RA plot

Definition

An RA plot, like it's cousin, the MA plot, is a re-scaled and (45 degree) rotated version of a simple two dimensional scatter plot (for example x=a vs y=b, where a and b are equal length vectors of positive values). . Essentially it is a log-log plot of the ratio [R] vs the average [A] of each pairing of the elements of a and b. Unlike an MA plot, however, because the RA plot takes non-negative integer counts as input, it must employ work-arounds to include mathematically invisible points (such as points where one element of the pair is zero). R and A can be defined as follows:

$\textstyle {R=log_{2}(a/b)}$ 
$\textstyle {A={\frac {1}{2}}\times (log_{2}a+log_{2}b)}$

R, like M, represents a log (fold change) ratio between a and b, and A is the average abundance for a point in the plot. The RA plot plots R on the y-axis and A on the x-axis. The RA plot provides a quick overview of the distribution and size of a dataset consisting of non-zero counts. Assuming that both a and b are drawing from identical distributions, it's safe to assume that the asymptotic central tendency of the plot should fall on the R=0 line (indicating zero fold change between conditions).

The RA plot is an integer (zero-inclusive) based version of an MA plot for visualizing two condition count data which has been transformed onto the R and A axes.

Etymology

The RA plot is sometimes referred to as a "Ray plot" because of it's characteristic arrow like shape (caused by Poisson distributed non-negative counts and thick condition-unique 'arms') which resembles a geometric Ray

Work-Arounds for Point Inclusion

Because a large portion of the pairs of a and b contain zeros (which makes them impossible to plot on a log scale) the RA plot adds a small epsilon factor (between .1 and .5) to these points to include them in an approximate location in the plot. Another problem with plotting this (or any) type of count data is overplotting which is solved in the RA plot by jittering the points out away from each other but no so far as to merge with other coordinates. The result of this feature is a patchwork-like appearance to the plot that fades away as the A increases.

Packages

The caroline CRAN package contains the only known implementation of an RA plot. However, the meta-transcriptomics "manta" R package provides a wrapper around this RA plot implimentation and is used for assessing fold change in transcription of genes (the points) while simultaneously visualizing each gene's taxonomic distributions as individual pie chart points.

Examples

library(caroline)
a <- rnbinom(n=10000, size=2)
b <- rnbinom(n=10000, size=2)

raPlot(a, b) 

See also

• MA plot
• DNA microarray
• Bland–Altman plot