Visual Exploration

The first tidyverse packages we are going to use are the tibble and ggplot2 ones.

• tibble - data tables (a reimaging of the classic R data.frame)

• ggplot2 - plots (second implementation of Haley’s layered grammar of graphics)

Both of these are automatically loaded when we load the tidyverse library

> library(tidyverse)

In this section we will be focusing on ggplot2. This implements Hadley’s layered grammar of graphics (which builds on Wilkinson’s original grammar of graphics) to allow a very simple and concisely expression of any type of plot.

Creating a Plot

Our data is tibble (tidyverse table/data-frame) containing a subset of the fuel economy data the US Environmental Protection Agency (EPA) provides on cars from 1999 and 2008 (run ?mpg for more details on the data set).

> mpg
# A tibble: 234 x 11
   manufacturer model      displ  year   cyl trans      drv     cty   hwy fl    class
   <chr>        <chr>      <dbl> <int> <int> <chr>      <chr> <int> <int> <chr> <chr>
 1 audi         a4           1.8  1999     4 auto(l5)   f        18    29 p     compact
 2 audi         a4           1.8  1999     4 manual(m5) f        21    29 p     compact
 3 audi         a4           2    2008     4 manual(m6) f        20    31 p     compact
 4 audi         a4           2    2008     4 auto(av)   f        21    30 p     compact
# … with 230 more rows

You probably already have some assumptions about relationships that may exist in this data, such as, the bigger the engine displacement (displ) the few miles-per-gallon (mpg) it will get on the highway (hwy). We can quickly verify this be creating a ggplot.

> ggplot(data=mpg) +
    geom_point(mapping = aes(x=displ, y=hwy))

Interestingly, while things look largely like we might expect, there does appear to be some large-engines outliers that still manage to achieve middle-of-the-road fuel economy.

The ggplot() command creates a coordinate system and set defaults. In this case we have specified our default data source is the mpg tibble. We then add a points geometry layer on top of this. For this layer we specify the mappings from the information in the data set (defaulted to mpg) we wish to convey to to the visual properties that of the points that is going to convey that information (their aesthetics)

• the displ value will be conveyed by the x coordinate of the point and

• the hwy value will be conveyed by the y coordinate of the point.

Two other entirely equivalent ways to generate this graph are

> ggplot(data=mpg, mapping = aes(x=displ, y=hwy)) +
    geom_point()
> ggplot() +
    geom_point(data=mpg, mapping = aes(x=displ, y=hwy))

The first one provides all the geom_point specifications as defaults via ggplot and the second provides none. In generally though you will mostly see the original form as most graphs are generated primarily from one data set (so it makes sense to make it a default) and aesthetics are generally layer specific.

The complete plot specification we will be covering in the next subsections are

> ggplot(data = <DATA>) +
    <GEOM_FUNCTION>(
      mapping = aes(<MAPPINGS>),
      stat = <STAT>,
      position = <POSITION>
    ) + ... +
    <COORDINATE_FUNCTION> +
    <FACET_FUNCTION> +
    <SCALE_FUNCTION> + ... +
    <GUIDE_FUNCTION> + ... +
    <THEME_FUNCTION> + ...

• DATA underlying data set providing the observations

• STAT statistical transformation (stat) of the information to be displayed

• GEOM_FUNCTION geometric object (geom) to represent information

• MAPPINGS how values to be display map to the levels of an aesthetic

• COORDINATE_FUNCTION coordinate system to place the geom into

• POSITION position adjustments in the coordinate system

• FACET_FUNCTION split the plot into subplots

• SCALE_FUNCTION how data values are translated to visual properties

• GUIDE_FUNCTION help readers interpret the plot

• THEME_FUNCTION controls the display of non-date items

Aesthetic Mappings

We have already been introduced to the (mandatory) x and y aesthetics of the point geom. If we run ?geom_point to check the documentation, we will find that points actually have an five more independent aesthetics we can use to encode our data. One of these is colour (or color if you prefer the US spelling). Let’s use this to encode the class of the cars in our data set to see what that may reveal.

> ggplot(data=mpg) +
    geom_point(mapping = aes(x=displ, y=hwy, colour=class))

It seems our large-engine outliers are actually sports cars, which makes sense. We certainly would expect them to have much better fuel economy than the SUVs and pickup trucks with similar sized engines below them.

