The melt function takes data in wide format and stacks a set of columns into a single column of data. To make use of the function we need to specify a data frame, the id variables (which will be left at their settings) and the measured variables (columns of data) to be stacked. The default assumption on measured variables is that it is all columns that are not specified as id variables.

Consider the following set of data:

> dat
  FactorA FactorB     Group1     Group2     Group3      Group4
1     Low     Low -1.1616334 -0.5228371 -0.6587093  0.45064563
2  Medium     Low -0.5991478 -1.0461138 -0.1942979  2.47985577
3    High     Low  0.8420797 -1.5413266  0.6318852 -0.98948125
4     Low  Medium  1.6225569 -1.2706469 -0.8026467 -0.32332181
5  Medium  Medium -0.3450745 -1.3377985  1.4988363  0.36541918
6    High  Medium  1.6025044  0.7631882 -0.5375833  0.85028148
7     Low    High -1.2991011 -0.2223622 -0.6321478 -1.57284216
8  Medium    High -0.4906400 -1.1802192  0.1235253  0.09891793
9    High    High  0.3897769 -0.3832142  0.6671101  0.23407257

There four groups are to used as part of a statistical analysis so we want to stack them into a single column and create an factor variable to indicate which group the measurement corresponds to and the melt function does the trick:

> melt(dat)
Using FactorA, FactorB as id variables
   FactorA FactorB variable       value
1      Low     Low   Group1 -1.16163338
2   Medium     Low   Group1 -0.59914783
3     High     Low   Group1  0.84207974
4      Low  Medium   Group1  1.62255690
5   Medium  Medium   Group1 -0.34507455
6     High  Medium   Group1  1.60250438
 
...
36    High    High   Group4  0.23407257

Consider a second set of data where there are two groups but we only want to retain the FactorB variable in the molten data set:

   FactorA   FactorB   Group1   Group2
1      Low  Very Low 6.851828 3.061329
2   Medium  Very Low 7.352169 1.303077
3     High  Very Low 6.918091 2.477875
4      Low       Low 7.402351 2.450527
5   Medium       Low 6.928385 4.334323
6     High       Low 7.400626 3.074158
7      Low    Medium 8.312145 5.725185
8   Medium    Medium 8.251806 4.384492
9     High    Medium 8.339398 3.443789
10     Low      High 5.127386 2.868952
11  Medium      High 8.561181 3.616898
12    High      High 6.993838 3.450634
13     Low Very High 7.880877 2.950622
14  Medium Very High 9.439892 3.220295
15    High Very High 8.799447 3.106060

We now need to specify both the id.vars and measure.vars arguments in the melt function to get the desired output:

> melt(dat, id.vars = "FactorB", measure.vars = c("Group1", "Group2"))
     FactorB variable    value
1   Very Low   Group1 6.851828
2   Very Low   Group1 7.352169
3   Very Low   Group1 6.918091
4        Low   Group1 7.402351
5        Low   Group1 6.928385
6        Low   Group1 7.400626
...
30 Very High   Group2 3.106060

Other useful resources are provided on the Supplementary Material page.

Fast Tube by Casper

The thickness of a line can be specified as part of a \draw command so when drawing a grid with thinner than standard lines we could add the very thin option to the tikz code:

\draw[step=.5cm,very thin,black!20] (0,0) grid (6,6);

The line pattern can also be specified as part of the draw options and the available patterns include solid lines, dashed lines and dotted lines:

\draw[solid,->] (0,0) -- (6,0);
\draw[dashed,<-] (0,1) -- (6,1);
\draw[dotted,<->] (0,2) -- (6,2);
\draw[solid,|<->|] (0,3) -- (6,3);

These settings can also be applied to decorations around nodes such as boxes. The command below draws a box with a blue outline filled with a background shade of red. The outline of the box around the node is thicker than usual (ultra thick) and the box itself is rectangular with rounded corners. The last option inner sep adds some padding inside the box around the text.

\node[draw=blue,fill=red!40,ultra thick,rectangle,rounded corners,
  inner sep=10pt] (b1) {Example};

Other useful resources are provided on the Supplementary Material page.

Consider an artifical data set create using the expand.grid function where there are duplicate rows in the data frame.

