Let’s get to coding!
We will start with an example where we take mpg
data and make a scatterplot.
How do we get from this:
The data
head(mpg)
to this:
The plot
Let’s plot!
Load the ggplot2 library:
library(ggplot2)
ggplot
is the base layer.
ggplot()
This is a good place to for us to define our plot’s default data.
ggplot(data = mpg)
There isn’t much being plotted yet… Let’s tell our plot about our mapping, where our x
will be our cty
and y
will be our hwy
.
ggplot(
data = mpg,
mapping = aes(x = cty, y = hwy)
)
Our plot now has enough information to set some automatic axis limits based on the data.
ggplot(
data = mpg,
mapping = aes(x = cty, y = hwy)
) +
geom_point()
We can map the number of cylinders as a set of discrete values to color.
ggplot(
data = mpg,
mapping = aes(x = cty, y = hwy)
) +
geom_point(
mapping = aes(color = factor(cyl))
)
At this point, we have the base of the plot. We can save this to a variable, mpg_base_plot
, and make additional adjustments.
mpg_base_plot <- ggplot(
data = mpg,
mapping = aes(x = cty, y = hwy)
) +
geom_point(
mapping = aes(color = factor(cyl))
)
mpg_base_plot
To add the reference line, we add a layer like so:
mpg_base_plot +
geom_abline(
slope = 1,
intercept = 0,
color = 'black',
linetype = 'dotted'
)
Note that this geom layer can be added on top of a blank plot. All geom_
prefixed functions return an environment
object that holds onto the information we call it with.
ggplot() +
geom_abline(
slope = 1,
intercept = 0,
color = 'black',
linetype = 'dotted'
)
Let’s continue. Our plot looks a bit funny – the grid for the x and y are not 1 to 1. Let’s use a coord_
function to adjust this:
mpg_base_plot +
geom_abline(
slope = 1,
intercept = 0,
color = 'black',
linetype = 'dotted'
) +
coord_fixed(ratio = 1)
We can clean up the plot like so:
mpg_plot <- mpg_base_plot +
geom_abline(
slope = 1,
intercept = 0,
color = 'black',
linetype = 'dotted'
) +
coord_fixed(ratio = 1) +
scale_color_manual(
name = '# of Cyl',
values = c('skyblue','royalblue', 'blue', 'navy')
) +
ggtitle('Miles per gallon') +
theme_light()
mpg_plot
We can further manipulate the plot using things like facet_
.
mpg_plot +
facet_grid(.~class)
Let’s experiment
We can get the base plots from the ggplot cheatsheets on our computer by sourcing this R script.
source('https://goo.gl/3EQSXt')
The magic behind the +
We can discover how the +
is helping us construct these plots by running:
methods('+')
[1] +.Date +.gg* +.POSIXt
see '?methods' for accessing help and source code
From the result, we can see that the +
function is overloaded for objects that match the gg
namespace. If we look at the code for this function, we learn more about how it works.
Object-oriented
We can explore more of how ggplot
works underneath by looking at:
base_plot <- ggplot()
names(base_plot)
[1] "data" "layers" "scales" "mapping" "theme" "coordinates" "facet" "plot_env"
[9] "labels"
It’s an object that can be mutated. Other functions output objects as well.
mpg_mapping <- aes(x = cty, y = hwy)
mpg_mapping
* x -> cty
* y -> hwy
Let’s mutate the base_plot
:
base_plot$data <- mpg
base_plot$mapping <- mpg_mapping
base_plot$layers <- c(base_plot$layers, geom_point())
base_plot
Extensibility
You can also create custom stat_
s, geom_
s, and theme_
s as needed. This vignette explains the object-oriented patterns for ggplot2, and how to extend the library for your needs.
There’s actually a lot we can learn from the source code, such as all possible aes
parameters.
The makings of a pie
Grammar-based graphics lends flexibility
Back to Leland Wilkinson’s point about making a pie – that a pie chart is really a stacked bar chart that has been transformed with polar coordinates where the y is mapped to the angle, a.k.a. theta.
We start with a bar chart:
diamonds_by_cut_base <- ggplot(data = diamonds, mapping = aes(x = cut, fill = cut))
diamonds_by_cut_base +
geom_bar()
Here, we have a stacked bar chart of diamonds grouped by cut.
diamonds_by_cut_stacked <- diamonds_by_cut_base +
geom_bar(width = 1, aes(x=factor("")))
diamonds_by_cut_stacked
Taking the bar chart, we simply “add” a coord_polar
to it.
diamonds_by_cut_stacked +
coord_polar() +
scale_x_discrete("")
By default, coord_polar
maps the theta
from x
and the radius
from y
.
bullseye_coords <- coord_polar()
bullseye_coords$theta
[1] "x"
bullseye_coords$r
[1] "y"
We need to a coord_polar
where the theta
maps from y
:
pie_coords <- coord_polar(theta = "y")
pie_coords$theta
[1] "y"
Now, we can transform the stacked bar chart to a pie chart:
diamonds_by_cut_stacked +
pie_coords
?coord_polar
A layered grammar is powerful
The full grammar consists of:
- The base plot –
ggplot
– with default data
and mapping
s
- Any number of layers –
geom_
or stat_
– each with
data
mapping
- plot’s
mapping
s by default
- defined by
aes
thetics
geom_
- Sometimes defined by default by
stat_
if defined
stat_
- Identity by default
- Sometimes defined by default by
geom_
if defined
position
- Optional, any adjustments necessary to geom positioning
Additionally, the grammar includes control over the whole plot’s
scale
s
- to define how data values map
aes
thetic values
coordinate
s
facet
s
---
title: "Grammar of Graphics in R"
output: html_notebook
---

```{r load_ggplot, include=FALSE}
library(ggplot2)
```

