Distributional shape is often characterized by two features (1) skewness: a measure of how far the shape of the distribution deviates from symmetry around its location and (2) kurtosis: a measure of how much weight is at the tails of the distribution relative to the weight around the location.
Similar to traditional moments, the theory of L-moments forms the basis of many statistical methods such as parameter estimation, hypothesis testing, and model selection. However, L-moments enjoy many theoretical and practical advantages over traditional moments. In this package we use L-moments ratios to provide robust summaries of the shape of high-throughput genomics data.
The first four L-moments L1, L2, L3 and L4 measure location, variance, skewness, and kurtosis of data respectively. Unit free measures of relative variance, skewness, and kurtosis are defined as: (L-CV) L2 / L1, (L-skew) L3 / L2, and (L-kurt) L4 / L2.
The purpose of this package is to compute the shape (i.e. L-skew and L-kurt) statistics of each transcript (e.g. gene) or sample in a high-throughput dataset (e.g. RNA-seq, microarry). When put together these shape statistics give an overall description of the entire high-throughput dataset.
The ability to describe the shape of high-throughput genomics data is useful for two reasons:
- It provides a universal means of checking the distributional assumptions of statisical methods,
- It provides a means for finding outlier genes, and
- It provides a means for testing whether the empirical distribution of samples differ across biological conditions.
There are four main functions in this package:
a. fitShape()
b. computeDvals()
c. plotSO()
d. shapeManova()
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Given a dataset such as a high-throughput expression matrix (or just a vector of measurements) the function
fitShape()will compute and return the L-CV, L-skew, and L-kurt estimates for each gene. -
Given the shape (i.e. L-skew and L-kurt) estimate of each gene, the function
computeDvals()computes a dissimilarity distance (d-values) between each gene's shape estimate
and the typical gene's shape estimate. The d-values range from 0 to 1; where 1 is very close and 0 is very far. -
The function
plotSO()shows each gene's shape esitmate on a single plot. -
The function
shapeManova()summarizes the shape, (i.e. L-skew and L-kurt) estimate, of each sample (column in expression matrix) and perfoms a one-way multivariate anova (MANOVA) to test whether sample shapes are different across biological groups.
Use devtools to install the latest version of shape from Github:
require(devtools)
install_github("kokrah/HTShape")If all went well you should now be able to load shape:
require(HTShape)
vignette("HTShape")