## Family Objects for Models

## Usage

    family(object)

    binomial(link = "logit")
    gaussian(link ="identity")
    Gamma(link = "inverse")
    inverse.gaussian(link = "1/mu^2")
    poisson(link = "log")
    quasi(link = "identity", variance = "constant")

    print.family(x, ...)

## Arguments

`link` | a specification for the model link function. The `binomial` family admits the links `logit`, `probit` and `cloglog` (complementary log-log); the `Gamma` family the links `identity`, `inverse` and `log`, the `poisson` family the links `identity` `log` and `sqrt`, and the `quasi` family the links `logit`, `probit`, `cloglog`, `identity`, `inverse`, `log`, `1/mu^2` and `sqrt`. The function `power` can also be used to create a power link function for the `quasi` family. The other families have only one permissible link function: `identity` for the `gaussian` family, and `1/mu^2` for the `inverse.gaussian` family.
`variance` | for all families, other than `quasi`, the variance function is determined by the family. The `quasi` family will accept the specifications `constant`, `mu(1-mu)`, `mu`, `mu^2` and `mu^3` as variance function.
`object` | the function `family` accesses the `family` objects which are stored within objects created by modelling functions (e.g. `glm`).

## Description

Family objects provide a convenient way to specify the details of the models used by functions such as `glm`. See the documentation for `glm` for the details on how such model fitting takes place.

## References

McCullagh P. and J. A. Nelder (1989). Generalized Linear Models. London: Chapman and Hall.

Dobson, A. J. (1983). An Introduction to Statistical Modelling. London: Chapman and Hall.

Cox, D. R. and E. J. Snell (1981). Applied Statistics; Principles and Examples. London: Chapman and Hall.

## See Also

`glm`, `power`.

## Examples

    nf <- gaussian()# Normal family
    nf
    str(nf)# internal STRucture

    gf <- Gamma()
    gf
    str(gf)
    gf$linkinv
    all(1:10 == gf$linkfun(gf$linkinv(1:10)))# is TRUE
    gf$variance(-3:4) #- == (.)^2

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