# Let's get to coding!

We will start with an example where we take `mpg` data and make a scatterplot.

How do we get from this:

## The data

```{r view_data}
head(mpg)
```

to this:

## The plot

```{r preview_plot, echo = F}
mpg_plot <- ggplot(
    data = mpg,
    mapping = aes(x = cty, y = hwy)
  ) +
  geom_point(
    mapping = aes(color = factor(cyl))
  ) +
  geom_abline(
    slope = 1,
    intercept = 0,
    color = 'black',
    linetype = 'dotted'
  ) +
  coord_fixed(
    ratio = 1
  ) +
  scale_color_manual(
    name = '# of Cyl',
    values = c('skyblue','royalblue', 'blue', 'navy')
  ) +
  ggtitle('Miles per gallon') +
  theme_light()

mpg_plot
```

# Let's plot!

Load the ggplot2 library:

```{r load_library_no_eval, eval = F}
library(ggplot2)
```

`ggplot` is the base layer.

```{r step00_base}
ggplot()
```

This is a good place to for us to define our plot's default data.

```{r step01_data}
ggplot(data = mpg)
```

There isn't much being plotted yet... Let's tell our plot about our mapping, where our `x` will be our `cty` and `y` will be our `hwy`.

```{r step02_mapping}
ggplot(
    data = mpg,
    mapping = aes(x = cty, y = hwy)
  )
```

Our plot now has enough information to set some automatic axis limits based on the data.

```{r step03_points}
ggplot(
    data = mpg,
    mapping = aes(x = cty, y = hwy)
  ) +
  geom_point()
```

We can map the number of cylinders as a set of discrete values to color.

```{r step04_colors}
ggplot(
    data = mpg,
    mapping = aes(x = cty, y = hwy)
  ) +
  geom_point(
    mapping = aes(color = factor(cyl))
  )
```

At this point, we have the base of the plot.  We can save this to a variable, `mpg_base_plot`, and make additional adjustments.

```{r step05_assign}
mpg_base_plot <- ggplot(
    data = mpg,
    mapping = aes(x = cty, y = hwy)
  ) +
  geom_point(
    mapping = aes(color = factor(cyl))
  )
mpg_base_plot
```


To add the reference line, we add a layer like so:

```{r step06_line}
mpg_base_plot +
  geom_abline(
    slope = 1,
    intercept = 0,
    color = 'black',
    linetype = 'dotted'
  )
```

Note that this geom layer can be added on top of a blank plot.  All `geom_` prefixed functions return an `environment` object that holds onto the information we call it with.

```{r line_layer_example}
ggplot() +
  geom_abline(
    slope = 1,
    intercept = 0,
    color = 'black',
    linetype = 'dotted'
  )
```

Let's continue.  Our plot looks a bit funny -- the grid for the x and y are not 1 to 1.  Let's use a `coord_` function to adjust this:

```{r step07_fixed}
mpg_base_plot +
  geom_abline(
    slope = 1,
    intercept = 0,
    color = 'black',
    linetype = 'dotted'
  ) +
  coord_fixed(ratio = 1)
```

We can clean up the plot like so:

```{r step08_cleanup}
mpg_plot <- mpg_base_plot +
  geom_abline(
    slope = 1,
    intercept = 0,
    color = 'black',
    linetype = 'dotted'
  ) +
  coord_fixed(ratio = 1) +
  scale_color_manual(
    name = '# of Cyl',
    values = c('skyblue','royalblue', 'blue', 'navy')
  ) +
  ggtitle('Miles per gallon') +
  theme_light()
mpg_plot
```

We can further manipulate the plot using things like `facet_`.

```{r facets_example}
mpg_plot +
  facet_grid(.~class)
```

# Let's experiment

We can get the base plots from the ggplot cheatsheets on our computer by sourcing [this R script](https://houstonusers.github.io/intro-to-ggplot2/examples_from_cheatsheet).

```{r eval = F}
source('https://goo.gl/3EQSXt')
```


# The magic behind the `+`

We can discover how the `+` is helping us construct these plots by running:

```{r what_the_plus}
methods('+')
```

From the result, we can see that the `+` function is overloaded for objects that match the `gg` namespace.  If we look [at the code](https://github.com/tidyverse/ggplot2/blob/master/R/plot-construction.r#L39) for this function, we learn more about how it works.

