| 5.LinearModels {limma} | R Documentation |
This page gives an overview of the LIMMA functions available to fit linear models and to interpret the results.
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 function modelMatrix is provided to assist with creation of an appropriate design matrix for two-color microarray experiments using a common reference.
Design matrices for Affymetrix or single-color arrays can be easily created using the function model.matrix which is part of the R base package.
For the direct two-color designs the design matrix often needs to be created by hand.
There are four main functions in the package which fit linear models:
lmFit lm.series rlm.series 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 correlation before using gls.series.
Each of these functions accepts essentially the same argument list and produces a fitted model object of the same form.
The first function lmFit formally produces an object of class MArrayLM.
The other three functions are lower level functions which produce similar output but in unclassed lists.
The main argument is the design matrix which specifies which target RNA samples were applied to each channel on each array. There is considerable freedom to choose the design matrix - there is always more than one choice which is correct provided it is interpreted correctly. The fitted model object consists of coefficients, standard errors and residual standard errors for each gene.
All the functions which fit linear models use unwrapdups which provides an unified method for handling duplicate spots.
All the above linear modeling functions accept two-color data in terms of log-ratios. See 6.SingleChannel for the modeling of two-color data in terms of the individual log-intensities.
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 classifyTestsF classifyTestsT and classifyTestsP are simpler methods using cutoffs for the t-statistics or p-values individually.FStat heatdiagram or heatDiagram TestResults matrix produced by classifyTests.vennCounts classifyTests and counts the number of genes in each classification.vennDiagram classifyTests or vennCounts and produces a Venn diagram plot.write.fit MarrayLM object to a file.
When evaluating test procedures with simulated or known results, the utility function auROC can be used to compute the area under the Receiver Operating Curve for the test results for a given probe.
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. (2003). The use of within-array duplicate spots for assessing differential expression in microarray experiments. http://www.statsci.org/smyth/pubs/dupcor.pdf