Lesson notes | Scatter plots and smoothing +lines
+ +1 Introduction
+Scatter plots - which are sometimes called +bivariate plots - allow you to visualize the +relationship between two numerical variables.
+They are among the most commonly used plots because they can provide +an immediate way to see how one numerical variable varies against +another.
+Scatter plots can also display multiple relationships by mapping +additional variable to aesthetic properties, such as color of the +points.
+Trends and relationships in a scatter plot can be made clearer by +adding a smoothing line over the points.
+We will use ggplot to do all that and more. Let’s get started!
+2 Learning +Objectives
+-
+
- You can visualize relationships between numerical variables using
+scatter plots with
+
geom_point().
+ - You can use
coloras an aesthetic +argument to map variables from the dataset onto individual points.
+ - You can change the size, shape, color, fill, and opacity of +geometric objects by setting fixed aesthetics. +
- You can add a trend line to a scatter plot with
+
geom_smooth().
+
3 Childhood diarrheal +diseases in Mali
+We will be using data collected for a prospective observational study +of acute diarrhea in children aged 0-59 months. The +study was conducted in Mali and in early 2020.
+The full dataset can be obtained from Dryad, and the paper can be viewed here.
+A prospective study watches for outcomes, such as the development of +a disease, during the study period and relates this to other factors +such as suspected risk or protection factors.
+Spend some time browsing through this dataset. Each row corresponds +to one patient surveyed. There are demographic, physiological, clinical, +socioeconomic, and geographic variables.
+ + +We will begin by visualizing the relationship between the following +two numerical variables:
+-
+
age_months: the patient’s age in +months on the horizontal x-axis and
+viral_load: the patient’s viral load +on the vertical y-axis
+
4 Scatter plots via
+geom_point()
+We will explore relationships between some numerical variables in the
+malidd data frame.
We will now examine at and run the code that will create the desired +scatter plot, while keeping in mind the GG framework. Let’s take a look +at the code and break it down piece-by-piece.
+Remember that we specify the first two GG layers as arguments (i.e.,
+inputs) within the ggplot() function:
-
+
- We provide the
malidddata frame with the +dataargument, by inputting +data = malidd.
+ - We define the variables to be plotted in the
aesthetics +function of themappingargument, by +inputting +mapping = aes(x = age_months, y = viral_load). +Specifically, the variableage_monthsis mapped to the +xaesthetic, while the variableviral_loadis +mapped to theyaesthetic.
+
We then add the geom_*() function on a
+new layer with a + sign. The geometric
+objects (i.e., shapes) needed for a scatter plot are points, so we add
+geom_point().
After running the following lines of code, you’ll produce the scatter +plot below:
+# Simple scatter plot of viral load vs age
+ggplot(data = malidd,
+ mapping = aes(x = age_months,
+ y = viral_load)) +
+ geom_point()
This suggests that viral load generally decreases +with age.
+-
+
- Using the
malidddata frame, create a scatter plot +showing the relationship between age and height +(height_cm).
+
5 Aesthetic +modifications
+An aesthetic is a visual property of the geometric objects
+(geoms) in your plot. Aesthetics include things like the
+size, the shape, or the color of your points. You can display a point in
+different ways by changing the values of its aesthetic properties.
Remember, there are two methods for changing the aesthetic properties
+of your geoms (in this case, points).
-
+
You can convey information about your data by mapping +the variables in your dataset to aesthetics in your plot. For this +method, you use
aes()in themappingargument +to associate the name of the aesthetic with a variable to +display.
+You can also set the aesthetic properties of your +
geoms manually. Here the aesthetic doesn’t convey +information about a variable, but only changes the appearance of the +plot. To change an aesthetic manually, you set the aesthetic by name as +an argument of yourgeom_*()function; i.e. it goes +outside ofaes().
+
5.1 Mapping data to +aesthetics
+In addition to mapping variables to the x and
+y axes like with did above, variables can be mapped to
+the color, shape, size, opacity, and other visual characteristics of
+geoms. This allows groups of observations to be
+superimposed in a single graph.
