Fit Negative Binomial Generalized Linear Model with Log-Link
Fit a generalized linear model with secure convergence.
glmnb.fit(X, y, dispersion, weights = NULL, offset = 0, coef.start = NULL,
start.method = "mean", tol = 1e-6, maxit = 50L, trace = FALSE)X |
design matrix, assumed to be of full column rank. Missing values not allowed. |
y |
numeric vector of responses. Negative or missing values not allowed. |
dispersion |
numeric vector of dispersion parameters for the negative binomial distribution. If of length 1, then the same dispersion is assumed for all observations. |
weights |
numeric vector of positive weights, defaults to all one. |
offset |
offset vector for linear model |
coef.start |
numeric vector of starting values for the regression coefficients |
start.method |
method used to find starting values, possible values are |
tol |
small positive numeric value giving convergence tolerance |
maxit |
maximum number of iterations allowed |
trace |
logical value. If |
This function implements a modified Fisher scoring algorithm for generalized linear models, analogous to the Levenberg-Marquardt algorithm for nonlinear least squares. The Levenberg-Marquardt modification checks for a reduction in the deviance at each step, and avoids the possibility of divergence. The result is a very secure algorithm that converges for almost all datasets.
glmnb.fit is in principle equivalent to glm.fit(X,y,family=negative.binomial(link="log",theta=1/dispersion)) but with more secure convergence.
Here negative.binomial is a function in the MASS package.
The dispersion parameter is the same as 1/theta for the MASS::negative.binomial function or 1/size for the stats::rnbinom function.
dispersion=0 corresponds to the Poisson distribution.
List with the following components:
coefficients |
numeric vector of regression coefficients |
fitted |
numeric vector of fitted values |
deviance |
residual deviance |
iter |
number of iterations used to convergence. If convergence was not achieved then |
Gordon Smyth and Yunshun Chen
Dunn, PK, and Smyth, GK (2018). Generalized linear models with examples in R. Springer, New York, NY. doi: 10.1007/978-1-4419-0118-7
The glmFit function in the edgeR package on Bioconductor is a high-performance version of glmnb.fit for many y vectors at once.
glm is the standard glm fitting function in the stats package.
negative.binomial in the MASS package defines a negative binomial family for use with glm.
y <- rnbinom(10, mu=1:10, size=5) X <- cbind(1, 1:10) fit <- glmnb.fit(X, y, dispersion=0.2, trace=TRUE)
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