Before you start, have you read the introduction to the Ternary package?

This guide gives a brief example of using the “Ternary” package, using road casualty data from Great Britain.

First, we’ll load and preview the data:

data("Seatbelts")

# View the first few entries:
head(Seatbelts)
##      DriversKilled drivers front rear   kms PetrolPrice VanKilled law
## [1,]           107    1687   867  269  9059   0.1029718        12   0
## [2,]            97    1508   825  265  7685   0.1023630         6   0
## [3,]           102    1507   806  319  9963   0.1020625        12   0
## [4,]            87    1385   814  407 10955   0.1008733         8   0
## [5,]           119    1632   991  454 11823   0.1010197        10   0
## [6,]           106    1511   945  427 12391   0.1005812        13   0

For our example study, we’ll explore the relative safety of car passengers through time by plotting the proportion of people killed or seriously injured in accidents who were drivers (column drivers), front-seat passengers (column front), or rear-seat passengers (column drivers).

Let’s start by loading the “Ternary” package and plotting the data:

# Load the Ternary library
library("Ternary")

# Define our columns of interest:
seat <- c("drivers", "front", "rear")

# Extract and plot the data
TernaryPlot(alab = seat[1], blab = seat[2], clab = seat[3])
TernaryPoints(Seatbelts[, seat])

The law column takes the value 1 for months in which the wearing of a seatbelt was made compulsory in UK law. Let’s explore the impact of this law by plotting data before and after the law with different symbols. R’s plotting characters are numbered thus:

par(mar = c(0, 0, 0, 0))
plot(0:20, rep(2, 21), pch = 0:20,
     cex = 2, ylim = c(-1, 3), ann = FALSE)
text(0:20, rep(0, 21), 0:20)

Let’s choose to plot a + (character 3) when seatbelts are legally required, and o (character 1) when they are not.

beltLawPch <- ifelse(Seatbelts[, 'law'], 3, 1)

Let’s also make the plot more readable by shrinking the margins:

# Shrink the margin so the plot's easier to read
par(mar = c(0, 0, 0, 0))

# Set up a blank plot
TernaryPlot(alab = seat[1], blab = seat[2], clab = seat[3])

# Add a legend
legend('topleft', c('Belt law', 'No law'), pch = c(3, 1))

# Use our beltLawPch variable to style points
TernaryPoints(Seatbelts[, seat], pch = beltLawPch)

This seems to show a clear pattern: the seatbelt law led to a higher proportion of deaths and serious injuries occurring in the rear of cars.

Let’s look for other trends through time by colouring each data point by when it was collected. Each row summarizes data for a consecutive month, so we can simply colour the points by row number.

Let’s define a spectrum. The “viridis” colour scale is free from perceptual artefacts, is colour-blind friendly, and works when printed in greyscale.

nPoints <- nrow(Seatbelts)
rowCol <- hcl.colors(nPoints, palette = "viridis", alpha = 0.8)

It’s a bit of a fuss to draw legends for continuous colour scales, so to keep our code clean let’s write a function to add our legends:

SpectrumLegend <- function (spectrum, labels) {
  nCol <- length(spectrum)
  
  # Spectrum legends are inconvenient to produce:
  xMax <- TernaryXRange()[2]
  yMax <- TernaryYRange()[2]
  legendY0 <- yMax * 0.75
  legendY1 <- yMax * 0.95
  legendHeight <- legendY1 - legendY0
  
  segX <- rep(xMax, nCol)
  segY <- seq_len(nCol) / nCol
  segY <- legendY0 + (segY * legendHeight)
  segments(segX, segY - segY[1] + legendY0, y1 = segY, col = spectrum,
           lwd = 4)
  text(range(segX), c(legendY0, legendY1), labels, pos = 2)
}

Now we can plot our data:

par(mar = c(0, 0, 0, 0))

TernaryPlot(alab = seat[1], blab = seat[2], clab = seat[3])
legend('topleft', c('Belt law', 'No law'), pch = c(3, 1))

# Now we can call our legend-adding function:
SpectrumLegend(rowCol, labels = c('Jan 1969', 'Dec 1984'))

# Use our rowCol variable to style points
TernaryPoints(Seatbelts[, seat], pch = beltLawPch,
              lwd = 2, # Use wider lines so points are clearer
              col = rowCol)

Our belt law appears to sit in the context of a longer term improvement in the relative safety of front-seat passengers. But how do we explain the scatter in the ‘drivers’ dimension? Let’s try plotting seasonal variation:

# Define a suitable cyclical spectrum
fourSeasons <- hcl.colors(4, 'Spectral')
monthCol <- colorRampPalette(fourSeasons[c(1:4, 1)])(13)[c(7:12, 1:6)]

par(mar = c(0, 0, 0, 0))

TernaryPlot(alab = seat[1], blab = seat[2], clab = seat[3])
legend('topleft', c('Belt law', 'No law'), pch = c(3, 1))

SpectrumLegend(monthCol, c('Jan', 'Dec'))

# Use our rowCol variable to style points
TernaryPoints(Seatbelts[, seat], pch = beltLawPch,
              lwd = 2, # Use wider lines so points are clearer
              col = monthCol)

With or without seatbelts, drivers are in more relative danger in winter!

Now let’s size each point by the number of casualties, scaled by distance driven. We’ll need to zoom in closer to the plot to see this clearly.

par(mar = c(0, 0, 0, 0))

TernaryPlot(alab = seat[1], blab = seat[2], clab = seat[3],
            # Magnify the 'action':
            xlim = c(0.055, 0.095), ylim = c(0.48, 0.52))

legend('topleft', c('No law', 'Belt law'),
       col = 2:3, pch = 1, lwd = 2, lty = NA)
sizes <- c(3, 7, 12)
 scale <- 200
legend('topright', title = 'Casualties / Mm', legend = sizes,
      pt.cex = sizes / 1000 * scale,
      pch = 1, lwd = 2, lty = NA)

# Use our rowCol variable to style points
TernaryPoints(Seatbelts[, seat], pch = 1, lwd = 2,
              cex = Seatbelts[, 'DriversKilled'] / Seatbelts[, 'kms'] * scale,
              col = 2 + Seatbelts[, 'law'])

The smaller size of points after mandatory seatbelt usage is evident.

Now let’s plot the annual trend as a line, taking the values for each October as representative:

# Subset our data to extract only Octobers:
oct <- month.name == 'October'
octBelts <- Seatbelts[oct, ]

par(mar = c(0, 0, 0, 0))
TernaryPlot(alab = seat[1], blab = seat[2], clab = seat[3],
            xlim = c(0.055, 0.095), ylim = c(0.48, 0.52),
            padding = 0.04)


TernarySegments(octBelts[-nrow(octBelts), seat], octBelts[-1, seat],
                col = rowCol, lwd = 2)

# Label each point by its year
TernaryText(octBelts[, seat], paste0("'", 69:84),
            font = 2, cex = 1.5,
            # Semi-transparent colours
            col = adjustcolor(rowCol[oct], alpha.f = 0.8))