To map a variable to an aesthetic, associate the name of the
+aesthetic to the name of the variable inside aes(). This
+way, we can visualize a third variable to our simple two dimensional
+scatter plot by mapping it to a new aesthetic.
For example, let’s map height_cm to the colors of our
+points, to show us how height varies with age and viral load:
ggplot(data = malidd,
+ mapping = aes(x = age_months,
+ y = viral_load)) +
+ geom_point(mapping = aes(color = height_cm))
We see that {ggplot2} has automatically assigned the values of our +variable to an aesthetic, a process known as scaling. +{ggplot2} will also add a legend that explains which levels correspond +to which values.
+Here the points are colored by different shades of the same blue hue, +with darker colors representing lower values.
+This shows us that height increases with age, as expected.
+Instead of a continuous variable like height_cm, we can
+also map a binary variable like breastfeeding, to show us
+the which children are breastfed and which ones are not:
ggplot(data = malidd,
+ mapping = aes(x = age_months,
+ y = viral_load)) +
+ geom_point(mapping = aes(color = breastfeeding))
We get the same gradual color scaling like with did with height. This +communicates a continuum of values, rather than the two distinct values +in our variable - 0 or 1.
+This is because of the data class of the breastfeeding
+variable in malidd:
## [1] "numeric"But even though binary variables are numerical, they represent two +discrete possibilities. So the continuous color scaling in the +plot above is not ideal.
+In cases like this, we add the function factor() around
+the breastfeeding variable to tell ggplot() to
+treat the variable as a factor. Let’s see what happens when we do
+that:
ggplot(data = malidd,
+ mapping = aes(x = age_months,
+ y = viral_load)) +
+ geom_point(mapping = aes(color = factor(breastfeeding)))
When the variable is treated like a factor, the colors chosen are
+clearly distinguishable. With factors, {ggplot2} will automatically
+assign a unique level of the aesthetic (here a unique color) to each
+unique value of the variable. (this is what happened with the
+region variable of the nigerm dataframe that
+we use in the last lesson)
This plot reveals a clear relationship between age and breastfeeding, +as we might expect. Children are likely to stop breastfeeding around 20 +months of age. In this study, no child at or above 25 months was being +breastfed.
+Adding colors to the scatter plot allowed us to visualize a +third variable in addition to the relationship between +age and viral load. The third variable could be either discrete or +continuous.
+-
+
Using the
malidddata frame, create a scatter plot +showing the relationship between age and viral load, and map a third +variable,freqrespi, to color:
+Create the same age vs. height scatterplot again, but this time, +map the binary variable
feverto the color of the points. +Keep in mind thatfevershould be treated as a +factor.
+
5.2 Setting fixed +aesthetics
+Aesthetic arguments set to a fixed value will be static, and the
+visual effect is not data-dependent. To add a fixed aesthetic, we add as
+a direct argument of the geom_*() function; i.e., it goes
+outside of mapping = aes().
Let’s look at some of the aesthetic arguments we can place directly
+within geom_point() to make visual changes to the points in
+our scatter plot:
-
+
color- point color or point outline color
+size- point size
+alpha- point opacity
+shape- point shape
+fill- point fill color (only applies if the point +has an outline)
+
To use these options to create a more attractive scatter plot, you’ll +need to pick a value for each argument that makes sense for that +aesthetic, as shown in the examples below.
+5.2.1 Changing
+color, size and alpha
+Let’s change the color of the points to a fixed value by setting the
+color argument directly within geom_point().
+The color we choose must be a character string that R recognizes as a
+color. Here we will set the point colors to steel blue:
# Modify original scatter plot by setting `color = "steelblue"`
+ggplot(data = malidd,
+ mapping = aes(x = age_months,
+ y = viral_load)) +
+ geom_point(color = "steelblue") # set color
In addition to changing the default color, now we will modify the
+size aesthetic of the points by assigning it to a fixed
+number (in millimeters). The default size is 1 mm, so let’s chose a
+larger value:
# Set size to 2 mm by ading `size = 2`
+ggplot(data = malidd,
+ mapping = aes(x = age_months,
+ y = viral_load)) +
+ geom_point(color = "steelblue", # set color
+ size = 2) # set size (mm)
The alpha aesthetic controls the level of opacity of
+geoms. alpha is also numerical, and ranges
+from 0 (completely transparent) to the default of 1 (completely opaque).
