06.LinearModels {limma}R Documentation

Linear Models for Microarrays


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.

Fitting Models

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:

Straightforward least squares fitting of a linear model for each gene.
An alternative to lm.series using robust regression as implemented by the rlm function in the MASS package.
Generalized least squares taking into account correlations between duplicate spots (i.e., replicate spots on the same array) or related arrays. The function 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.

Forming the Design Matrix

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.

Making Comparisons of Interest

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.

Assessing Differential Expression

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.

Summarizing Model Fits

After the above steps the results may be displayed or further processed using:

toptable or topTable
Presents a list of the genes most likely to be differentially expressed for a given contrast.
Volcano plot of fold change versus the B-statistic for any fitted coefficient.
Writes an 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.

[Package limma version 2.4.7 Index]