of cars that had better than expected mileage. How can you explain these cars? 

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 cars or, perhaps, subcompact cars (keep in mind that this data was collected before hybrid trucks and suvs became popular).

You can add a third value, like `class`, to a two dimensional scatterplot by mapping it to an _aesthetic_.

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.

`r bookdown::embed_png("images/visualization-2.png", dpi = 150)`

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.

To map an aesthetic to a variable, set the name of the aesthetic to the name of the variable, _and do this in your plot's `aes()` call_:

```{r}
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy, color = class))
```

`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 cars don't seem like hybrids. In fact, they seem like sports cars---and that's what they 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 large engines.

In the above example, we mapped `class` to the color aesthetic, 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. 

```{r}
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy, size = class))
```

Or we could have mapped `class` to the _alpha_ aesthetic, which controls the transparency of the points. Now the transparency of each point corresponds with its class affiliation. 

```{r}
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy, alpha = class))
```

We also could have mapped `class` to the shape of the points.

```{r warning=FALSE}
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy, shape = class))
```

***

**Tip** - What happened to the suv's? `ggplot2` will only use six shapes at a time. See Section 2 for more details.

***

In each case, you set the name of the aesthetic to the variable to display, and you do this within the `aes()` function. The syntax highlights a useful insight because you also set `x` and `y` to variables within `aes()`. The insight is that the x and y locations of a point are themselves 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 levels 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 as a legend; it explains the mapping between locations and values.

#### Exercises

Now that you know how to use aesthetics, take a moment to experiment with the `mpg` data set. 

* Attempt to match different types of variables to different types of aesthetics. 
    + The continuous variables in `mpg` are: `displ`, `year`, `cyl`, `cty`, `hwy`
    + The discrete variables in `mpg` are: `manufacturer`, `model`, `trans`, `drv`, `fl`, `class`
* Attempt to use more than one aesthetic at a time. 
* Attempt to set an aesthetic to something other than a variable name, like `displ < 5`.

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.

#### Position adjustments

Did you notice that there is another riddle hidden in our scatterplot? The plot displays 126 points, but the `mpg` data set contains 234 observations. Also, the points appear to fall on a grid. Why should this be? 

```{r}
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy))
```

The points appear in a grid because the `hwy` and `displ` measurements in `mpg` are rounded to the nearest integer and tenths values. This also explains why our graph appears to contain 126 points. Many points overlap each other because they have been rounded to the same values of `hwy` and `displ`. 108 points are hidden on top of other points located at the same value.

You can avoid this overplotting problem by setting the position argument of `geom_point()` to "jitter".  `position = "jitter"` adds a small amount of random noise to each point. This spreads the points out since 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 random noise, 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. Occasionally, jittering will reveal a pattern that was hidden within the grid.


### Bar Charts

You now know how to make scatterplots, but there are many different types of plots that you can use to visualize your data. After scatterplots, one of the most used types of plot is the bar chart.

To make a bar chart with `ggplot2` use the function `geom_bar()`.

```{r}
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = cut))
```

The chart above 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 53,940 diamonds, including the `price`, `carat`, `color`, `clarity`, and `cut` of each diamond. The chart shows that more diamonds are available with high quality cuts than with 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.

```{r echo=FALSE}
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = cut, fill = cut))
```

It may be tempting to call the color aesthetic, but for bars the color aesthetic controls the _outline_ of the bar, e.g.

```{r}
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = cut, color = cut))
```

The effect is interesting, sort of psychedelic, but not what we had in mind.

To control the interior fill of a bar, you must call the _fill_ aesthetic.

```{r}
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = cut, fill = cut))
```

If you map the fill aesthetic to a third variable, like `clarity`, you get a stacked bar chart.

```{r}
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = cut, fill = clarity))
```

Bar charts also use different position adjustments than scatterplots. Every geom function in `ggplot2` accepts a position argument, but it wouldn't make sense to set `position = "jitter"` for a bar chart. However, you could set `position = "dodge"` to create an unstacked bar chart.

```{r}
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = cut, fill = clarity), position = "dodge")
```

See Section 2 to learn about other position options.

#### Stats

Bar charts are interesting because they reveal something subtle about many types of plots. Consider our basic bar chart. 

```{r}
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = cut))
```

On the x axis, the chart displays `cut`, a variable in the `diamonds` data set. On the y axis, it displays count. But count is not a variable in the diamonds data set:

```{r}
head(diamonds)
```

Nor did we tell `ggplot2` in our code where to find count values.

```{r eval = FALSE}
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = cut))
```

Where does count come from?

Some graphs, like scatterplots, plot the raw values of your data set. Other graphs, like bar charts, do not plot raw values at all. These graphs apply an algorithm to your data and then plot the results of the algorithm. Consider how often graphs do this.

