The Grammar of Graphics

Abstract

Part of the R for Artists and Designers at the School of Foundation Studies, Srishti Manipal Institute of Art, Design, and Technology, Bangalore.

1 Introduction

This RMarkdown document is part of the Generic Skills Component (GSK) of the Course of the Foundation Studies Programme at Srishti Manipal Institute of Art, Design, and Technology, Bangalore India. The material is based on A Layered Grammar of Graphics by Hadley Wickham. The course is meant for First Year students pursuing a Degree in Art and Design.

The intent of this GSK part is to build Skill in coding in R, and also appreciate R as a way to metaphorically visualize information of various kinds, using predominantly geometric figures and structures.

All RMarkdown files combine code, text, web-images, and figures developed using code. Everything is text; code chunks are enclosed in fences (```)

2 Goals

At the end of this Lab session, we should: - know the types and structures of tidy data and be able to work with them - be able to create data visualizations using ggplot - Understand aesthetics and scales in `ggplot

3 Pedagogical Note

The method followed will be based on PRIMM:

• PREDICT Inspect the code and guess at what the code might do, write predictions
• RUN the code provided and check what happens
• INFER what the parameters of the code do and write comments to explain. What bells and whistles can you see?
• MODIFY the parameters code provided to understand the options available. Write comments to show what you have aimed for and achieved.
• MAKE : take an idea/concept of your own, and graph it.

3.1 Set Up

The setup code chunk below brings into our coding session R packages that provide specific computational abilities and also datasets which we can use.

To reiterate: Packages and datasets are not the same thing !! Packages are (small) collections of programs. Datasets are just….information.

4 Tidy Data

“Tidy Data” is an important way of thinking about what data typically look like in R.

The three features described in the figure above define the nature of tidy data:

• Variables in Columns
  
• Observations in Rows and
  
• Measurements in Cells.

Data are imagined to be resulting from an experiment. Each variable represents a parameter/aspect in the experiment. Each row represents an additional datum of measurement. A cell is a single measurement on a single parameter(column) in a single observation(row).

4.1 Kinds of Variables

Kinds of Variable are defined by the kind of questions they answer to:

1. What/Who/Where? -> Some kind of Name. Categorical variable
2. What Kind? How? -> Some kind of “Type”. Factor variable ( Categorical with)
3. How Many? How large? -> Some kind of Quantity. Numerical variable. Most Figures in R are computed with variables, and therefore, with columns.

5 Interrogations and Graphs

Creating graphs from data is an act of asking questions and viewing answers in a geometric way. Let us write some simple English descriptions of measures and visuals and see what commands they use in R.

6 Components of the layered grammar of graphics

Layers are used to create the objects on a plot. They are defined by five basic parts:

1. Data (What dataset/spreadsheet am I using?)
2. Mapping (What does each column do in my graph?) ( Metaphors!)
3. Statistical transformation (stat) (Do I have count something first?)
4. Geometric object (geom) (What shape, colour, size…do I want?)
5. Position adjustment (position) (Where do I want it on the graph?)

6.1 Data

We will use “real world” data. Let’s use the penguins dataset in the palmerpenguins package. Run ?penguins in the console to get more information about this dataset.

6.1.1 Head

head(penguins)

## # A tibble: 6 × 8
##   species island    bill_length_mm bill_depth_mm flipper_length_mm body_mass_g sex     year
##   <fct>   <fct>              <dbl>         <dbl>             <int>       <int> <fct>  <int>
## 1 Adelie  Torgersen           39.1          18.7               181        3750 male    2007
## 2 Adelie  Torgersen           39.5          17.4               186        3800 female  2007
## 3 Adelie  Torgersen           40.3          18                 195        3250 female  2007
## 4 Adelie  Torgersen           NA            NA                  NA          NA <NA>    2007
## 5 Adelie  Torgersen           36.7          19.3               193        3450 female  2007
## 6 Adelie  Torgersen           39.3          20.6               190        3650 male    2007

6.1.2 Tail

tail(penguins)

