**Software for Exploratory Data Analysis and Statistical Modelling**, and kindly contributed to R-bloggers)

A level plot is a type of graph that is used to display a surface in two rather than three dimensions – the surface is viewed from above as if we were looking straight down and is an alternative to a contour plot – geographic data is an example of where this type of graph would be used. A contour plot uses lines to identify regions of different heights and the level plot uses coloured regions to produce a similar effect.

To illustrate this type of graph we will consider some surface elevation data that is available in the **geoR** package. The data set in this package is called **elevation** and stores the elevation height in feet (as multiples of ten feet) for a grid region of x and y coordinates (recorded as multiples of 50 feet). To access this data we load the **geoR** pacakage and then use the **data** function:

require(geoR) data(elevation)

For some packages we need the call to the **data** function to make a set of data available for our use. The **elevation** object is not a data frame so our first step is to create our own data frame to be used to create the level plots using the different graphics packages.

elevation.df = data.frame(x = 50 * elevation$coords[,"x"], y = 50 * elevation$coords[,"y"], z = 10 * elevation$data)

We extract the x and y grid coordinates and the height values, multiplying them by 50 and 10 respectively to convert to feet for the graphs. Rather than trying to plot the individual values we need to create a surface to cover the whole grid region as the points themselves are too sparse. We make use of the **loess** function to fit a local polynomial trend surface (using weighted least squares) to approximate the elevation across the whole region. The function call for a local quadratic surface is shown below:

elevation.loess = loess(z ~ x*y, data = elevation.df, degree = 2, span = 0.25)

The next stage is to extract heights from this fitted surface at regular intervals across the whole grid region of interest – which runs from 10 to 300 feet in both the x and y directions. The **expand.grid** function creates an array of all combinations of the x and y values that we specify in a list. We choose a range every foot from 10 to 300 feet to create a fine grid:

elevation.fit = expand.grid(list(x = seq(10, 300, 1), y = seq(10, 300, 1)))

The **predict** function is then used to estimate the surface height at all of these combinations of x and y coordinates covering our grid region. This is saved as an object **z** which will be used by the **base** graphics function:

z = predict(elevation.loess, newdata = elevation.fit)

The **lattice** and **ggplot2** expect the data in a different format so we make use of the **as.numeric** function to convert from a table of heights to a single column and append to the object we create based on all combinations of x and y coordinates:

elevation.fit$Height = as.numeric(z)

The data is now in a format that can be used to create the level plots in the various packages.

**Base Graphics**

The function **image** in the **base** graphics package is the function we use to create a level plot. This function requires a list of x and y values that cover the grid of vertical values that will be used to create the surface. These heights are specified as a table of values, which in our case was saved as the object **z** during the calculations on the local trend surface.

The text on the axis labels are specified by the **xlab** and **ylab** function arguments and the **main** argument determines the overall title for the graph. The function call below creates the level plot:

image(seq(10, 300, 1), seq(10, 300, 1), z, xlab = "X Coordinate (feet)", ylab = "Y Coordinate (feet)", main = "Surface elevation data") box()

After the **image** function is used we call the **box** function mainly for aesthetic purposes to ensure there is a line surrounding the level plot. The graph that is created is shown below:

The default colour scheme used by the **base** graphics produces an attractive level plot graph where we can easily see the variation in height across the grid region. It is basically a fancy version of a contour plot where the regions between the contour lines are coloured with different shades indicating the height in those regions.

**Lattice Graphics**

The **lattice** graphics package provides a function **levelplot** for this type of graphical dispaly. We use the data stored in the object **elevation.fit** to create the graph with **lattice** graphics.

levelplot(Height ~ x*y, data = elevation.fit, xlab = "X Coordinate (feet)", ylab = "Y Coordinate (feet)", main = "Surface elevation data", col.regions = terrain.colors(100) )

The formula is used to specify which variable to use for the three axes and a data frame where the values are stored – as there are three dimensions it is the z axis that is specified on the left hand side of the formula. The axes labels and title are specified in the same way as the **base** graphics.

The range of colours used in the **lattice** level plot can be specified as a vector of colours to the **col.regions** argument of the function. We make use of the **terrian.colors** function to create this vector which a range of 100 colours which are less striking than those used above with the **base** graphics. The level plot that we can is shown here:

This is in general similar to the **base** graphics display but the actual plot region is a different shape that makes things look slightly different.

**ggplot2**

The **ggplot2** package also provides facilities for creating a level plot making use of the tile geom to create the desired graph. The function **ggplot** forms the basis of the graph and various other options are used to customise the graph:

ggplot(elevation.fit, aes(x, y, fill = Height)) + geom_tile() + xlab("X Coordinate (feet)") + ylab("Y Coordinate (feet)") + opts(title = "Surface elevation data") + scale_fill_gradient(limits = c(7000, 10000), low = "black", high = "white") + scale_x_continuous(expand = c(0,0)) + scale_y_continuous(expand = c(0,0))

This large number of options that are added to the graph change various settings. The choice of colours for the heights used on graph is selected by the **scale_fill_gradient** function with colours ranging from black to white. The **scale_x_continuous** and **scale_y_continuous** options are used to stretch the tiles to cover the whole grid region covering up the default gray background – this makes the graph more visually appealing. The graph that is produced is shown here:

The graph from **ggplot2** is visually as impressive as the other graphs – there is more smoothing between the colours which blurs some of the lines on the other graphs because of the type of colour gradient that was selected.

This blog post is summarised in a pdf leaflet on the Supplementary Material page.

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