Our aesthetic mapping is not limited to just aesthetic equals variable, but rather it can be any R expression involving the variables. We can also set the default values used for non-mapped aesthetics by assigning them values outside of aes. For example, let us decrease the point size for fun, and plot gallons-per-100-miles instead of miles-per-gallon as miles-per-gallon makes bad fuel economy less evident (e.g., going from 10 to 15 mpg looks to be the same as going from 25 to 30 mpg, even though the former is a fuel savings of 33% while the later is only 17%).

> ggplot(data=mpg) +
    geom_point(mapping = aes(x=displ, y=100/hwy, colour=class), size=0.75)

Exercises

From the mpg data set help page (?mpg), there are several other variables that we might expect to be related to fuel consumption. This includes the transmission (number of gears and automatic/standard), the drivetrain (front-wheel/rear-wheel/four-wheel), the number of cylinders, and the fuel type.

1. Choose additional geom_point aesthetics (?geom_point) to map these variables too as well and see if there are any obvious patterns.

2. Some aesthetics, like position or size, are continuous, while others, like shape, are discrete. What makes an mpg variables continuous or discrete. What does ggplot handle discrete/continuous mismatches between aesthetics and variables?

Faceting

While mapping variables to aesthetics is useful for helping understand more about our data, it can become overwhelming and hard to tell what is going on (is front wheel drive more fuel efficient, or are just most small cars are front wheel drive?). It is often helpful to compare a common graph (on a common scale) plotted across different subsets of our data in order to reveal patterns. This is called faceting. It is done by adding a facet_wrap (1D) or facet_grid (2D) to our plot.

For example, we can compare our standard fuel economy plot across the different manufactures to get an idea if American manufactures deserve their large gas guzzlers reputation.

> ggplot(data=mpg) +
    geom_point(mapping = aes(x=displ, y=100/hwy, colour=class), size=0.5) +
    facet_wrap(facets = vars(manufacturer))

Here we have used the newer vars syntax to specify what variables to facet on. You will also frequently see the older formula syntax that would look like facets = . ~ manufacture (this is a one-sided formula because facet_wrap is 1D). For the grid variant, you pass both a rows = vars(...) and cols = vars(...) specification or a single rows = ... ~ ... using the older formula syntax (a two sided formula because facet_grid is 2D).

Exercises

1. What happens if you specify multiple variables inside of vars (say class and drv)? How is this expressed using the formula syntax?

2. Use facet_grid to facet on both drv and class. What does this tell us about fuel consumption for the different classes? What happens if class is also used for a colour aesthetic at the same time?

3. Fill in the following template to create the following faceted plot. What do the "free" parameters do (try removing them and see what happens to the plot).

   > ggplot(data=mpg) +
       geom_point(mapping = aes(x=..., y=...)) +
       facet_grid(rows = vars(...), scales="free", space="free")
   

   

Geometric Objects

So far we have been representing our data with a point geom. This is just one of the many geoms (there are over 40 of them!) we can choose from when creating plots, and we can add as many as we want in each plot. For example, we can add a geom_smooth to show the smoothed conditional in our relations along with its 95% confidence interval (the more points there are, and the closer they are together, the more confident we are in our means calculation).

> ggplot(data=mpg) +
    geom_smooth(mapping = aes(x=displ, y=100/hwy)) +
    geom_point(mapping = aes(x=displ, y=100/hwy, colour=class))

In this case we can also avoid some duplicate aes definitions by putting the common ones in the initial ggplot call to make them the defaults.

> ggplot(data=mpg, mapping = aes(x=displ, y=100/hwy)) +
    geom_smooth() +
    geom_point(mapping = aes(colour=class))

Generally, when creating a plot, it is easiest to go to the ggplot2 reference page on the tidyverse website and scroll down through the 40+ geometric objects (geoms) available until we find what we are looking for. Clicking on it brings up a detailed page including many example ggplot calls and their output.

Exercises

1. What geom would you use to draw a line chart? A histogram? To put arbirary text labels on your plot?

2. What happens when we add the group=class mapping to geom_smooth? How does this compare to adding the colour=class mapping?

Statistical Transformations

Data in ggplot actually goes through a series of transformations on its way to be plotted. This includes a specified statistical transformation and a final scale transformation. Values can be pulled from either of these stages in our aesthetics mapping by using the after_stat and after_scale wrappers. The default stat for geom_point is identity (do nothing) because it is used to plot raw values. The default stat for geom_smooth is smooth because it plots the smoothed average and its estimated standard error.