## # A tibble: 6 × 8
##   species   island bill_length_mm bill_depth_mm flipper_length_mm body_mass_g sex     year
##   <fct>     <fct>           <dbl>         <dbl>             <int>       <int> <fct>  <int>
## 1 Chinstrap Dream            45.7          17                 195        3650 female  2009
## 2 Chinstrap Dream            55.8          19.8               207        4000 male    2009
## 3 Chinstrap Dream            43.5          18.1               202        3400 female  2009
## 4 Chinstrap Dream            49.6          18.2               193        3775 male    2009
## 5 Chinstrap Dream            50.8          19                 210        4100 male    2009
## 6 Chinstrap Dream            50.2          18.7               198        3775 female  2009

6.1.3 Dim

dim(penguins)

## [1] 344   8

So we know what our data looks like. We pass this data to ggplot use to plot as follows: in R this creates an empty graph sheet!! Because we have not (yet) declared the geometric shapes we want to use to plot our information.

ggplot(data = penguins) # Creates an empty graphsheet, ready for plotting!!

6.2 Mapping

Now that we have told R what data to use, we need to state what variables to plot and how.

Aesthetic Mapping defines how the variables are applied to the plot, i.e. we take a variable from the data and “metaphorize” it into a geometric feature. We can map variables metaphorically to a variety of geometric things: coordinate, length, height, size, shape, colour, alpha(how dark?)….

The syntax uses: aes(some_geometric_thing = some_variable)

Remember variable = column.

So if we were graphing information from penguins, we might map a penguin’s flipper_length_mm column to the \(x\) position, and the body_mass_g column to the \(y\) position.

6.2.1 Mapping Example-1: Histogram

We can try another example of aesthetic mapping with the same dataset:

6.2.1.1 Plot-1a

ggplot(data = penguins)

6.2.1.2 Plot-1b

ggplot(penguins) + 

# Plot geom = histogram. So we need a quantity on the x
  geom_histogram(
    aes(x = body_mass_g))

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Warning: Removed 2 rows containing non-finite values (stat_bin).

6.2.1.3 Plot-1c

ggplot(penguins) +

# Plot geom = histogram. So we need a quantity on the x
  geom_histogram(
    aes(x = body_mass_g,
        fill = island)    # color aesthetic = another variable
    )

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Warning: Removed 2 rows containing non-finite values (stat_bin).

6.2.2 Mapping Example-2: Boxplot

We can try another example of aesthetic mapping with the same dataset:

6.2.2.1 Plot-2a

ggplot(data = penguins)

6.2.2.2 Plot-2b

ggplot(penguins) + 

# Plot geom = boxplot. So we need a quantity on the x
  geom_boxplot(
    aes(x = body_mass_g))

## Warning: Removed 2 rows containing non-finite values (stat_boxplot).

6.2.2.3 Plot-2c

ggplot(penguins) +

# Plot geom = boxplot. So we need a quantity on the x
  geom_boxplot(
    aes(x = body_mass_g,
        fill = island)    # fill aesthetic = another variable
    )

## Warning: Removed 2 rows containing non-finite values (stat_boxplot).

6.2.3 Mapping Example-3:Distribution

We can try another example of aesthetic mapping with the same dataset:

6.2.3.1 Plot-3a

ggplot(data = penguins)

6.2.3.2 Plot-3b

ggplot(penguins) + 

# Plot geom = histogram. So we need a quantity on the x
  geom_density(
    aes(x = body_mass_g))

## Warning: Removed 2 rows containing non-finite values (stat_density).

6.2.3.3 Plot-3c

ggplot(penguins) +

# Plot geom = histogram. So we need a quantity on the x
  geom_density(
    aes(x = body_mass_g,
        fill = island)    # color aesthetic = another variable
    )

## Warning: Removed 2 rows containing non-finite values (stat_density).

6.2.4 Mapping Example-4

We can try another example of aesthetic mapping with the same dataset:

6.2.4.1 Plot-4a

ggplot(data = penguins)

6.2.4.2 Plot-4b

ggplot(penguins) + 

# Plot geom = histogram. So we need a quantity on the x
  geom_histogram(
    aes(x = body_mass_g))

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Warning: Removed 2 rows containing non-finite values (stat_bin).

