dispCoxReid {edgeR} | R Documentation

## 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

`y` | 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

### 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.

### Value

Numeric vector of length one giving the estimated common dispersion.

### Author(s)

Gordon Smyth

### 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)

### See Also

`estimateGLMCommonDisp`, `optimize`, `uniroot`

### Examples

    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)

[Package edgeR version 3.24.3 Index]