+Let’s make our points more transparent by reducing the opacity:
# Set opacity to 75% by adding `alpha = 0.75`
+ggplot(data = malidd,
+ mapping = aes(x = age_months,
+ y = viral_load)) +
+ geom_point(color = "steelblue", # set color
+ size = 2, # set size (mm)
+ alpha = 0.75) # set level of opacity
Now we can see where multiple points overlap. This is a useful +parameter for scatter plots where there is +overplotting.
+Remember, changing the color, size, or opacity of our points here is +not conveying any information in the data - they are design choices we +make to create prettier plots.
+-
+
- Create a scatter plot with the same variables as the previous
+example, but change the color of the points to
+
cornflowerblue, increase the size of points to 3 mm and set +the opacity to 60%.
+
5.2.2 Changing
+shape and fill
+We can change the appearance of points in a scatter plot with the
+shape aesthetic.
To change the shape of your geoms to a fixed value, set
+shape equal to a number corresponding to your desired
+shape.
{ggplot2} will accept the following numbers:
+
Notice that
+some of the shapes are filled in with red. This indicates that objects
+21-24 are sensitive to both color and fill,
+but the others are only sensitive to color.
First let’s modify our original scatterplot by changing the shapes to +a something that can be filled in:
+# Set shape to fillable circles by adding `shape = 21`
+
+ggplot(data = malidd,
+ mapping = aes(x = age_months,
+ y = viral_load)) +
+ geom_point(shape = 21) # set shapes to display
Fillable shapes can have different colors for the outline and
+interior. Changing the color aesthetic will only change the
+outline of our points:
# Set outline color of the shapes by adding `color = cyan4`
+
+ggplot(data = malidd,
+ mapping = aes(x = age_months,
+ y = viral_load)) +
+ geom_point(shape = 21, # set shapes to display
+ color = "cyan4") # set outline color
Now let’s fill in the points:
+# Set interior color of the shapes by adding `fill = "seagreen"`
+
+ggplot(data = malidd,
+ mapping = aes(x = age_months,
+ y = viral_load)) +
+ geom_point(shape = 21, # set shapes to display
+ color = "cyan4", # set outline color
+ fill = "seagreen") # set fill color
We can improve the readability by increasing size and reducing
+opcaity with size and alpha, like we did
+before:
ggplot(data = malidd,
+ mapping = aes(x = age_months,
+ y = viral_load)) +
+ geom_point(shape = 21, # set shapes to display
+ color = "cyan4", # set outline color
+ fill = "seagreen", # set fill color
+ size = 2, # set size (mm)
+ alpha = 0.75) # set level of opacity
6 Adding a trend +line
+It can be hard to view relationships or trends with just points +alone. Often we want to add a smoothing line in order to see what the +trends look like. This can be especially helpful when trying to +understand regressions.
+To get a better idea of the relationship between these to variables, +we can add a trend line (also known as a best fit line or a smoothing +line).
+To do this, we add the function geom_smooth() to our
+scatter plot:
ggplot(data = malidd,
+ mapping = aes(x = age_months,
+ y = viral_load)) +
+ geom_point() +
+ geom_smooth()## `geom_smooth()` using method = 'loess' and formula = 'y ~ x'
The smoothing line comes after our points an another geometric layer +added onto our plot.
+The default smoothing function used in this scatter plot is “loess” +which stands for for locally weighted +scatter plot smoothing. Loess +smoothing is a process used by many statistical softwares. In {ggplot2} +this generally should be done when you have less than 1000 points, +otherwise it can be time consuming.
+Many other smoothing functions can also be used in
+geom_smooth().
Let’s request a linear regression method. This time we will use a
+generalized linear model by setting the method argument
+inside geom_smooth():
# Change to a linear smoothing function with `method = "glm"`
+ggplot(data = malidd,
+ mapping = aes(x = age_months,
+ y = viral_load)) +
+ geom_point() +
+ geom_smooth(method = "glm")## `geom_smooth()` using formula = 'y ~ x'
By default, 95% confidence limits for these lines are displayed.
