negbin1 function

Alternative negative-binomial family

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)

Arguments

• shape: 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.
• link: 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).
• trunc: Either 0L for zero-truncated distribution, or -1L for default untruncated distribution.

Details

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.

Returns

A list, formally of class c("LLF", "family"). See LL-family for details about the structure and usage of such objects.

See Also

Examples in LL-family. resid.model for an example with a residual-dispersion model.