* **bar charts** and **histograms** bin your data and then plot bin counts
* **smooth lines** (e.g. trend lines) apply a model to your data and then plot the model line
* **boxplots** calculate the quartiles of your data and then plot the quartiles as a box.
* and so on.

`ggplot2` calls the algorithm that a graph uses to transform raw data a _stat_, which is short for statistical transformation. Each geom in `ggplot2` is associated with a stat that it uses to plot your data. `geom_bar()` uses the "bin" stat, which bins raw data and computes bin counts. `geom_point()` uses the "identity" stat, which applies the identity transformation, i.e. no transformation. 

You can change the stat that your geom uses. For example, you can ask `geom_bar()` to use the "identity" stat. This is a useful way to plot data that already lists the heights for each bar, like the data set below.  

```{r}
demo <- data.frame(
  bars = c("bar_1","bar_2","bar_3"),
  counts = c(20, 30, 40)
)

demo
```

To use the identity stat, set the stat argument of `geom_bar()` to "identity".

```{r}
ggplot(data = demo) +
  geom_bar(mapping = aes(x = bars, y = counts), stat = "identity")
```

***

*Tip*: To learn which stat a geom uses, visit the geom's help page, e.g. `?geom_bar`.

***

### Polar charts

Here's another riddle: how is a bar chart similar to a coxcomb plot, like the one below?

```{r echo = FALSE, message = FALSE, fig.show='hold', fig.width=3, fig.height=4}
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = cut, fill = cut))
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = cut, fill = cut), width = 1) + 
  coord_polar()
```

Answer: A coxcomb plot is a bar chart plotted in polar coordinates.

#### Coordinate systems

You can make coxcomb plots with `ggplot2` by first building a bar chart and then plotting it in polar coordinates.

To plot your data in polar coordinates, add `coord_polar()` to your plot call. Polar bar charts will look better if you also set the width parameter of `geom_bar()` to 1. This will ensure that no space appears between the bars.

```{r}
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = cut, fill = cut), width = 1) + 
  coord_polar()
```

You can add `coord_polar()` to any plot in `ggplot2` to draw the plot in polar coordinates. `ggplot2` will map the y variable to $r$ and your x variable to $\theta$. 

#### Facets

Coxcomb plots are especially useful when you make many plots to compare against each other. Each coxcomb will act as a glyph that you can use to compare subgroups of data.

You can create a separate coxcomb plot for each subgroup in your data by _faceting_ your plot. For example, here we create a separate subplot for each level of the `clarity` variable.

```{r fig.height = 7, fig.width = 7}
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = cut, fill = cut), width = 1) + 
  coord_polar() + 
  facet_wrap( ~ clarity)
```

The first subplot displays the group of points that have the `clarity` value `I1`. The second subplot displays the group of points that have the `clarity` value `SI2`. And so on.

To facet your plot on a single discrete variable, add `facet_wrap()` to your plot call. The first argument of `facet_wrap()` is a formula, always a `~` followed by a variable name. 

To facet your plot on the combinations of two variables, add `facet_grid()` to your plot call. The first argument of `facet_grid()` is also a formula. This time the formula should contain two variable names separated by a `~`. 

```{r fig.height = 7, fig.width = 7}
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = cut, fill = cut), width = 1) + 
  coord_polar() + 
  facet_grid(color ~ clarity)
```

Here the first subplot displays all of the points that have an `I1` code for `clarity` _and_ a `D` code for `color`. Don't be confused by the word color here; `color` is a variable name in the `diamonds` data set. `facet_grid(color ~ clarity)` is not invoking the color aesthetic.

faceting works on more than just polar charts. You can add `facet_wrap()` or `facet_grid()` to any plot in `ggplot2`. For example, you could facet our original scatterplot.

```{r fig.height = 6, fig.width = 6}
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy)) +
  facet_wrap(~ class)
```

### Bringing it together

> "Wax on. Wax off."---*The Karate Kid* (1984)

In this section, you learned more than how to make scatterplots, bar charts, and coxcomb plots; you learned a foundation that you can use to make _any_ type of plot with `ggplot2`.

To see this, let's add position adjustments, stats, coordinate systems, and faceting to our code template. In `ggplot2`, each of these parameters will work with every plot and every geom. 

```{r eval = FALSE}
ggplot(data = <DATA>) + 
  <GEOM_FUNCTION>(
     mapping = aes(<MAPPINGS>),
     stat = <STAT>, 
     position = <POSITION>
  ) +
  <COORDINATE_FUNCTION> +
  <FACET_FUNCTION>
```

The template takes seven parameters, the bracketed words that appear in the template. In practice, you rarely need to supply all seven parameters because `ggplot2` will provide useful defaults for everything except the data, the mappings, and the geom function.

The seven parameters in the template are connected by a powerful idea known as the _Grammar of Graphics_, a system for describing plots. The grammar shows that you can uniquely describe _any_ plot as a combination of---you guessed it: a data set, a geom, a set of mappings, a stat, a position adjustment, a coordinate system, and a faceting scheme.

