a design matrix specifiying the mean structure
of each row.
method
the method for estimating the dispersion
parameter. Currenlty, the only implemented option is
"log-linear-rel-mean", which assumes that log dispersion
is a log-linear function of the relative mean.
...
additional parameters.
Value
a list of two components:
estiamtesdispersion
estimates for each read count, a matrix of the same
dimensions as the counts matrix in nb.data.
modelsa list of dispersion models, NOT intended
for use by end users.
Details
We use a negative binomial (NB) distribution to model the
read frequency of gene $i$ in sample $j$. A
negative binomial (NB) distribution uses a dispersion
parameter $\phi_{ij}$ to model the extra-Poisson
variation between biological replicates. Under the NB
model, the mean-variance relationship of a single read
count satisfies $\sigma_{ij}^2 = \mu_{ij} + \phi_{ij}
\mu_{ij}^2$. Due to the typically small sample sizes of
RNA-Seq experiments, estimating the NB dispersion
$\phi_{ij}$ for each gene $i$ separately is not
reliable. One can pool information across genes and
biological samples by modeling $\phi_{ij}$ as a
function of the mean frequencies and library sizes. The
"log-linear-rel-mean" method assumes a parametric
dispersion model $$\phi_{ij} = \alpha_0 + \alpha_1
\log(\pi_{ij}),$$ where $\pi_{ij} = \mu_{ij}/(N_j
R_j)$ is the relative mean frequency after normalization.
The parameters $(\alpha_0, \alpha_1)$ in this
dispersion model are estimated by maximizing the adjusted
profile likelihood.