spaMM (version 2.6.1)

negbin: Family function for GLMs and mixed models with negative binomial and zero-truncated negative binomial response.

Description

family object that specifies the information required to fit a negative binomial generalized linear model, with known or unknown underlying Gamma shape parameter. The zero-truncated variant can be specified either as Tnegbin(.) or as negbin(., trunc = 0L).

Usage

negbin(shape = stop("negbin's 'shape' must be specified"), link = "log", trunc = -1L)
Tnegbin(shape = stop("negbin's 'shape' must be specified"), link = "log")
# (the shape parameter is actually not requested unless this is used in a glm() call)

Arguments

shape

Shape parameter of the underlying Gamma distribution, given that the negbin family can be represented as a Poisson-Gamma mixture, where the conditional Poisson mean is $\mu$ times a Gamma random variable with mean 1 and shape shape (as produced by rgamma(., shape=shape,scale=1/shape)).

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 dsitribution.

Value

A family object.

Details

shape is the $k$ parameter of McCullagh and Nelder (1989, p.373) and the theta parameter of Venables and Ripley (2002, section 7.4). The latent Gamma variable has mean 1 and variance 1/shape, and the negbin with mean $mu$ has variance $mu+m{u}^2$/shape. The negbin family is sometimes called the NegBin1 model in the literature on negative binomial models.

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))).

References

McCullagh, P. and Nelder, J.A. (1989) Generalized Linear Models, 2nd edition. London: Chapman & Hall.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth Edition. Springer.

Examples

# NOT RUN {
## Fitting negative binomial model with estimated scale parameter:
data("scotlip")
fitme(cases~I(prop.ag/10)+offset(log(expec)),family=negbin(), data=scotlip)
negfit <- fitme(I(1+cases)~I(prop.ag/10)+offset(log(expec)),family=Tnegbin(), data=scotlip)
simulate(negfit,nsim=3)
# }