Before we look at the grammar of graphics, let's take a look at the different choices that `ggplot2` offers for geoms, stats, position adjustments, coordinate systems, and facetting schemes.

## The Vocabulary of `ggplot2`

`ggplot2` comes with 37 geom functions, 22 stats, eight coordinate systems, six position adjustments, two facetting schemes, and an uncounted number of aesthetics to map. Each of these components introduces new decisions for you to make and new dilemma's for you to consider.

Tackling these details can seem overwhelming to a new student, but you are ready. You understand the big picture that these details fits into, and you know how to make your own graphs, so you can try things out as you go.

This section will explain all of the options that you can use to make graphs with `ggplot2`. Read through this section once, then return to it as a reference guide when you need it. 

### Geoms

The geom of a plot is the geometric object that the plot uses to represent its data. People often describe plots by the type of geom that they use. For example, bar charts use bar geoms, line charts use line geoms, boxplots use boxplot geoms, and so on.

`ggplot2` provides 37 `geom_` functions that you can use to visualize your data. Each geom is particularly well suited for displaying a certain type of data or a certain type of relationship.

This section organizes geoms according to these relationships. It describes each geom and lists the aesthetics to use with the geom.

Throughout the section we will rely on an important distinction between two types of variables: 

* A variable is **continuous** if you can arrange its values in order _and_ an infinite number of values exists between any two values of the variable. 

    Numbers and date-times are examples of continuous variables. `ggplot2` will treat your variable as continuous if it is a numeric, integer, or a recognizable date-time class (but not a factor, see `?factor`). 

* A variable is **discrete** if it is not continuous. Discrete variables can only contain a finite (or countably infinite) set of unique 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. 

#### Visualizing Distributions

Recall that a variable is a quantity, quality, or property whose value can change between measurements. 

This unique property---that the values of a variable can vary---gives the word "variable" its name. It also motivates all of data science. Scientists attempt to predict the value of variables and to understand what determines what those values will be.

One of the most useful tools in this quest are the values themselves. As you collect more data, the values of a variable will reveal which states of the variable are common, which are rare, and which are seemingly impossible. The pattern of the values that emerges is known as the variable's _distribution_.

##### Discrete distributions

To visualize the distribution of a discrete variable, count how many observations are associated with each value of the variable. You can compute these numbers quickly with R's `table()` function, but the easiest way to visualize the results is with `geom_bar()`.

```{r}
table(diamonds$cut)
```

##### `geom_bar()`

`geom_bar()` counts the number of observations that are associated with each value of a variable and displays the results as a bar. The height of each bar reveals the count of observations that are associated with the x value of the bar.

```{r}
ggplot(data = diamonds) +
  geom_bar(mapping = aes(x = cut))
```

Useful aesthetics for `geom_bar()` are:

* x (required)
* alpha
* color
* fill
* linetype
* size
* weight

Useful position adjustments for `geom_bar()` are

* "stack" (default)
* "dodge"
* "fill"

##### Continuous distributions

Plotting the distribution of a continuous variable is more tricky than plotting the distribution of a discrete variable. 

To reveal the distribution, you must first _bin_ the range of the variable, which means to divide the range into equally spaced intervals. 

`r bookdown::embed_png("images/blank.png", dpi = 150)`

You can then count the number of observations that fall into each bin.

`r bookdown::embed_png("images/blank.png", dpi = 150)`

And display them as a bar, or some other object.

`r bookdown::embed_png("images/blank.png", dpi = 150)`

This method is temperamental because the appearance of the distribution can change dramatically if the bin size changes. As no bin size is "correct," you should explore several bin sizes when examining data.

Several geoms exist to help you, and they almost all use the "bin" stat to implement the above strategy. For each of these geoms, you can set the following arguments for "bin" to use:

* binwidth - the width to use for the bins in the same units as the x variable
* origin - origin of the first bin interval
* right - if `TRUE` bins will be right closed (e.g. points that fall on the border of two bins will be counted with the bin to the left)
* breaks - a vector of actual bin breaks to use. If you set the breaks argument, it will overide the binwidth and origin arguments.

###### Histograms
###### Freqpoly
###### Dotplots
###### Density
###### Boxplots
##### Bivariate Distributions
###### bin2d
###### hex
###### density2d
###### rug
#### Visualizing Relationships
##### Discrete x, discrete y
###### Jitter
##### Discrete x, continuous y
###### Bar Charts
###### Boxplots
###### Dotplots
###### Violin plots
###### crossbar
###### errorbar
###### linerange
###### point range
##### Continuous x, continuous y
###### Points
###### Text
###### Jitter
###### Smooth
###### Quantile
##### Functions
###### line
###### area
###### step
##### Discrete x, discrete y, continuous z
###### raster
###### tile
##### Continuous x, continuous y, continuous z
###### contour
##### Maps

### Mappings

Have you experimented with aesthetics? Great! Here are some things that you may have noticed.