> des = expand.grid(A = c(2,2,3,4), B = c(1,3,5,5,7))
> des
   A B
1  2 1
2  2 1
3  3 1
4  4 1
5  2 3
6  2 3
7  3 3
8  4 3
9  2 5
10 2 5
11 3 5
12 4 5
13 2 5
14 2 5
15 3 5
16 4 5
17 2 7
18 2 7
19 3 7
20 4 7

If we want to identify rows that are duplicates then the duplicated function comes in handy:

> duplicated(des)
 [1] FALSE  TRUE FALSE FALSE FALSE  TRUE FALSE FALSE
 FALSE  TRUE FALSE FALSE  TRUE  TRUE  TRUE  TRUE FALSE  TRUE FALSE FALSE

We can pick out the unique rows of the data frame with the following code:

> des[!duplicated(des),]
   A B
1  2 1
3  3 1
4  4 1
5  2 3
7  3 3
8  4 3
9  2 5
11 3 5
12 4 5
17 2 7
19 3 7
20 4 7

After loading a large file into a data frame we might be interested in checking some of the data to ensure that it is as expected. Rather than printing out the entirity of the data frame we can use the head and tail functions to view the top or bottom few rows of the data frame. An example using the rock data set that is available within R:

> head(rock)
  area    peri     shape perm
1 4990 2791.90 0.0903296  6.3
2 7002 3892.60 0.1486220  6.3
3 7558 3930.66 0.1833120  6.3
4 7352 3869.32 0.1170630  6.3
5 7943 3948.54 0.1224170 17.1
6 7979 4010.15 0.1670450 17.1
> tail(rock)
   area     peri    shape perm
43 5605 1145.690 0.464125 1300
44 8793 2280.490 0.420477 1300
45 3475 1174.110 0.200744  580
46 1651  597.808 0.262651  580
47 5514 1455.880 0.182453  580
48 9718 1485.580 0.200447  580

The constraint on proportions means that the mixture data can be described in one dimension lower than the total number of components. For example when there are three mixture components a two dimension plot can be used to represent the mixture within an equilateral triangle.

To create a surface within the mixture triangle we can create a grid of points and then convert these pairs of points into mixture triples.

mygrid = rbind(
	expand.grid(
		x = seq(0, 1.0, length.out = 500),
		y = seq(0, sqrt(3)/2, length.out = 500)
	)
)

The conversion formulae are shown below:

mygrid$a = (sqrt(3) * (mygrid$x - 0.5) + (mygrid$y - 0.5 * sqrt(3))) /
  (- sqrt(3) - 0.5 * sqrt(3))
mygrid$b = (- sqrt(3) * (mygrid$x - 0.5) + (mygrid$y - 0.5 * sqrt(3))) /
  (- sqrt(3) - 0.5 * sqrt(3))
mygrid$c = 1 - mygrid$a - mygrid$b

The next step is to calculate our surface values, a trivial example of which is:

mygrid$z = 10 + 4 * mygrid$a + 3 * mygrid$b

We then need to trick the plotting function by setting all invalid mixture combinations to be missing values.

mygrid$z[mygrid$a < 0 | mygrid$b < 0 | mygrid$c < 0] = NA
mygrid$z[mygrid$a > 1 | mygrid$b > 1 | mygrid$c > 1] = NA

Lastly we use the levelplot function in the lattice package.

trellis.par.set("axis.line",list(col=NA,lty=1,lwd=1))
levelplot(z ~ x*y, data = mygrid,
	col.regions = gray(101:0/101), scales = list(draw=FALSE),
	xlab = "", ylab = "",
	panel = function(x, y, z, ...)
	{
		panel.levelplot(x, y, z, ...)
		panel.lines(c(0,1), c(0,0), col = "black")
		panel.lines(c(0,0.5), c(0,sqrt(3)/2), col = "black")
		panel.lines(c(0.5,1), c(sqrt(3)/2,0), col = "black")
		panel.text(0.5, sqrt(3)/2, "C", pos=3)
		panel.text(0, 0, "A", pos=2)
		panel.text(1, 0, "B", pos=4)
	},
	xlim = c(-0.2,1.2),
	ylim = c(-0.2, 0.2+sqrt(3)/2)
)

This forms the basis of a ternary surface plot and various adjustments can be easily made to customise the plot.