6.2.4.3 Plot-4c

ggplot(penguins) +

# Plot geom = histogram. So we need a quantity on the x
  geom_histogram(
    aes(x = body_mass_g,
        fill = island)    # color aesthetic = another variable
    )

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Warning: Removed 2 rows containing non-finite values (stat_bin).

6.3 Position adjustment

Sometimes with dense data we need to adjust the position of elements on the plot, otherwise data points might obscure one another. Bar plots frequently stack or dodge the bars to avoid overlap:

count(x = penguins, species, island) %>%
  ggplot(mapping = aes(x = species, y = n, fill = island)) +
  geom_bar(stat = "identity") +
  ggtitle(label = "A stacked bar chart")

count(x = penguins, species, island) %>%
  ggplot(mapping = aes(x = species, y = n, fill = island)) +
  geom_bar(stat = "identity", position = "dodge") +
  ggtitle(label = "A dodged bar chart")

Sometimes scatterplots with few unique \(x\) and \(y\) values are jittered (random noise is added) to reduce overplotting.

ggplot(data = penguins, 
       mapping = aes(x = species, 
                     y = body_mass_g)) +
  geom_point() +
  ggtitle("A point geom with obscured data points")

## Warning: Removed 2 rows containing missing values (geom_point).

ggplot(data = penguins, 
       mapping = aes(x = species, 
                     y = body_mass_g)) +
  geom_jitter() +
  ggtitle("A point geom with jittered data points")

## Warning: Removed 2 rows containing missing values (geom_point).

6.4 Statistical transformation

A statistical transformation (stat) pre-transforms the data, before plotting. For instance, in a bar graph you might summarize the data by counting the total number of observations within a set of categories, and then plotting the count.

6.4.1 Count

count(x = penguins, island)

## # A tibble: 3 × 2
##   island        n
##   <fct>     <int>
## 1 Biscoe      168
## 2 Dream       124
## 3 Torgersen    52

6.4.2 Count and Bar Graph

mydat <- count(penguins,island)

ggplot(data = mydat) +
    geom_col(aes(x = island, y = n))

6.4.3 Tidy Count and Bar Graph

penguins %>%           # This IS a pipe Operator!!
  
  count(., island) %>% # "." represents what is passed from the preceding command
  
  ggplot(.) +    
  
  geom_col(aes(x = island, y = n))

6.4.4 Count inside the Plot

penguins %>%           # Our pipe Operator
  
  ggplot(.) +          # "." becomes the penguins dataset
  
  geom_bar(aes(x = island)) # Note: y = count, and is computed internally!!

Sometimes you don’t need to make a statistical transformation. For example, in a scatterplot you use the raw values for the \(x\) and \(y\) variables to map onto the graph. In these situations, the statistical transformation is an identity transformation - the stat simply passes in the original dataset and exports the exact same dataset.

6.5 Scale

A scale controls how data is mapped to aesthetic attributes, so we need one scale for every aesthetic property employed in a layer. For example, this graph defines a scale for color:

ggplot(data = penguins, 
       mapping = aes(x = bill_depth_mm, 
                     y = bill_length_mm, 
                     color = species)) +
  geom_point() 

## Warning: Removed 2 rows containing missing values (geom_point).

The scale can be changed to use a different color palette:

ggplot(data = penguins, 
       mapping = aes(x = bill_length_mm, 
                     y = body_mass_g, 
                     color = species)) +
  geom_point() +
  scale_color_brewer(palette = "Dark2",direction = -1)

## Warning: Removed 2 rows containing missing values (geom_point).

Now we are using a different palette, but the scale is still consistent: all Adelie penguins utilize the same color, whereas Chinstrap use a new color, and so do all the Gentoos.

