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.
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(s)
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.
See Also
sage.test
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)