#### Continuous data

A continuous variable can contain an infinite number of values that can be put in order, like numbers or date-times. `ggplot2` will treat your variable as continuous if it is a numeric, integer, or a recognizable date-time structure (but not a factor, see `?factor`). 


If your variable is continuous, `ggplot2` will treat it in a special way. `ggplot2` will

* use a gradient of colors from blue to black for the color aesthetic
* display a colorbar in the legend for the color aesthetic
* not use the shape aesthetic

 `ggplot2` will not use the shape aesthetic to display continuous information 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?

`ggplot2` will treat your variable as continuous if it is a numeric, integer, or a recognizable date-time structure (but not a factor, see `?factor`). 

#### Discrete data

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. 

If your data is discrete, `ggplot2` will:

* 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.
* use equally spaced values of size and alpha
* display up to six shapes for the shape aesthetic.

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.

```{r}
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy, shape = class))
```

See _Section 7_ to learn how to pick your own colors, shapes, sizes, etc. for `ggplot2` to use.

#### Multiple aesthetics

You can use more than one aesthetic at a time. `ggplot2` will combine aesthetic legends when possible.

```{r}
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy, 
    color = drv, shape = drv, size = cty))
```

#### Expressions

You can map an aesthetic to more than a variable. You can map an aesthetic to raw data, or an expression.

```{r}
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy, 
    color = 1:234))
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy, 
    color = displ < 5))
```

```{r}
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy, color = "blue"))
```

#### Setting vs. Mapping

You can also manually set an aesthetic to a specific level. For example, you can make all of the points in your plot blue.

```{r}
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy), color = "blue")
```

To set an aesthetic manually, call the aesthetic as an argument of your geom function. Then pass the aesthetic a value that R will recognize, such as 

* the name of a color as a character string
* the size of a point as a cex expansion factor (see `?par`)
* the shape as a point as a number code

R uses the following numeric codes to refer to the following shapes. 

```{r echo=FALSE}
pchShow <-
  function(extras = c("*",".", "o","O","0","+","-","|","%","#"),
           cex = 2, 
           col = "red3", bg = "gold", coltext = "brown", cextext = 1.1,
           main = "")
  {
    nex <- length(extras)
    np  <- 26 + nex
    ipch <- 0:(np-1)
    k <- floor(sqrt(np))
    dd <- c(-1,1)/2
    rx <- dd + range(ix <- ipch %/% k)
    ry <- dd + range(iy <- 3 + (k-1)- ipch %% k)
    pch <- as.list(ipch) # list with integers & strings
    if(nex > 0) pch[26+ 1:nex] <- as.list(extras)
    plot(rx, ry, type = "n", axes  =  FALSE, xlab = "", ylab = "", main = main)
    abline(v = ix, h = iy, col = "lightgray", lty = "dotted")
    for(i in 1:np) {
      pc <- pch[[i]]
      points(ix[i], iy[i], pch = pc, col = col, bg = bg, cex = cex)
      if(cextext > 0)
          text(ix[i] - 0.4, iy[i], pc, col = coltext, cex = cextext)
    }
  }

pchShow()
```

If you get an odd result, double check that you are calling the aesthetic as its own argument (and not calling it from inside of `mapping = aes()`. 


Here, `ggplot2` treats `color = "blue"` as a mapping because it appears in the mapping argument. `ggplot2` assumes that "blue" is a value in the data space. It uses R's recycling rules to pair the single value "blue" with each row of data in `mpg`. Then `ggplot2` creates a mapping from the value "blue" in the data space to the pinkish color that we see in the visual space. `ggplot2` 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.

If you experience this type of behavior, remember:

* define an aesthetic _within_ the `aes()` function to map levels of the aesthetic to values of data. You would expect a legend after this operation.
* define an aesthetic _outside of_ the `aes()` function to manually set the aesthetic to a specific level. You would not expect a legend after this operation.

Remember:

* define an aesthetic _within_ the `aes()` function to map levels of the aesthetic to values of data. You would expect a legend after this operation.
* define an aesthetic _outside of_ the `aes()` function to manually set the aesthetic to a specific level. You would not expect a legend after this operation.

#### Group aesthetic

The _group_ aesthetic is a useful way to apply a monolithic geom, like a smooth line, to multiple subgroups. 

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.

```{r message = FALSE}
ggplot(data = mpg) + 
  geom_smooth(mapping = aes(x = displ, y = hwy, group = displ < 5))
```

`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.

```{r message = FALSE}
ggplot(data = mpg) + 
  geom_smooth(mapping = aes(x = displ, y = hwy, linetype = drv))
```




### Stats

#### Change a stat

In many cases, it does not make sense to change a geom's default stat. In other cases, you can change or fine tune the stat to make new graphs. 