6.6 Coordinate system

A coordinate system (coord) maps the position of objects onto the plane of the plot, and controls how the axes and grid lines are drawn. Plots typically use two coordinates (\(x, y\)), but could use any number of coordinates. Most plots are drawn using the Cartesian coordinate system:

x1 <- c(1, 10)
y1 <- c(1, 5)
p <- qplot(x = x1, y = y1, geom = "point", xlab = NULL, ylab = NULL) +
  theme_bw()
p +
  ggtitle(label = "Cartesian coordinate system")

ggplot(penguins, aes(x = flipper_length_mm, y = body_mass_g)) +
  geom_point() + 
  coord_polar()

## Warning: Removed 2 rows containing missing values (geom_point).

This system requires a fixed and equal spacing between values on the axes. That is, the graph draws the same distance between 1 and 2 as it does between 5 and 6. The graph could be drawn using a semi-log coordinate system which logarithmically compresses the distance on an axis:

p +
  coord_trans(y = "log10") +
  ggtitle(label = "Semi-log coordinate system")

Or could even be drawn using polar coordinates:

p +
  coord_polar() +
  ggtitle(label = "Polar coordinate system")

6.7 Faceting

Faceting can be used to split the data up into subsets of the entire dataset. This is a powerful tool when investigating whether patterns are the same or different across conditions, and allows the subsets to be visualized on the same plot (known as conditioned or trellis plots). The faceting specification describes which variables should be used to split up the data, and how they should be arranged.

ggplot(data = penguins, 
       mapping = aes(x = bill_length_mm, 
                     y = body_mass_g)) +
  geom_point() +
  facet_wrap(~ island)

## Warning: Removed 2 rows containing missing values (geom_point).

ggplot(data = penguins, mapping = aes(x = bill_length_mm, y = body_mass_g, color = sex)) +
  geom_point() +
  facet_grid(species ~ island, scales = "free_y")

## Warning: Removed 2 rows containing missing values (geom_point).

# Ria's explanation: This code did not work becasue....

6.8 Defaults

Rather than explicitly declaring each component of a layered graphic (which will use more code and introduces opportunities for errors), we can establish intelligent defaults for specific geoms and scales. For instance, whenever we want to use a bar geom, we can default to using a stat that counts the number of observations in each group of our variable in the \(x\) position.

Consider the following scenario: you wish to generate a scatterplot visualizing the relationship between penguins’ bill_length and their body_mass. With no defaults, the code to generate this graph is:

ggplot() +
  layer(
    data = penguins, 
    mapping = aes(x = bill_length_mm, 
                  y = body_mass_g),
    geom = "point", 
    stat = "identity", 
    position = "identity"
  ) +
  scale_x_continuous() +
  scale_y_continuous() +
  coord_cartesian()

## Warning: Removed 2 rows containing missing values (geom_point).

The above code:

• Creates a new plot object (ggplot)

• Adds a layer (layer)

  • Specifies the data (penguins)
  • Maps engine bill length to the \(x\) position and body mass to the \(y\) position (mapping)
  • Uses the point geometric transformation (geom = "point")
  • Implements an identity transformation and position (stat = "identity" and position = "identity")

• Establishes two continuous position scales (scale_x_continuous and scale_y_continuous)

• Declares a cartesian coordinate system (coord_cartesian)

How can we simplify this using intelligent defaults?

1. We only need to specify one geom and stat, since each geom has a default stat.

2. Cartesian coordinate systems are most commonly used, so it should be the default.

3. Default scales can be added based on the aesthetic and type of variables.

   • Continuous values are transformed with a linear scaling.
   • Discrete values are mapped to integers.
   • Scales for aesthetics such as color, fill, and size can also be intelligently defaulted.

Using these defaults, we can rewrite the above code as:

ggplot() +
  geom_point(data = penguins, 
             mapping = aes(x = bill_length_mm, 
                           y = body_mass_g))

## Warning: Removed 2 rows containing missing values (geom_point).

This generates the exact same plot, but uses fewer lines of code. Because multiple layers can use the same components (data, mapping, etc.), we can also specify that information in the ggplot() function rather than in the layer() function:

ggplot(data = penguins, 
       mapping = aes(x = bill_length_mm, 
                     y = body_mass_g)) +
  geom_point()

## Warning: Removed 2 rows containing missing values (geom_point).

And as we will learn, function arguments in R use specific ordering, so we can omit the explicit call to data and mapping:

ggplot(penguins, aes(bill_length_mm, body_mass_g)) +
  geom_point()

## Warning: Removed 2 rows containing missing values (geom_point).