edge (version 2.4.2)

adjustedProfileLik: Adjusted Profile Likelihood for the Negative Binomial Dispersion Parameter

Description

Compute adjusted profile-likelihoods for estimating the dispersion parameters of genewise negative binomial glms.

Usage

adjustedProfileLik(dispersion, y, design, offset, weights=NULL, adjust=TRUE, 
            start=NULL, get.coef=FALSE)

Arguments

dispersion

numeric scalar or vector of dispersions.

y

numeric matrix of counts.

design

numeric matrix giving the design matrix.

offset

numeric matrix of same size as y giving offsets for the log-linear models. Can be a scalor or a vector of length ncol(y), in which case it is expanded out to a matrix.

weights

optional numeric matrix giving observation weights.

adjust

logical, if TRUE then Cox-Reid adjustment is made to the log-likelihood, if FALSE then the log-likelihood is returned without adjustment.

start

numeric matrix of starting values for the GLM coefficients, to be passed to glmFit.

get.coef

logical, specifying whether fitted GLM coefficients should be returned.

Value

• If get.coef==FALSE, a vector of adjusted profile log-likelihood values is returned containing one element for each row of y.

  Otherwise, a list is returned containing apl, the aforementioned vector of adjusted profile likelihoods; and beta, a numeric matrix of fitted GLM coefficients.

Details

For each row of data, compute the adjusted profile-likelihood for estimating the dispersion parameter of the negative binomial glm. The adjusted profile likelihood is described by McCarthy et al (2012), and is based on the method of Cox and Reid (1987).

The adjusted profile likelihood is an approximate log-likelihood for the dispersion parameter, conditional on the estimated values of the coefficients in the NB log-linear models. The conditional likelihood approach is a technique for adjusting the likelihood function to allow for the fact that nuisance parameters have to be estimated in order to evaluate the likelihood. When estimating the dispersion, the nuisance parameters are the coefficients in the linear model.

This implementation calls the LAPACK library to perform the Cholesky decomposition during adjustment estimation.

The purpose of start and get.coef is to allow hot-starting for multiple calls to adjustedProfileLik, when only the dispersion is altered. Specifically, the returned GLM coefficients from one call with get.coef==TRUE can be used as the start values for the next call.

References

Cox, DR, and Reid, N (1987). Parameter orthogonality and approximate conditional inference. Journal of the Royal Statistical Society Series B 49, 1-39.

McCarthy, DJ, Chen, Y, Smyth, GK (2012). Differential expression analysis of multifactor RNA-Seq experiments with respect to biological variation. Nucleic Acids Research 40, 4288-4297. http://nar.oxfordjournals.org/content/40/10/4288

See Also

glmFit

Examples

y <- matrix(rnbinom(1000, mu=10, size=2), ncol=4)
design <- matrix(1, 4, 1)
dispersion <- 0.5
apl <- adjustedProfileLik(dispersion, y, design, offset=0)
apl