Another example of a geom that has a non-identity default stat is geom_bar. It is stat=count, and it counts the number of observations for each unique group (which is, by default, the interaction of all discrete variables as implied by the aesthetics mapping). This lets us easily do things like generate stacked bar charts giving the number of vehicles for each class and drivetrain type

> ggplot(data=mpg) +
    geom_bar(mapping = aes(x=class, fill=drv), colour="black")

When we add a geom layer, we are being explicitly stating our geom and implicitly about our stat. An alternative is to add a stat layer, which is explicit about our stat and implicit about our geom. The equivalent stat layer to geom_bar is stat_count. Its default geom is bar. This means either of these give us a bar geom with a count stat. The above plot is equally well specified as

> ggplot(data=mpg) +
    stat_count(mapping = aes(x=class, fill=drv), colour="black")

As mentioned earlier, the height of the bar (its y aesthetic) is implicitly coming from the count stat transform, and we can also be explicitly about this mapping by using the after_stat wrapper in our aes. An example of where we might want to do this is to normalize the counts to the unit interval.

> ggplot(data=mpg) +
    geom_bar(mapping = aes(x=class, y=after_stat(count/sum(count)), fill=drv), colour="black")

Exercises

1. Adding stat_summary gives the a summary value along with a min and max bound (defaulting to the mean and its standard error). What would the equivalent geom_* layer be (start with the help page for stat_summary)?

   > ggplot(data=mpg, mapping = aes(x=class, y=100/hwy)) +
       geom_point() + stat_summary(colour="red")
   

2. Provide appropriate fun, fun.min, and fun.max parameters to change the above to showing the median and 25% and 75% quantiles?

Position Adjustments

An interesting thing revealed in explicitly specifying the y aesthetic is that geom_bar (or stat_count) doesn’t actually put the individual bars at the specified position. Rather, it offsets the individual bars for each driveline type upwards so they stack on top of each other to give a stacked bar chart.

This is due to a position adjustment specification which tweaks the layout to achieve various desired effects. As with stats, the various geoms have different default position adjustments. For geom_bar it is position="stack" (equivalently position=position_stack()). We can override this though with a variety of specifications (see ?geom_bar) include dodge, which places the bars side-by-side.

> ggplot(data=mpg) +
    geom_bar(mapping = aes(x=class, y=after_stat(count/sum(count)), fill=drv), position="dodge", colour="black")

As with the stat, the geom_point default is position="identity" (do nothing). A useful override for scatter plots is position="jitter". This perturbs the final positions by a small random amount which, while making the final plot slightly less accurate on a local scale, reveals more large scale detail by avoiding overlapping points. Here we plot this over top of the original scatter plot for reference

> ggplot(data=mpg) +
    geom_point(mapping = aes(x=displ, y=100/hwy, colour=class), position="jitter", alpha=0.75)

Exercises

1. How does geom_jitter and geom_count compare to using position="jitter" with geom_point as above?

2. How would you control the amount of jitter added to the positions?

Coordinate Systems

While one of the most complex part of ggplot2 is the coordinate system, the layered grammar of graphics makes it very easy to use. If we want to override the default Cartesian coordinate system, we just add in a coordinate system layer. There are a number commonly used ones, including

• coord_fixed - Cartesian coordinates with a fixed aspect ratio

• coord_flip - Cartesian coordinates with a x and y flipped

• coord_map - map projections

• coord_polar - polar coordinates

Bar charts in polar coordinates make a variety of interesting looking pie-style charts (these should be avoided due to the numerous interpretation issues inherent in pie-style charts as an internet search will reveal).

> ggplot(data=mpg) +
    geom_bar(mapping = aes(x=class, fill=drv), width=1, colour="black") +
    coord_polar()

Exercises

1. Compare using coord_flip to specifying a y aesthetic mapping instead of an x one for the bar chart.

2. Create a pie chart of the number of vehicles of each class. You will need a mapping that gives a constant radius and incrementing (stacked) angles to your polar coordinates.

Scales and Labels

Each aesthetic is associated with a single shared scale that maps the input range to the output range. Examples we have already seen of this include the coordinate mapping for the x and y aesthetics and the colour mapping for the colour and fill aesthetics. A default is chosen for each aesthetic based on the aesthetics mappings we provide. Adding a scale function allows us to take custom control of this.

The default discrete colour and fill scales use equally spaced hue values. This isn’t ideal as hue isn’t colour blind friendly (1 in every 12 people have some form of colour blindness), nor does it photocopy well. A better choice, for a discrete data set, would be to use the qualitative scheme from ColorBrewer.