## Object-oriented

We can explore more of how `ggplot` works underneath by looking at:

```{r}
base_plot <- ggplot()
names(base_plot)
```

It's an object that can be mutated.  Other functions output objects as well.

```{r}
mpg_mapping <- aes(x = cty, y = hwy)
mpg_mapping
```

Let's mutate the `base_plot`:

```{r}
base_plot$data <- mpg
base_plot$mapping <- mpg_mapping
base_plot$layers <- c(base_plot$layers, geom_point())
base_plot
```


## Extensibility

You can also create custom `stat_`s, `geom_`s, and `theme_`s as needed.  This [vignette](http://docs.ggplot2.org/current/vignettes/extending-ggplot2.html) explains the object-oriented patterns for ggplot2, and how to extend the library for your needs.

There's actually a lot we can learn from [the source code](https://github.com/tidyverse/ggplot2/tree/master/R), such as all possible [`aes` parameters](https://github.com/tidyverse/ggplot2/blob/master/R/aes.r#L4-L8).

# The makings of a pie

### Grammar-based graphics lends flexibility

Back to Leland Wilkinson's point about making a pie -- that a pie chart is really a stacked bar chart that has been transformed with polar coordinates where the y is mapped to the angle, a.k.a. theta.

### We start with a bar chart:

```{r pie00_bar}
diamonds_by_cut_base <- ggplot(data = diamonds, mapping = aes(x = cut, fill = cut))
diamonds_by_cut_base +
  geom_bar()
```

Here, we have a stacked bar chart of diamonds grouped by cut.

```{r pie01_stacked}
diamonds_by_cut_stacked <- diamonds_by_cut_base +
  geom_bar(width = 1, aes(x=factor("")))

diamonds_by_cut_stacked
```

Taking the bar chart, we simply "add" a `coord_polar` to it.

```{r pie02_bullseye}
diamonds_by_cut_stacked +
  coord_polar()  +
  scale_x_discrete("")
```

By default, `coord_polar` maps the `theta` from `x` and the `radius` from `y`.

```{r what_is_a_coord_anyway}
bullseye_coords <- coord_polar()
bullseye_coords$theta
bullseye_coords$r
```

We need to a `coord_polar` where the `theta` maps from `y`:

```{r pie_coords}
pie_coords <- coord_polar(theta = "y")
pie_coords$theta
```

Now, we can transform the stacked bar chart to a pie chart:

```{r pie03_pie}
diamonds_by_cut_stacked +
  pie_coords
```

```{r}
?coord_polar
```


# A layered grammar is powerful

The full grammar consists of:

  * The base plot -- `ggplot` -- with default `data` and `mapping`s
  * Any number of layers -- `geom_` or `stat_` -- each with
    * `data`
        * plot's `data` by default
    * `mapping`
        * plot's `mapping`s by default
        * defined by `aes`thetics
    * `geom_`
        * Sometimes defined by default by `stat_` if defined
    * `stat_`
        * Identity by default
        * Sometimes defined by default by `geom_` if defined
    * `position`
        * Optional, any adjustments necessary to geom positioning

Additionally, the grammar includes control over the whole plot's

  * `scale`s
    * to define how data values map `aes`thetic values
  * `coordinate`s
  * `facet`s
    * subplots


# Reading and Sources

[A Layered Grammar of Graphics](http://vita.had.co.nz/papers/layered-grammar.pdf)

[Mastering the Grammar](https://rpubs.com/flowertear/224424)

[R for Data Science: Visualizing Data](http://r4ds.had.co.nz/data-visualisation.html#introduction-1)

[Extending ggplot2](http://docs.ggplot2.org/current/vignettes/extending-ggplot2.html)

[The R Graph Gallery](http://www.r-graph-gallery.com/portfolio/ggplot2-package/)

[Data Camp: Data Visualization with ggplot2](https://www.datacamp.com/courses/data-visualization-with-ggplot2-1)

[Swirl: Exploratory Data Analysis](http://swirlstats.com/scn/eda.html)

[ggplot2 Cheatsheet](https://www.rstudio.com/wp-content/uploads/2016/11/ggplot2-cheatsheet-2.1.pdf)

[Telling stories with data using the grammar of graphics](https://codewords.recurse.com/issues/six/telling-stories-with-data-using-the-grammar-of-graphics)

[Introduction to R Graphics with ggplot2](http://tutorials.iq.harvard.edu/R/Rgraphics/Rgraphics.html)

[ggplot2 source code](https://github.com/tidyverse/ggplot2/tree/master/R)

[ggplot2: Elegant Graphics for Data Analysis](http://ggplot2.org/book/)

[The Grammar of Graphics](https://www.amazon.com/Grammar-Graphics-Statistics-Computing/dp/0387245448)

[Semiology of Graphics](https://www.amazon.com/Semiology-Graphics-Diagrams-Networks-Maps/dp/1589482611)