You can map the heights of bars in a bar chart to data values---not counts---by changing the stat of the bar chart. This works best if your data set contains one observation per bar, e.g.

```{r}
demo <- data.frame(
  a = c("bar_1","bar_2","bar_3"),
  b = c(20, 30, 40)
)
```

By default, `geom_bar()` uses the bin stat, which creates a count for each bar.

```{r}
ggplot(data = demo) +
  geom_bar(mapping = aes(x = a))
```

To change the stat of a geom, set its `stat` argument to the name of a stat. You may need to supply or remove mappings to accomodate the new stat. 

```{r}
ggplot(data = demo) +
  geom_bar(mapping = aes(x = a, y = b), stat = "identity")
```

To find a list of available stats, run `help(package = "ggplot2")`. Each stat is listed as a function that begins with `stat_`. Set a geom's stat argument to the part of the function name that follows the underscore, surrounded in quotes, as above. 

Use consideration when you change a stat. Many combinations of geoms and stats create incompatible results. 

#### Set parameters

Many stats use _parameters_ arguments that fine tune the statistical transformation. For example, the bin stat takes the parameter `width`, which controls the width of the bars in a bar chart. 

To set a parameter of a stat, pass the parameter as an argument to the geom function.

```{r}
ggplot(data = diamonds) +
  geom_bar(mapping = aes(x = cut), width = 1)
```

To learn which parameters are used by a stat, visit the stat's help page, e.g. `?stat_bin`.

#### Use data from a stat

Many stats in `ggplot2` create more data than they display. For example, the `?stat_bin` help page explains that the `stat_bin()` transformation creates four new variables: `count`, `density`, `ncount`, and `ndensity`. `geom_bar()` uses only one of these variables. It maps the `count` variable to the y axis of your plot. 

You can use any of the variables created by a stat in an aesthetic mapping. To use a variable created by a stat, surround its name with a pair of dots, `..`.

```{r message = FALSE, fig.show='hold', fig.width=4, fig.height=4}
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = carat))

ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = carat, 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 `..`

### Positions

At the beginning of this section, you learned how to use the fill aesthetic to make a stacked bar chart. 

```{r}
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = cut, fill = clarity))
```

But what if you don't want a stacked bar chart? What if you want the chart below? Could you make it?

```{r echo = FALSE}
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = cut, fill = clarity), position = "dodge")
```

This chart displays the same 40 color coded bars as the stacked bar chart above. Each bar represents a combination of `cut` and `clarity`. 

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.

To see how such a graph would appear, set `position = "identity"`.

```{r}
ggplot(data = diamonds) + 
  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") +
  ggtitle('Position = "dodge"')
```

#### Position = "fill"

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.

```{r}
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = cut, fill = clarity), position = "fill") +
  ggtitle('Position = "fill"')
```


#### Position = "jitter"

The last type of position doesn't make sense for bar charts, but it is very useful for scatterplots. Recall our first scatterplot.

```{r echo = FALSE}
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy))
```

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).

```{r eval=FALSE}
?position_jitter
```

```{r}
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy), 
    position = position_jitter(width = 0.03, height = 0.3))
```

### Coordinate systems

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 to make a coxcomb plot or a polar clock chart.

```{r echo = FALSE, message = FALSE, fig.show='hold', fig.width=3, fig.height=4}
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = cut, fill = cut))
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = cut, fill = cut)) + 
  coord_flip()
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = cut, fill = cut), width = 1) + 
  coord_polar()
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = cut, fill = cut), width = 1) + 
  coord_polar(theta = "y")
```

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.

#### Cartesian coordinates

`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.

Zooming is not very useful in our bar graph, but it can help us study the sports cars in our scatterplot.

```{r}
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy, color = class)) + 
  coord_cartesian(xlim = c(4.5, 7.5), ylim = c(20, 30))
```

You can use the same arguments to zoom with any of the coordinate functions in `ggplot2`.

***

*Tip*: You can also zoom by adding `xlim()` and/or `ylim()` to your plot call. 

```{r eval = FALSE}
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy, color = class)) + 
  xlim(4.5, 7.5) + 
  ylim(20, 30)
```

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.

***

#### Fixed coordinates

`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.

$$\text{ratio} = \frac{\text{length of one Y unit}}{\text{length of one X unit}}$$

```{r}
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = factor(1), fill = cut)) + 
  coord_fixed(ratio = 0.5)
```

`coord_equal()` does the same thing as `coord_fixed()`.

#### Flipped coordinates

Add `coord_flip()` to your plot to switch the x and y axes.

```{r}
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = cut, fill = cut)) + 
  coord_flip()
```

#### Map coordinates

Add `coord_map()` or `coord_quickmap()` to plot map data on a cartographic projection. See _Section 6_ for more details.

#### Polar coordinates

Add `coord_polar()` to your plot to plot your data in polar coordinates. 

