Slide 5: Graphics in R

• R is renown for it's plotting facilities; not only does it have all the well known graphs, it also offers an opportunity to build an entirely new type of graph
• There three well known graphics in R; “base graphics”, “grid graphics (often implemented with package Lattice)” and “ggplot2”
• On start-up, R initiates a graphical device; calls X11() IN UNIX, windows() in Windows and quartz() in mac
• Plotting functions fall under three types of commands; High-level, Low-level, and Interactive
• Plots can be customized with “graphical parameters”

• They are designed to generate a complete plot with axes, labels and titles unless they are suppressed (with graphical parameters)
• They start a new plot
• Core R's plotting function is plot()
• plot() can produce a variety of different plots depending on type/class of first argument (hence, plot() is completely reliant on class(object))

• If only “x” is given only;
  • if it is a time series object (class = ts), a line plot is produced; other wise if it's numeric a scatter plot of it's index against it (x) is generated
  • if class(x) = "factor", a bar plot is produced
  • it's an error when class(x) == "character" as plot needs a finite object to set a plotting window
    
• If two variables are given and they are both numeric, output is a scatter plot

• If a factor and a numeric vector are given, box plots are produced
• If both vectors are factors, stacked bar plot is produced
• If objected parsed is not a vector but a matrix, data frame or list, plot() will make plots per elements type
• We produce a few of these as example using plain plot(obj) (without changing/giving other arguments)

• In all these plots, axis, labels (except title) and in some, color is give, this makes them communicative
• However, they might not be aesthetically up to requirements, this can be changed by passing other arguments including suppression of axis

• Type of plot produced by plot() depends on first (and “y”) argument, but how it is generated depends on values parsed to other argument
• Plot type can also be changed with argument “type”, though do this when sure it makes sense
• “xlim” and “ylim” define x and y limits (min and max axis values), this can be changed especially if need a bit more padding

• For customized axis like logs, argument “axes” can be suppressed
• To annotate plot with additional graphical parameters, add them as argument to high and low level plots or make a call to par()… more on this later (read ?par)

• hist() for histograms (univariate continuous distributions)
• boxplot() for box-and-whiskers plot (for univariate numerical variables alone or categorised by a categorical variable)
• barplot() for bar plots (for categorical distribution)
• pie() for pie chart (for categorical distribution)

• These functions add more information to an existing plot
• Used to customize plots
• Some of the most frequently used functions are; point(), lines(), text(), title(), abline(), polygon(), legend(), and axis()
• We use some of these when plotting some of the example distributions

• Interaction means extracting or adding information to a plot using a mouse (rather than inputting data to plot)
• Two function for interaction in R are locator() and identify()
• locator(n, type): one can select “n” number of points using left mouse button and if type is not specified, a list with two components x and y is outputted otherwise plotting over selected points given “type” is done
• locator() is particularly handy in locating position for legends, and labels e.g. text(locator(1), "Outlier", adj=0)

• identify(x, y, labels) is used to highlight any of the points defined by x and y (using left mouse button)
• These can be used to identify certain points and possibly label

Demonstration on interacting with graphics

• Almost every aspect of a plot can be customized by graphical parameters
• Graphical parameters come in “name=value” pair with all having a default value
• Accessing current default parameters call par() for complete list
• For a specific list call par detailing parameter of interest par("parameter") e.g. par("mfrow")
• Changing any parameters can be done globally (not recommended) or individually

• Plotting of any distribution depends on whether it's univariate (one variable), bi-variate (two variables) or multi-variate
• Plots for univariate categorical variables (dichotomous included) are:
  • Pie charts (for few values e.g. 2)
  • Bar plots, and
  • Cleveland's dot plots

• Bi-variate plots
  • Stacked/besides bar plots
  • Four-fold display
• Multi-variate plots
  • Mosaic
  • Four-fold plots

set.seed(5)
response <- sample(c("Yes", "No"), 300, T, c(0.68, 0.32))
tab_response <-  table(response)
pie(tab_response, col = c("#99CCFF", "#6699CC"))
labs <- paste0("(", round(as.vector(prop.table(tab_response)*100)), "%)")
text(x = c(0.78, -0.50), y = c(0.80, -1), labels = c(labs[1], labs[2]))

barplot(sort(tab_response, decreasing = TRUE), las = 1, col = c("#6699CC", "#99CCFF"))
title("Bar chart", xlab = "Response", ylab = "Frequency")

• An alternative to bar chart (uses less data:ink ratio)
• As an example, generate a “Cleveland's dot plot” of the following data set and it should be:
  • titled “Total student's trained by quarters (2016)”
  • have an x axis titled “Total student's trained”
  • a sub-title “Data Mania Inc” (grey in color and slant), and
  • Y axis titled “Quarters”, balled according to (ordered) months given (March, Jun, Sep and Dec)
  • have blue colored points

• Example data: Hypothetical random number of students trained by quarter totals for year 2016

set.seed(5)
months <- sample(month.abb[c(3, 6, 9, 12)], size = 300, replace = TRUE)
tab_months <- table(months)[c("Mar", "Jun", "Sep", "Dec")] 
tab_months

months
Mar Jun Sep Dec 
 81  78  60  81 

• Following earlier example, generate stacked/besides bar plot and bi-variate Cleveland's dot plot
• Adding second variable; Gender composition of students trained

set.seed(5)
gender <- sample(c("Female", "Male"), 300, TRUE, c(0.7, 0.3))
monthgen_tab <- table(gender, months)[, c("Dec", "Sep", "Jun", "Mar")]
monthgen_tab

        months
gender   Dec Sep Jun Mar
  Female   0  49  78  81
  Male    81  11   0   0