> ggplot(data=mpg) +
    geom_point(mapping = aes(x=displ, y=100/hwy, colour=class), position="jitter") +
    scale_colour_brewer(type="qual")

Another common coordinate scale change to make is linear to logarithmic. This converts constant multiples to constant increments, making relative comparisons natural, and is a good choice to expand out small values and compress large ones. Earlier we switched from miles-per-gallon to gallons-per-mile as the former was visually compressing the bad-fuel-economy range. Another option would have been to use a log scale.

> ggplot(data=mpg) +
    geom_point(mapping = aes(x=displ, y=hwy, colour=class), position="jitter") +
    scale_colour_brewer(type="qual") +
    scale_y_log10()

The scale legends are provided by guides. These inherit a lot of their details from the scale specifications, but it is also possible to explicitly configure them on either a global of per-scale/aesthetic level. The former is done by adding a guide_* to the plot with the desired parameters. The later is done by specifying a guide=... argument in a scale_* call or a guide aesthetic map to our plot. As an example of the last of these, the class colour legend is trivially hid by specifying the guide mapping colour="none" (equivalently colour=guide_none()).

ggplot(data=mpg) +
    geom_point(mapping = aes(x=displ, y=100/hwy, colour=class), position="jitter") +
    scale_colour_brewer(type="qual") +
    guides(colour="none")

Details of labels and limits of scales can also be adjusted by providing appropriate options to scale_* and guide_*. These operations are so common though that the convenience functions labs (further ggtitle, xlab, and ylab) and lims (further xlim, ylim, and various expansion routines) have been provided.

> ggplot(data=mpg) +
    geom_point(mapping = aes(x=displ, y=100/hwy, colour=class), position="jitter") +
    scale_colour_brewer(type="qual", labels=c("Two-seater","Compact","Midsize",
                                              "Minivan","Pickup","Subcompact","SUV")) +
    labs(title="Subset of EPA Fuel Economy Data (1999 and 2008)", subtitle="mpg data set",
         x="Engine Displacement", y="Gallons per 100-Miles", colour="Vehicle Class")

The above specification of the legends labels is fragile as changing the data can result in the plot labels becoming mismatched. A minimum solution is to also specify limits=("2seater","compact",...) (this is defaulting to all values in alphabetical order) so both parts are explicit and together. A better solution would be to use the tidyverse forcats package to correct and order the data labels in the data itself.

Exercises

1. Use ggtitle, xlab, and ylab to specify the title and axis labels instead of labs.

2. Use the limit functions to ensure 0 is included in the gallons-per-100-miles axis. Would it be best to do this with lims, ylim, or expand_limits?

3. Override the guide in the following plot so cylinder numbers are shown discretely instead of continuously.

   > ggplot(data=mpg) +
       geom_point(mapping = aes(x=displ, y=100/hwy, colour=cyl), position="jitter")
   

Themes

Themes control the display of all non-data elements of plots. There are several complete themes to choose from, as well as a system of inheritance that makes it possible to specify styling at many levels. For example, axis.title.x.top inherits from axis.title.x, which inherits from axis.title, which inherits from title making it possible to easily specify very general or specific tweaks.

As an example, we can use the minimal theme to entirely change the look of our plot while also moving the legend into the open space in the upper-right corner to recover the area on the far right for plotting.

> ggplot(data=mpg) +
    geom_point(mapping = aes(x=displ, y=100/hwy, colour=class), position="jitter") +
    scale_colour_brewer(type="qual", labels=c("Two-seater","Compact","Midsize",
                                              "Minivan","Pickup","Subcompact","SUV")) +
    labs(title="Subset of EPA Fuel Economy Data (1999 and 2008)", subtitle="mpg data set",
         x="Engine Displacement", y="Gallons per 100-Miles", colour="Vehicle Class") +
    theme_minimal() +
    theme(legend.justification=c("left","top"), legend.position=c(0.025,0.925))

Exercises

1. Make all text in the above plot approximately 25% as smaller. Decrease only the legend text by approximately 25%. Why is it a good idea to use rel when specifying text sizes?

2. In an earlier exercise we created the following plot. Change the orientation of the manufacteur facets on the far right to horizontal from vertical so they are not cut off.

   > ggplot(data=mpg) +
       geom_point(mapping = aes(x=100/hwy, y=model)) +
       facet_grid(rows = vars(manufacturer), scales="free", space="free")