A function called within QL.fit to compute Poisson
deviances of each window for a given design matrix.
PoisDev(counts, design, log.offset, print.progress = TRUE,
bias.fold.tolerance = 1.1, chip.col.indicator)A matrix of integer counts obtained by counting reads across a genomic partition. Each row contains observations from a single window of the genomic partition. Each column contains observations from a single sample (either ChIP or control/input).
A design matrix for the full model, including a column that
indicates whether the observation is a ChIP sample (1) or control/input
(0). The number of rows must be ncol(counts). Means are modeled with
a log link function.
A vector of log-scale, additive factors used to adjust
estimated log-scale means for differences in library sizes across samples.
Commonly used offsets include log.offset=log(colSums(counts)) and
log.offset=log(apply(counts[rowSums(counts)!=0,],2,quantile,.75)).
If NULL, the later offset is used.
logical. If TRUE, the function will provide an update on which window (row number) is being analyzed. Updates occur frequently to start then eventually occur every 5000 windows.
A numerical value no smaller than 1. If the bias
reduction of maximum likelihood estimates of (log) fold change is likely to
result in a ratio of fold changes greater than this value, then bias
reduction will be performed on such windows. Setting
bias.fold.tolerance=Inf will completely disable bias reduction;
setting bias.fold.tolerance=1 will always perform bias reduction
(see details). If the constrained estimate differs from the unconstrained
estimate, bias reduction is not performed.
A binary vector of length
ncol(design.matrix) that indicates which column of the full design
matrix corresponds to the ChIP indicator.
A list containing:
Vector containing the deviance for each
window under a Poisson model fit to design matrix specified by design. This vector is passed
along within the QL.fit function.
Matrix of fitted mean values for each window.
Matrix of estimated coefficients for each window.
Same as dev, subject to the
constraint that the ChIP coefficient is non-negative. If fitting a reduced
model with no ChIP coefficient, this will be NA.
Same as means, subject to
the constraint that the ChIP coefficient is non-negative. If fitting a
reduced model with no ChIP coefficient, this will be NA.
Same as parms,
subject to the constraint that the ChIP coefficient is non-negative. If
fitting a reduced model with no ChIP coefficient, this will be NA.
This functions fits, for each row of counts, a Poisson
log-linear model.
Asymptotic biases of regression coefficients (i.e., log fold changes) are
then estimated by a plug-in estimate [eqn. (15.4) of McCullagh and Nelder,
1989] from the last iteration of iteratively reweighted least squares (IWLS)
procedure. The fitted response values are then compared with or without such
a bias term. If the ratio of fitted response values are larger than
bias.fold.tolerance for any observation and the unconstrained
estimate equals the constrained estimate, then the bias-reduction (not
bias-correction) procedure according to Firth (1993) and Kosmidis & Firth
(2009) is applied to such rows of counts, by adjusting the score
equation with a term based on the observed information. Such bias-reduced
estimates are more advantageous than directly subtracting the estimated bias
from the maximum likelihood estimates as the latter may not exist (e.g., when
all counts in one treatment group are zeros).
When the ChIP coefficient is constrained to be non-negative, quadratic
programming is applied during IWLS using solve.QP. Note that if
the constrained estimate of the regression coefficient differs from the
unconstrained estimate for a given window, bias reduction is not performed
for that window.
Firth (1993) "Bias reduction of maximum likelihood estimates" Biometrika, 80, 27--38.
Kosmidis and Firth (2009) "Bias reduction in exponential family nonlinear models" Biometrika, 96, 793--804.
Lund, Nettleton, McCarthy and Smyth (2012) "Detecting differential expression in RNA-sequence data using quasi-likelihood with shrunken dispersion estimates" emphSAGMB, 11(5).
McCullagh and Nelder (1989) "Generalized Linear Models", 2nd edition. London: Chapman and Hall.