```{r}
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = cut, fill = cut), width = 1) + 
  coord_polar()
```

By default, `ggplot2` will map your y variable to $r$ and your x variable to $\theta$. When applied to a bar chart, this creates a coxcomb plot. 

Reverse this behavior with the argument `theta = "y"`. When applied to a bar chart, this creates a polar clock chart.

```{r}
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = cut, fill = cut), width = 1) + 
  coord_polar(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).

***

*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)`
* `width = 1`
* `theta = "y"`

```{r}
ggplot(data = diamonds) + 
  geom_bar(mapping = aes(x = factor(1), fill = cut), width = 1) + 
  coord_polar(theta = "y")
```

***

#### Transformed coordinates

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.

```{r}
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy)) +
  coord_trans(xtrans = "log", ytran = "log")
```

### Facets

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. 

For example, we can divide our data set into four subgroups based on the `cyl` variable: 

1. all of the cars that have four cylinder engines
2. all of the cars that have five cylinder engines (there are some)
3. all of the cars that have six cylinder engines, and
4. all of the cars that have eight cylinder engines

Or we could divide our data into three groups based on the `drv` variable:

1. all of the cars with four wheel drive (4)
2. all of the cars with front wheel drive (f)
3. all of the cars with rear wheel drive (r)

We could even divide our data into subgroups based on the combination of two variables:

1. all of the cars with four wheel drive (4) and 4 cylinders
2. all of the cars with four wheel drive (4) and 5 cylinders
3. all of the cars with four wheel drive (4) and 6 cylinders
4. all of the cars with four wheel drive (4) and 8 cylinders
5. all of the cars with front wheel drive (f) and 4 cylinders
6. all of the cars with front wheel drive (f) and 5 cylinders
7. all of the cars with front wheel drive (f) and 6 cylinders
8. all of the cars with front wheel drive (f) and 8 cylinders
9. all of the cars with rear wheel drive (r) and 4 cylinders
10. all of the cars with rear wheel drive (r) and 5 cylinders
11. all of the cars with rear wheel drive (r) and 6 cylinders
12. all of the cars with rear wheel drive (r) and 8 cylinders

#### `facet_grid()`

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:

* Which variables determine how the graph is split into rows?
* Which variables determine how the graph is split into columns?
* What parts of the syntax always stay the same? 
* And what does the `.` do?

Make an honest effort at answering these questions, and then read on past the graphs.

```{r}
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy)) +
  facet_grid(drv ~ cyl)
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy)) +
  facet_grid(drv ~ .)
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy)) +
  facet_grid(. ~ cyl)
```

Ready for the answers?

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 

* `"free_y"` - to let y limits vary accross rows
* `"free_x"` - to let x limits vary accross columns
* `"free"` - to let both x and y limits vary

For example, the code below lets the limits of the x axes vary across columns.

```{r}
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy)) +
  facet_grid(drv ~ cyl, scales = "free_x")
```


#### `facet_wrap()`

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.

```{r}
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy)) +
  facet_grid(. ~ class)
```

`facet_wrap()` provides a more pleasant way to facet a plot across many values. It wraps the subplots into a multi-row, roughly square result.

```{r}
ggplot(data = mpg) + 
  geom_point(mapping = aes(x = displ, y = hwy)) +
  facet_wrap(~ class)
```

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.

In other words, you can use the template above to make any graph that you can imagine---at least in theory. Section 2 will examine how this works in practice. The section explains the details of the grammar of graphics works, and it shows how `ggplot2` implements the grammar to build real graphs. 

## The Grammar of Graphics

The "gg" of `ggplot2` stands for the grammar of graphics, a system for describing plots. According to the grammar, a plot is a combination of seven elements:

$$\text{plot} = \Big( \text{data} + \text{stat} + \text{geom} + \text{mappings} + \text{position} \Big) + \text{coordinate system} + \text{facet scheme}$$

You might not be used to thinking of plots in this way, so let's explore the formula above with a thought exercise. If you had to build a graph from scratch, how would you do it? 

Here's one way. To build a plot, you could begin with a data set to visualize and a coordinate system to visualize the data in. For this thought exercise, we will visualize an abbreviated version of the `mpg` data set, and we will use the cartesian coordinate system.

`r bookdown::embed_png("images/visualization-3.png", dpi = 400)`


You could then choose whether to visualize the data in its raw form, or whether to summarize the data with a transformation and then visualize the summary. Let's visualize our data as in its raw form. This would be the same as applying an identity transformation to the data, since an identity transformation returns the data as it is.

`r bookdown::embed_png("images/visualization-4.png", dpi = 400)`


Next, you would need to choose some sort of visual object to represent the observations in your data set. This object will be what you actually draw in the coordinate system. 

Here we will use a set of points. Each point will represent one row of data. Let's call the points "geoms", short for geometrical object. 

