Negative Binomial Model for SAGE Libraries with Pearson Estimation of Dispersion

Fit a multi-group negative-binomial model to SAGE data, with Pearson estimation of the common overdispersion parameter.

fitNBP(y, group=NULL, lib.size=colSums(y), tol=1e-5, maxit=40, verbose=FALSE)

Arguments

y

numeric matrix giving counts. Rows correspond to tags (genes) and columns to SAGE libraries.

group

factor indicating which library belongs to each group. If NULL then one group is assumed.

lib.size

vector giving total number of tags in each library.

tol

small positive numeric tolerance to judge convergence

maxit

maximum number of iterations permitted

verbose

logical, if TRUE then iteration progress information is output.

Details

The overdispersion parameter is estimated equating the Pearson goodness of fit to its expectation. The variance is assumed to be of the form Var(y)=mu*(1+phi*mu) where E(y)=mu and phi is the dispersion parameter. All tags are assumed to share the same dispersion.

For given dispersion, the model for each tag is a negative-binomial generalized linear model with log-link and log(lib.size) as offset. The coefficient parametrization used is that corresponding to the formula ~0+group+offset(log(lib.size).

Except for the dispersion being common rather than genewise, the model fitted by this function is equivalent to that proposed by Lu et al (2005). The numeric algorithm used is that of alternating iterations (Smyth, 1996) using Newton's method as the outer iteration for the dispersion parameter starting at phi=0. This iteration is monotonically convergent for the dispersion.

Note

This function has been made obsolete by the edgeR package on Bioconductor.

Value

List with components

coefficients

numeric matrix of rates for each tag (gene) and each group

fitted.values

numeric matrix of fitted values

dispersion

estimated dispersion parameter

Author

Gordon Smyth

References

Lu, J, Tomfohr, JK, Kepler, TB (2005). Identifying differential expression in multiple SAGE libraries: an overdispersed log-linear model approach. BMC Bioinformatics 6,165.

Smyth, G. K. (1996). Partitioned algorithms for maximum likelihood and other nonlinear estimation. Statistics and Computing, 6, 201-216. doi:10.1007/BF00140865

See also

sage.test

The edgeR package on Biconductor provides new and better functions to fit negative-binomial glms to SAGE or RNA-seq data. See particularly the glmFit and mglmOneWay functions.

Examples

# True value for dispersion is 1/size=2/3
# Note the Pearson method tends to under-estimate the dispersion
y <- matrix(rnbinom(10*4,mu=4,size=1.5),10,4)
lib.size <- rep(50000,4)
group <- c(1,1,2,2)
fit <- fitNBP(y,group=group,lib.size=lib.size)
logratio <- fit$coef %*% c(-1,1)