Returns a family object suitable as a fitme argument for fitting negative-binomial models with variance linearly (affinely) related to the mean \(\mu\): variance=\(\mu+\mu\)/shape, where the shape parameter need or need not be specified, depending on usage.
The model described by such a family is characterized by a linear predictor, a link function, and such a negative-binomial model for the residual variation. The zero-truncated variant of this family is also handled.
A fixed-effect residual-dispersion model can be fitted, using the resid.model argument, which is used to specify the form of the logarithm of the shape parameter. Thus the variance of the response become \(\mu+\mu\)/exp(<specified linear expression>).
negbin1(shape = stop("negbin1's 'shape' must be specified"), link = "log", trunc = -1L)A list, formally of class c("LLF", "family"). See LL-family for details about the structure and usage of such objects.
Parameter controlling the mean-variance relationship of the negbin1 distribution. This distribution can be represented as a Poisson-Gamma mixture, where the conditional Poisson mean is \(\mu\) times a Gamma random variable with mean 1 and variance 1/(shape*\(\mu\)) as produced by rgamma(., shape=sh,scale=1/sh) where sh=shape*\(\mu\), meaning that the family shape parameter controls, but differs from, the gamma shape parameter.
log, sqrt or identity link, specified by any of the available ways for GLM links (name, character string, one-element character vector, or object of class link-glm as returned by make.link).
Either 0L for zero-truncated distribution, or -1L for default untruncated distribution.
The name NB_shape should be used to set values of shape in optimization control arguments of the fitting functions (e.g., fitme(.,init=list(NB_shape=1))); but fixed values are set by the shape argument.
The family should not be used as a glm argument as the results would not be correct.
Examples in LL-family. resid.model for an example with a residual-dispersion model.