Family function for GLMs and mixed models with negative binomial and zero-truncated negative binomial response.
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).
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)shape |
Shape parameter of the underlying Gamma distribution, given that the |
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 |
trunc |
Either |
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+mu^2/shape. The negbin family is sometimes called the NegBin1 model (as the first, historically) in the literature on negative binomial models, and sometimes the NegBin2 model (because its variance is a quadratic function of its mean).
spaMM does not handle models with the “other” negative-binomial response family where the variance is a linear function of the mean, because this is not an exponential-family model. However, it can approximate it, through a Laplace approximation and a bit of additional programming, as a Poisson-Gamma mixture model with an heteroscedastic Gamma random-effect, specified e.g. as (weights-1|.) where the weights need to be updated iteratively as function of predicted response. File test-negbin1.R in the /test directory provides one example. Other mean-variance relationship can be handled in the same way.
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))).
A family object.
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.
## 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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.