fbrNBglm: Firth-Type Bias-Reduced Negative Binomial Log-Linear Model
In gitlongor/QuasiSeq: Analyzing RNA Sequencing Count Tables Using Quasi-Likelihood

Description Usage Arguments Value Author(s) Examples

This is the estimation algorithm for generalized linear model with negative binomial responses and log link function. Sore functions are modified properly such that bias in the coefficients are reduced.

fbrNBglm.fit(x, y, weights = rep(1, length(y)), offset = rep(0, length(y)),
  family, odisp, control = fbrNBglm.control())

fbrNBglm.control(standardizeX = TRUE, coefOnly = TRUE,
  solvers = nlSolvers, verbose = FALSE, maxit = 25L, start = NULL,
  infoParms = list(j = 1, k = 1, m = 1), order = 2L,
  tol = sqrt(.Machine$double.eps), qr.tol = tol)

`x, y, weights, offset`	Defined the same as in `glm.fit`.
`family`	The same as in `glm.fit`, but the default (and the only currently supported) choice is `negbin{'log', odisp}`, where `odisp` is defined below.
`odisp`	A numeric scalar of negative binomial over-dispersion parameter. This is the same as `1/size`, where `size` is the parameter as in `dnbinom`.
`control`	A list returned from `fbrNBglm.control`.
`standardizeX`	A logical scalar. If `TRUE`, columns of design matrix will be standardized with norm 1 during the fitting process, except for columns with identical values.
`coefOnly`	A logical scalar. If `TRUE`, only the regression coefficients will be returned. This is useful when being called from other functions, e.g. `NBDev`. If `coef=FALSE`, a `glm` object will be returned.
`solvers`	The non-linear equation solvers to be used if iterative fitting is necessary.
`verbose`	A logical scalar, indicating whether intermediate messages should be printed.
`maxit`	A positive integer, the maximum number of iterations allowed if iterative fitting is necessary.
`start`	A numeric vector of starting values, with length being the same as the number of columns of `x`.
`infoParms`	A list of three components, named `j`, `k`, and `m`, respectively. These parameters control the type of adjustment made to the score function. When all j, k, and m are 1, the observed information is used in the adjustment. When `k=0`, the expected information is used. See reference for details.
`order`	A positive integer. Usually this should be set to 2, indicating the second order, i.e., O(n^{-1}) bias being reduced by the adjustment. For one-way design, if `infoParms$j=1` and offsets are constants within each treatment, the third order bias reduction with `order=3` is also support, resulting in an estimate with both O(n^{-1}) order and O(n^{-2}) order biases being reduced.
`tol`	Small positive integer, indicating the desired accuracy of parameter estimates.
`qr.tol`	The same as the `tol` argument of qr.

It depends.

Long Qu <rtistician@gmail.com>

 ## prepare example data
 data(mockRNASeqData)
 x=mockRNASeqData$design.matrix
 y=mockRNASeqData$counts[3462,]
 offset = log(mockRNASeqData$estimated.normalization)
 overDisp = mockRNASeqData$estimated.nbdisp[3462]
 nbfam = negbin('log', overDisp)
 
 ## usual maximum likelihood estimate
 coef(glm.fit(x, y, offset=offset, family=nbfam))
 
 ## 2nd-order biased reduced fit with observed information
 ctrl= fbrNBglm.control(infoParms=list(j=1,k=1,m=1), order=2L, coefOnly=TRUE)
 fbrNBglm.fit(x, y, offset=offset, family=nbfam, control=ctrl)

 ## 2nd-order biased reduced fit with expected information
 ctrl= fbrNBglm.control(infoParms=list(j=0,k=1,m=1), order=2L, coefOnly=TRUE)
 fbrNBglm.fit(x, y, offset=offset, family=nbfam, control=ctrl)
 
 ## 3rd-order biased reduced fit with observed information
 ## Not available yet if offsets are non-constants with a treatment
 offset.avg = ave(offset, mockRNASeqData$treatment)
 ctrl= fbrNBglm.control(infoParms=list(j=1,k=1,m=1), order=3L, coefOnly=TRUE)
 fbrNBglm.fit(x, y, offset=offset.avg, family=nbfam, control=ctrl)