limma (version 3.22.7)

normexp.fit: Fit Normal+Exp Convolution Model to Observed Intensities

Description

Fit the normal+exponential convolution model to a vector of observed intensities. The normal part represents the background and the exponential part represents the signal intensities. This function is called by backgroundCorrect and is not normally called directly by users.

Usage

normexp.fit(x, method="saddle", n.pts=NULL, trace=FALSE)

Arguments

x

numeric vector of (background corrected) intensities

method

method used to estimate the three parameters. Choices for normexp.fit are "mle", "saddle", "rma" and "rma75".

n.pts

number of quantiles of x to use for the fit. If NULL then all values of x will be used.

trace

logical, if TRUE, tracing information on the progress of the optimization is given.

Value

A list containing the components

par

numeric vector giving estimated values of the mean and log-standard-deviation of the background-normal part and the log-mean of the signal-exponential part.

m2loglik

numeric scalar giving minus twice the maximized log-likelihood

convergence

integer code indicating successful convergence or otherwise of the optimization.

Details

The Normal+Exp (normexp) convolution model is a mathematical model representing microarray intensity data for the purposes of background correction. It was proposed originally as part of the RMA algorithm for Affymetrix microarray data. For two-color microarry data, the normexp background correction method was introduced and compared with other methods by Ritchie et al (2007).

This function uses maximum likelihood estimation to fit the normexp model to background-corrected intensities. The model assumes that the observed intensities are the sum of background and signal components, the background being normal and the signal being exponential distributed.

The likelihood may be computed exactly (method="mle") or approximated using a saddle-point approximation (method="saddle"). The saddle-point approximation was proposed by Ritchie et al (2007). Silver et al (2008) added some computational refinements to the saddle-point approximation, making it more reliable in practice, and developed the exact likelihood maximization algorithm. The "mle" method uses the best performing algorithm from Silver et al (2008), which calls the optimization function nlminb with analytic first and second derivatives. Derivatives are computed with respect to the normal-mean, the log-normal-variance and the log-exponential-mean.

Two ad-hoc estimators are also available which do not require iterative estimation. "rma" results in a call to the bg.parameters function of the affy package. This provides the kernel estimation method that is part of the RMA algorithm for Affymetrix data. "rma75" uses the similar but less biased RMA-75 method from McGee and Chen (2006).

If the length x is very large, it may be worth saving computation time by setting n.pts to a value less than the total number of probes, for example n.pts=2^14.

References

McGee, M., and Chen, Z. (2006). Parameter estimation for the exponential-normal convolution model for background correction of Affymetrix GeneChip data. Stat Appl Genet Mol Biol, 5(1), Article 24.

Ritchie, M. E., Silver, J., Oshlack, A., Silver, J., Holmes, M., Diyagama, D., Holloway, A., and Smyth, G. K. (2007). A comparison of background correction methods for two-colour microarrays. Bioinformatics http://bioinformatics.oxfordjournals.org/cgi/content/abstract/btm412

Silver, JD, Ritchie, ME, and Smyth, GK (2009). Microarray background correction: maximum likelihood estimation for the normal-exponential convolution. Biostatistics 10, 352-363. http://biostatistics.oxfordjournals.org/cgi/content/abstract/kxn042

See Also

normexp.signal, normexp.fit.control. Also bg.parameters in the affy package.

An overview of background correction functions is given in 04.Background.

Examples

x <- c(2,3,1,10,3,20,5,6)
out <- normexp.fit(x)
normexp.signal(out$par, x=x)