06.LinearModels {limma} | R Documentation |
This page gives an overview of the LIMMA functions available to fit linear models and to interpret the results. This page covers models for two color arrays in terms of log-ratios or for single-channel arrays in terms of log-intensities. If you wish to fit models to the individual channel log-intensities from two colour arrays, see 07.SingleChannel.
The core of this package is the fitting of gene-wise linear models to microarray data. The basic idea is to estimate log-ratios between two or more target RNA samples simultaneously. See the LIMMA User's Guide for several case studies.
The main function for model fitting is lmFit
.
This is recommended interface for most users.
lmFit
produces a fitted model object of class MArrayLM
containing coefficients, standard errors and residual standard errors for each gene.
lmFit
calls one of the following three functions to do the actual computations:
lm.series
mrlm
lm.series
using robust regression as implemented by the rlm
function in the MASS package.gls.series
duplicateCorrelation
is used to estimate the inter-duplicate or inter-block correlation before using gls.series
.
All the functions which fit linear models use unwrapdups
which provides an unified method for handling duplicate spots.
lmFit
has two main arguments, the expression data and the design matrix.
The design matrix is essentially an indicator matrix which specifies which target RNA samples were applied to each channel on each array.
There is considerable freedom in choosing the design matrix - there is always more than one choice which is correct provided it is interpreted correctly.
Design matrices for Affymetrix or single-color arrays can be created using the function model.matrix
which is part of the R base package.
The function modelMatrix
is provided to assist with creation of an appropriate design matrix for two-color microarray experiments.
For direct two-color designs, without a common reference, the design matrix often needs to be created by hand.
Once a linear model has been fit using an appropriate design matrix, the command makeContrasts
may be used to form a contrast matrix to make comparisons of interest.
The fit and the contrast matrix are used by contrasts.fit
to compute fold changes and t-statistics for the contrasts of interest.
This is a way to compute all possible pairwise comparisons between treatments for example in an experiment which compares many treatments to a common reference.
After fitting a linear model, the standard errors are moderated using a simple empirical Bayes model using ebayes
or eBayes
.
A moderated t-statistic and a log-odds of differential expression is computed for each contrast for each gene.
ebayes
and eBayes
use internal functions fitFDist
, tmixture.matrix
and tmixture.vector
.
The function zscoreT
is sometimes used for computing z-score equivalents for t-statistics so as to place t-statistics with different degrees of freedom on the same scale.
zscoreGamma
is used the same way with standard deviations instead of t-statistics.
These functions are for research purposes rather than for routine use.
After the above steps the results may be displayed or further processed using:
toptable
or topTable
volcanoplot
write.fit
MarrayLM
object to a file.
Note that if fit
is an MArrayLM
object, either write.fit
or write.table
can be used to write the results to a delimited text file.For multiple testing functions which operate on linear model fits, see 08.Tests.
Gordon Smyth
Smyth, G. K. (2004). Linear models and empirical Bayes methods for assessing differential expression in microarray experiments. Statistical Applications in Genetics and Molecular Biology, 3, No. 1, Article 3. http://www.bepress.com/sagmb/vol3/iss1/art3
Smyth, G. K., Michaud, J., and Scott, H. (2005). The use of within-array replicate spots for assessing differential expression in microarray experiments. Bioinformatics 21(9), 2067-2075.