Specifies the information required to fit a negative binomial 1 (NB1) model.
negbin1(link, phi = stop("'phi' must be given"))the value of the scale parameter of the NB1 distribution (see
"Details"). This can be set to NA for initialisation,
but during estimation the family should be updated with the
current estimate, and must be strictly positive.
An object of class "family": see family for
full details. Note that when the estimate of phi is updated in
a model, this family object must be reloaded using the new
estimate.
The NB1 distribution can be parameterised in
terms of a mean \(\mu\) and scale parameter \(\phi\) (the
phi argument of this function), such that if
\(Y \sim NB1(\mu, \phi)\), then \(E(Y) = \mu\) and
\(Var(Y) = (1+\phi)\mu\).
These can be related to the size and prob arguments
of the NegBinomial functions by size = \(\mu / \phi\)
and prob = \(1 / (1 + \phi)\).