• Used to display association (or lack of)
• Designed for two binary variables (2 x 2 tables), this can be categorized by a third categorical variable with K levels (2 x 2 x k tables)
• Association established if diagonal opposite cells in one direction tend to differ in size from those in the other direction
• Color used to show this direction

• Rings around circle are confidence rings and if adjacent quadrants rings overlap then it corresponds to \( H_0: \) No association
• Example data: R's “Titanic” data (but only for passengers)

# Convert Titanic data
titanic_passengers <- colSums(Titanic[-4,,,])

• Originally proposed by Hartigan and Kleiner (1981, 1984)
• Similar to a divided bar plot where it displays counts of a contingency table directly by tiles whose area is proportional to the observed cell frequency
• Later extended by Friendly (1992, 1994b)
• Extended version generates greater visual impact by using color and shading to reflect size of residuals from independence (no association)
• Used for exploratory data analysis (establish associations) and model building (display residuals of log-linear model)

• Display will depend on whether it univariate, bi-variate or multivariate
• Some often used displays for univariate:
  • Histograms
  • Density plots
  • Box-and-whisker plots
  • Dot plot
  • Stem-and-leave plot

• Some bi-variate displays
  • Scatter plot (both variables are continuous)
  • Box-and-whisker plot (one variable is continuous and the other categorical)

• Display distribution of observation in intervals called “bins”
• Each bin is represented by a rectangle whose width is the intervals
• Intervals can be equal through out (equidistant, R's default) or not
• Heights of each rectangle corresponds to number of observations falling within an interval (bin)
• Generated with function “hist” or plot(x, type = “h”)
• Hist constructs bins from argument “breaks”

• Breaks are breaking points for each interval or bin
• Giving a vector without this argument is okay (R will compute them), but it's usually good to change them to show best picture of distribution
• Argument “nclass” (compatible with S) can also be used to get number of breaks needed
• Histograms are excellent for data with numerous observations

# Example data: Edgar Anderson's Iris Data
sepal <- iris$Sepal.Length
sepal

  [1] 5.1 4.9 4.7 4.6 5.0 5.4 4.6 5.0 4.4 4.9 5.4 4.8 4.8 4.3 5.8 5.7 5.4
 [18] 5.1 5.7 5.1 5.4 5.1 4.6 5.1 4.8 5.0 5.0 5.2 5.2 4.7 4.8 5.4 5.2 5.5
 [35] 4.9 5.0 5.5 4.9 4.4 5.1 5.0 4.5 4.4 5.0 5.1 4.8 5.1 4.6 5.3 5.0 7.0
 [52] 6.4 6.9 5.5 6.5 5.7 6.3 4.9 6.6 5.2 5.0 5.9 6.0 6.1 5.6 6.7 5.6 5.8
 [69] 6.2 5.6 5.9 6.1 6.3 6.1 6.4 6.6 6.8 6.7 6.0 5.7 5.5 5.5 5.8 6.0 5.4
 [86] 6.0 6.7 6.3 5.6 5.5 5.5 6.1 5.8 5.0 5.6 5.7 5.7 6.2 5.1 5.7 6.3 5.8
[103] 7.1 6.3 6.5 7.6 4.9 7.3 6.7 7.2 6.5 6.4 6.8 5.7 5.8 6.4 6.5 7.7 7.7
[120] 6.0 6.9 5.6 7.7 6.3 6.7 7.2 6.2 6.1 6.4 7.2 7.4 7.9 6.4 6.3 6.1 7.7
[137] 6.3 6.4 6.0 6.9 6.7 6.9 5.8 6.8 6.7 6.7 6.3 6.5 6.2 5.9

op <- par("mfrow")
par(mfrow = c(1, 2))

hist(sepal, col = "#99CCFF", ann = FALSE)
title("Breaks = 10", xlab = "Sepal Length", ylab = "Frequency")
hist(sepal, nclass = 15, col = "#6699cc", ann = FALSE)
title("Breaks = 15", xlab = "Sepal Length", ylab = "Frequency")

par(mfrow = op)

• Fit “smooth” curve by computing kernel density estimates
• Based on probability theory

• Used to visualize data distribution in terms of quarters
• Shows outliers
• Good comparison displays as multiple variables or groups can be plotted side-by-side

states <- as.data.frame(state.x77[, c("Illiteracy", "Life Exp", "Murder", "HS Grad")])

• An alternative to box plot when n (sample size) is small
• They are one dimensional scatter plots
• Called stripchart in R
• Example data: 49.3, 48.1, 51.4, 48.1, 49, 49.3, 49.5, 49.8, 49.9, 50.4, 50.1 and 50.3

• Used to show distribution of observation
• Use actual values rather than points
• Stem is the whole number and is plotted on the left side while on the right side (separated by a vertical bar) are the fractions
  

• Used to show relationship between two continuous variables
• Relationship is said to exist if points have a visible pattern (positive or negative)
• No relationship exists if not pattern is visible; points are scattered

• Useful to display numerical variable by strata's or groups of another categorical variable
• Can also be used to compare two numerical distributions