+You can suppress the confidence bands by including the argument
+se = FALSE inside geom_smooth():
# Remove confidence interval bands by adding `se = FALSE`
+ggplot(data = malidd,
+ mapping = aes(x = age_months,
+ y = viral_load)) +
+ geom_point() +
+ geom_smooth(method = "glm",
+ se = FALSE)## `geom_smooth()` using formula = 'y ~ x'
In addition to changing the method, let’s add the color
+argument inside geom_smooth() to change the color of the
+line.
# Change the color of the trend line by adding `color = "darkred"`
+ggplot(data = malidd,
+ mapping = aes(x = age_months,
+ y = viral_load)) +
+ geom_point() +
+ geom_smooth(method = "glm",
+ se = FALSE,
+ color = "darkred")## `geom_smooth()` using formula = 'y ~ x'
This linear regression concurs with what we initially observed in the
+first scatter plot. A negative relationship exists between
+age_months and viral_load: as age increases,
+viral load tends to decrease.
Let’s add a third variable from the malidd dataset
+calledvomit. This which is a binary variable that records
+whether or not the patient vomited. We will add the vomit
+variable to the plot by mapping it to the color aesthetic. We will again
+change the smoothing method to generalized additive model
+(“gam”) and make some aesthetic modifications to the line
+in the geom_smooth() layer.
ggplot(data = malidd,
+ mapping = aes(x = age_months,
+ y = viral_load)) +
+ geom_point(mapping = aes(color = factor(vomit))) +
+ geom_smooth(method = "gam",
+ size = 1.5,
+ color = "darkgray")## Warning: Using `size` aesthetic for lines was deprecated in ggplot2
+## 3.4.0.
+## ℹ Please use `linewidth` instead.
+## This warning is displayed once every 8 hours.
+## Call `lifecycle::last_lifecycle_warnings()` to see where this
+## warning was generated.## `geom_smooth()` using formula = 'y ~ s(x, bs = "cs")'
Observe the distribution of blue points (children who vomited) +compared to red points (children who did not vomit). The blue points +mostly occur above the trend line. This shows that higher viral loads +were not only associated with younger children, but that children with +higher viral loads were more likely to exhibit symptoms of vomiting.
+-
+
Create a scatter plot with the
age_monthsand +viral_loadvariables. Set the color of the points to +“steelblue”, the size to 2.5mm, the opacity to 80%. Then add trend line +with the smoothing method “lm” (linear model). To make the trend line +stand out, set its color to “indianred3”.
+Recreate the plot you made in the previous question, but this +time adapt the code to change the shape of the points to tilted +rectangles (number 23), and add the body temperature variable +(
temp) by mapping it to fill color of the +points.
+
7 Summary
+Scatter plots display the relationship between two numerical +variables.
+With medium to large datasets, you may need to play around with the +different modifications to scatter plots we saw such as adding trend +lines, changing the color, size, shape, fill, or opacity of the points. +This tweaking is often a fun part of data visualization, since you’ll +have the chance to see different relationships emerge as you tinker with +your plots.
+Contributors
+The following team members contributed to this lesson: +
JOY VAZ
Loves doing science and teaching science
ADMIN TEAM
The GRAPH Courses team is building epidemiological training courses to enhance disease surveillance and data science for public health across the globe
References
+Some material in this lesson was adapted from the following +sources:
+-
+
- Ismay, Chester, and Albert Y. Kim. 2022. A ModernDive into R and +the Tidyverse. https://moderndive.com/. +
- Kabacoff, Rob. 2020. Data Visualization with R. https://rkabacoff.github.io/datavis/. +
- Giroux-Bougard, Xavier, Maxwell Farrell, Amanda Winegardner, Étienne +Low-Decarie and Monica Granados. 2020. Workshop 3: Introduction to +Data Visualisation with {ggplot2}. http://r.qcbs.ca/workshop03/book-en/. +
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