## Family Functions for Negative Binomial 1 Models

### Description

Specifies the information required to fit a negative binomial 1 (NB1) model.

### Usage

```negbin1(link, phi = stop("'phi' must be given"))
```

### Arguments

 `link` included for compatibility with `family`. For `addreg` models, this will always be `"identity"`. `phi` 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.

### Details

The NB1 distribution can be parameterised in terms of a mean μ and scale parameter φ (the `phi` argument of this function), such that if Y \sim NB1(μ, φ), then E(Y) = μ and Var(Y) = (1+φ)μ.

These can be related to the `size` and `prob` arguments of the `NegBinomial` functions by `size` = μ / φ and `prob` = 1 / (1 + φ).

### Value

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.

### Author(s)

Mark W. Donoghoe markdonoghoe@gmail.com