dispCoxReid: Estimate Common Dispersion for Negative Binomial GLMs

Description

Estimate a common dispersion parameter across multiple negative binomial generalized linear models.

Usage

dispCoxReid(y, design=NULL, offset=NULL, weights=NULL, AveLogCPM=NULL, interval=c(0,4), tol=1e-5, min.row.sum=5, subset=10000)
dispDeviance(y, design=NULL, offset=NULL, interval=c(0,4), tol=1e-5, min.row.sum=5, subset=10000, AveLogCPM=NULL, robust=FALSE, trace=FALSE)
dispPearson(y, design=NULL, offset=NULL, min.row.sum=5, subset=10000, AveLogCPM=NULL, tol=1e-6, trace=FALSE, initial.dispersion=0.1)

Arguments

numeric matrix of counts. A glm is fitted to each row.

design

numeric design matrix, as for glmFit.

offset

numeric vector or matrix of offsets for the log-linear models, as for glmFit. Defaults to log(colSums(y)).

weights

optional numeric matrix giving observation weights

AveLogCPM

numeric vector giving average log2 counts per million.

interval

numeric vector of length 2 giving minimum and maximum allowable values for the dispersion, passed to optimize.

tol

the desired accuracy, see optimize or uniroot.

min.row.sum

integer. Only rows with at least this number of counts are used.

subset

integer, number of rows to use in the calculation. Rows used are chosen evenly spaced by AveLogCPM.

trace

logical, should iteration information be output?

robust

logical, should a robust estimator be used?

initial.dispersion

starting value for the dispersion

Value

Numeric vector of length one giving the estimated common dispersion.

Details

These are low-level (non-object-orientated) functions called by estimateGLMCommonDisp.

dispCoxReid maximizes the Cox-Reid adjusted profile likelihood (Cox and Reid, 1987). dispPearson sets the average Pearson goodness of fit statistics to its (asymptotic) expected value. This is also known as the pseudo-likelihood estimator. dispDeviance sets the average residual deviance statistic to its (asymptotic) expected values. This is also known as the quasi-likelihood estimator.

Robinson and Smyth (2008) and McCarthy et al (2011) showed that the Pearson (pseudo-likelihood) estimator typically under-estimates the true dispersion. It can be seriously biased when the number of libraries (ncol(y) is small. On the other hand, the deviance (quasi-likelihood) estimator typically over-estimates the true dispersion when the number of libraries is small. Robinson and Smyth (2008) and McCarthy et al (2011) showed the Cox-Reid estimator to be the least biased of the three options.

dispCoxReid uses optimize to maximize the adjusted profile likelihood. dispDeviance uses uniroot to solve the estimating equation. The robust options use an order statistic instead the mean statistic, and have the effect that a minority of genes with very large (outlier) dispersions should have limited influence on the estimated value. dispPearson uses a globally convergent Newton iteration.

References

Cox, DR, and Reid, N (1987). Parameter orthogonality and approximate conditional inference. Journal of the Royal Statistical Society Series B 49, 1-39.

Robinson MD and Smyth GK (2008). Small-sample estimation of negative binomial dispersion, with applications to SAGE data. Biostatistics, 9, 321-332

McCarthy, DJ, Chen, Y, Smyth, GK (2012). Differential expression analysis of multifactor RNA-Seq experiments with respect to biological variation. Nucleic Acids Research. http://nar.oxfordjournals.org/content/early/2012/02/06/nar.gks042 (Published online 28 January 2012)

Examples

Run this code

ngenes <- 100
nlibs <- 4
y <- matrix(rnbinom(ngenes*nlibs,mu=10,size=10),nrow=ngenes,ncol=nlibs)
group <- factor(c(1,1,2,2))
lib.size <- rowSums(y)
design <- model.matrix(~group)
disp <- dispCoxReid(y, design, offset=log(lib.size), subset=100)

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