`r bookdown::embed_png("images/visualization-5.png", dpi = 400)`

Next, you could map variables in your data to the visual properties of your geoms. These visual properties are what we call aesthetics. Once you do this, the visual information contained in the point will communicate recorded information contained in the data set. 

Let's map the `cyl` variable to the shape of our points.

`r bookdown::embed_png("images/visualization-6.png", dpi = 400)`

One pair of mappings would be particularly important. To place your points into your coordinate system, you would need to map a variable to the x location of the points, which is an aesthetic. Here we map `displ` to the x location.

`r bookdown::embed_png("images/visualization-7.png", dpi = 400)`

And you would need to map a variable to the y location of the points, which is also an aesthetic. Here we map `hwy` to the y location.

`r bookdown::embed_png("images/visualization-8.png", dpi = 400)`

The process creates a complete graph: 

`r bookdown::embed_png("images/visualization-9.png", dpi = 400)`

However, you could modify the graph further. You could choose to adjust the position of the points (or not) and to facet the graph (or not).

`r bookdown::embed_png("images/visualization-10.png", dpi = 400)`

This process works to make any graph. If you change any of the elements involved, you would end up with a new graph. For example, we could change our geom to a line to make a line graph, or to a bar to make a bar chart. Or we could change the position to "jitter" to make a jittered plot.

`r bookdown::embed_png("images/visualization-11.png", dpi = 400)`

You could also switch the data set, coordinate system, or any other component of the graph.

Let's extend the thought expercise to add a model line to the graph. To do this, we will add a new _layer_ to the graph.

### Layers

A layer is a collection of a data set, a stat, a geom, and a position adjustment. You can add a layer to a coordinate system and faceting scheme to make a complete graph, or you can add a layer to an existing graph to make a layered graph.

Let's build a layer that uses the same data set as our previous graph. In this layer, we will apply a "smooth" stat to the data. The stat fits a model to the data and then returns a transformed data set with three new columns: 

* `y` - the value of the model line at each data point
* `ymin` - the y value of the bottom of the confidence interval associated with the model at each data point
* `ymax` - the y value of the top of the confidence interval associated with the model at each point 

`r bookdown::embed_png("images/visualization-12.png", dpi = 400)`

In this layer, we will represent the observations with a line geom. We map the x values of the line to `displ` and we map the y values to our new `y` variable. We won't use a position adjustment.

`r bookdown::embed_png("images/visualization-13.png", dpi = 400)`

We now have a "layer" that we can add to a coordinate system and faceting scheme to make a complete graph.

`r bookdown::embed_png("images/visualization-14.png", dpi = 400)`

Or we can add the layer to our previous graph to make a plot that shows both summary information and raw data.

`r bookdown::embed_png("images/visualization-15.png", dpi = 400)`

For completion, let's add one more layer. This layer will begin with the same data set as the previous layer. It will also use the same stat. However, we will use the ribbon geom to visualize the data points. A ribbon is similar to a shaded region contained by two lines.

We map the top of the ribbon to `ymax` and the bottom of the ribbon to `ymin`. We map the x position of the ribbon to `displ`. We will not use a position adjustment.

We can now add the layer to our graph to show in one plot:

* raw data
* a visual summary of the data (the smooth line)
* the uncertainty associated with the summary

`r bookdown::embed_png("images/visualization-16.png", dpi = 400)`

If you like, you can continue to add layers to the graph (but the graph will soon become cluttered).

The thought exercise shows that the elements of the grammar of graphics work together to build a graph. You can describe any graph with these elements, and each unique combination of elements makes a single, unique graph. You can also extend a graph by adding layers of new data, stats, geoms, mappings, and positions.


In other words, you can extend the grammar of graphics formula indefinitely to make layered plots:

$$
\begin{aligned}
\text{plot} = & \Big( \text{data} + \text{stat} + \text{geom} + \text{mappings} + \text{position} \Big) + \\
& \Big( \text{data} + \text{stat} + \text{geom} + \text{mappings} + \text{position} \Big)^{*} + \\
& \Big( \text{data} + \text{stat} + \text{geom} + \text{mappings} + \text{position} \Big)^{*} + \\
& \text{coordinate system} + \text{facet scheme}
\end{aligned}
$$

### Working with layers

`ggplot2` syntax matches this formulation almost exactly. The basic low level function of `ggplot2` is `layer()` which combines data, stats, geoms, mappings, and positions into a single layer to plot. 