Example of a surface plot in a ternary diagram

Other useful resources are provided on the Supplementary Material page.

To change the paper to A3 in our document and in landscape orientation we would use the following:

\documentclass[12pt,landscape]{article}
\usepackage[a3paper]{geometry}
\begin{document}
...
\end{document}

The use of nodes and the current.page label in conjunction with some other parameters attached to the tikz drawing will allow us to achieve the absolute positioning on the page.

As an example consider a one page drawing where we want to put a text box in the centre of the page.

\begin{tikzpicture}[remember picture,overlay]
\draw (current page.center) node {Add Text};
\end{tikzpicture}

If we wanted to add elements to the edge of a page we could use the current page.north west anchor to locate in the top left of the page.

Other useful resources are provided on the Supplementary Material page.

Fast Tube by Casper

When creating a tikz picture the origin is assumed to be at (0,0) and objects are placed with positioning relative to the origin on the picture. If we wanted to add a grid with lines from -3 to +3 in both the horizontal and vertical axes then we would use the \draw command combined with grid.

\draw (-3,-3) grid (3,3);

We can use the draw options to change how the grid is displayed. To make the grid lines thin we could add very thin and change the colour to a light gray (black!20):

\draw[very thin,black!20] (-3,-3) grid (3,3);

To add a node with text we use a combination of \draw and node, For example to put the node with a single letter A at (1,1):

\draw (1,1) node {A};

We can put an outline around the text in a node by specifying a shape and the draw option (which refers to the colour of the outline of the shape).

\node[shape=rectangle,draw=black] at (0,2) {B};

The fill option is for the inside of the shape. A circle with outline and filled background could be drawn with the following code:

\node[shape=circle,draw=blue,fill=blue!50] at (2,2) {D};

Other useful resources are provided on the Supplementary Material page.

Fast Tube by Casper

As with all LaTeX documents we need to select a document class and include some preamble material prior to the body of our document. A blank template for a document with a single tikz picture is shown here:

\documentclass{article}
\usepackage{tikz}
\begin{document}
\pagestyle{empty}
\begin{tikzpicture}
...
\end{tikzpicture}
\end{document}

The tikz picture has a coordinate system similar to that which you would expect where moving from left to right on the page corresponds to increasing the x value and bottom to top increases the y value. A line can be drawn between two points wit the \draw command:

\draw (0,0) -- (1,0);

To draw a line between multiple points these can be chained together in a single draw command:

\draw (0,0) -- (1,0) -- (1, 4);

The line style can be altered by adding various options in square brackets directly after the draw command. So to change to a dashed red line we would write the following code:

\draw[red,dashed] (0,0) -- (2,0);

A circle of a given radius can be draw using the \draw command and we specify the radius of the circle in round brackets:

\draw (0,0) circle (2.5cm);

This will draw a circle with radius of 2.5 cm. The circle could be changed into an ellipse and we would then need to specify the radius in two directions, an example of this:

\draw (0,0) ellipse (2cm and 3.5cm);

Other useful resources are provided on the Supplementary Material page.

It is difficult to specify a set of criteria to determine whether a player can be described as an all-rounder. To compare the performances of various all-rounders we can look at the subset of crickters who have scored at least 1,000 runs and taken at least 100 wickets at Test Match level. This is not a perfect criteria as there will be players who have taken part in sufficient test matches that they will be included even though they are clearly much stronger in one of the two disciplines but very handy in the other.

A total of 54 test match cricketers were identified based on this criteria (up to and including test match 2004) and a scatter plot of the performances can be seen here. The graph shows that the majority of players in the bottom left region of the graph with a handful of batsmen and bowlers at the extremes in terms of runs or wickets.

To get a better idea of the balance between wickets and runs we can zoom in on the bottom left hand region of the graph to get this display. This new graph suggests that although there have been a number of English cricketers that has scored 1,000 runs and taken 100 wickets they do not have the longevity of players from other countries.

There are naturally other measures of performance that could be used to compare this set of allround cricketers which might provided a more illuminating insight into all round performances.