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, with known or unknown underlying Gamma shape parameter.
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.
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 negative binomial distribution. Given that the 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 (distinct) shape sh (as produced by rgamma(., shape=sh,scale=1/sh)), the latter shape is then determined as sh=shape*\(\mu\).
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 control arguments of the fitting functions (e.g., fitme(.,init=list(NB_shape=1))).
Examples in LL-family.