If you have time on your hands, you can use `layer()` to create a multi-level plot like the one above. Initialize your plot with `ggplot()`. Then add as many calls to `layer()` as you like. Give each layer its own `data`, `stat`, `geom`, `mapping`, and `position` arguments. 

```{r message = FALSE}
ggplot() + 
  layer(
    data = mpg, 
    stat = "identity", 
    geom = "point", 
    mapping = aes(x = displ, y = hwy),
    position = "identity"
  ) + 
  layer(
    data = mpg, 
    stat = "smooth", 
    geom = "ribbon", 
    mapping = aes(x = displ, y = hwy),
    position = "identity"
  ) + 
  layer(
    data = mpg, 
    stat = "smooth", 
    geom = "line", 
    mapping = aes(x = displ, y = hwy),
    position = "identity"
  ) +
  coord_cartesian()
```

Although you can build all of your graphs this way, few people do because `ggplot2` supplies some very efficient shortcuts.

For example, you will find in practice that you almost always pair the same geoms with the same stats and position adjustments. For instance, you will almost always use the point geom with the "identity" stat and the "identity" position. Similarly, you will almost always use the bar geom with the "bin" stat and the "stack" position.

The `geom_` functions in `ggplot2` take advantage of these common combinations. Like `layer()`, each geom function builds a layer, but the geom functions preset the geom, stat, and position values of the layer to useful defaults. The geom that appears in the function name becomes the geom of the layer. The stat and postion most commonly asscoiated with the geom become the default stat and position of the layer.

`ggplot2` even provides geom functions for less common, but still useful combinations of geoms, stats, and positions. For example, the function `geom_jitter()` builds a layer that has a point geom, an "identity" stat, and a "jitter" position. The function `geom_smooth()` builds a "layer" that is made of two sub-layers: a line layer that displays a model line and ribbon layer that displays a standard error band.

As a result, `geom_` functions provide a more direct syntax for making plots, one that you are already familiar with from Section 1.

```{r message = FALSE}
ggplot() +
  geom_point(data = mpg, mapping = aes(x = displ, y = hwy)) +
  geom_smooth(data = mpg, mapping = aes(x = displ, y = hwy))
```

#### Multiple geoms

As with `layer()`, you can add multiple geom functions to a single plot call.

This system lets you build sophisticated graphs geom by geom, but it also makes it possible to write repetitive code. For example, the code above repeats the arguments `data = mpg` and `mapping = aes(x = displ, y = hwy)`. Repetition makes your code harder to read and write, and it also increases the chance of typos and errors.

You can avoid repetition by passing the repeated mappings to `ggplot()`. `ggplot2` will treat mappings that appear in `ggplot()` as global mappings to be applied to each layer. For example, we can eliminate the duplication of `mapping = aes(x = displ, y = hwy)` in our previous code with a global mapping argument:

```{r, eval = FALSE}
ggplot(mapping = aes(x = displ, y = hwy)) + 
  geom_point(data = mpg) + 
  geom_smooth(data = mpg)
```

You can even combine global mappings with local mappings to differentiate geoms.

* Mappings that appear in `ggplot()` will be applied to each geom.
* Mappings that appear in a geom function will be applied to that geom only.
* If a local aesthetic mapping conflicts with a global aesthetic mapping, `ggplot2` will use the local mapping. This is arbitrated on an aesthetic by aesthetic basis.

```{r, message = FALSE}
ggplot(mapping = aes(x = displ, y = hwy)) + 
  geom_point(data = mpg, mapping = aes(color = class)) + 
  geom_smooth(data = mpg)
```

This system lets us overlay a single smooth line on a set of colored points. Notice that this would not occur if you add the color aesthetic to the global mappings. In that case, smooth would use the color mapping to draw a different colored line for each class of cars.

You can use the same system to specify a global data set for every layer. In other words,

```{r, eval = FALSE}
ggplot(data = mpg, mapping = aes(x = displ, y = hwy)) + 
  geom_point() + 
  geom_smooth()
```

is analagous to 

```{r, eval = FALSE}
ggplot(mapping = aes(x = displ, y = hwy)) + 
  geom_point(data = mpg) + 
  geom_smooth(data = mpg)
```

As with mappings, you can define a local data argument to override the global data argument on a layer by layer basis.

```{r, message = FALSE, warning = FALSE}
ggplot(data = mpg, mapping = aes(x = displ, y = hwy)) + 
  geom_point() + 
  geom_smooth(data = subset(mpg, cyl == 8))
```

### Recap

Your understanding of the `ggplot2` syntax is now complete. You understand the grammar written into the syntax, and you know how to extend the syntax by adding extra layers to your plot, as well as how to truncate the syntax by relying on `ggplot2`'s default settings.

Only one thing remains. You need to learn the vocabulary of function names and argument options that you can use with your code template.

Section 3 will guide you through these functions and arguments. It catalogues all of the options that `ggplot2` puts at your fingertips for geoms, mappings, stats, position adjustments, and coordinate systems.

## Customizing plots
### Titles
### Guides
### Scales
#### Color
#### Size
#### Shape
### Themes
### Zoom
### Saving plots




## Summary

> "A picture is not merely worth a thousand words, it is much more likely to be scrutinized than words are to be read."---John Tukey