\Header{family}{Family Objects for Models}
\alias{family.lm}{family}
\alias{binomial}{family}
\alias{gaussian}{family}
\alias{Gamma}{family}
\alias{inverse.gaussian}{family}
\alias{poisson}{family}
\alias{quasi}{family}
\alias{print.family}{family}
\keyword{models}{family}
\begin{Usage}
\begin{verbatim}
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, ...)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\texttt{link}] a specification for the model link function.
The \texttt{binomial} family admits the links \texttt{logit},
\texttt{probit} and \texttt{cloglog} (complementary log-log);
the \texttt{Gamma} family the links \texttt{identity},
\texttt{inverse} and \texttt{log},
the \texttt{poisson} family the links \texttt{identity}
\texttt{log} and \texttt{sqrt}, and
the \texttt{quasi} family the links \texttt{logit}, \texttt{probit},
\texttt{cloglog},  \texttt{identity}, \texttt{inverse}, \texttt{log},
\texttt{1/mu$\,\hat{\,}$2} and \texttt{sqrt}.
The function \texttt{\Link{power}} can also be used to create a
power link function for the \texttt{quasi} family.

The other families have only one permissible link function:
\texttt{identity} for the \texttt{gaussian} family, and \texttt{1/mu$\,\hat{\,}$2}
for the \texttt{inverse.gaussian} family.
\item[\texttt{variance}] for all families, other than \texttt{quasi}, the
variance function is determined by the family.  The \texttt{quasi}
family will accept the specifications \texttt{constant},
\texttt{mu(1-mu)}, \texttt{mu}, \texttt{mu$\,\hat{\,}$2} and \texttt{mu$\,\hat{\,}$3} as variance
function.
\item[\texttt{object}] the function \texttt{family} accesses the \texttt{family}
objects which are stored within objects created by modelling
functions (e.g. \texttt{glm}).
\end{ldescription}
\end{Arguments}
\begin{Description}
Family objects provide a convenient way to specify the details of the
models used by functions such as \texttt{\Link{glm}}.  See the
documentation for \texttt{\Link{glm}} for the details on how such model
fitting takes place.\end{Description}
\begin{References}
McCullagh P. and J. A. Nelder (1989).
\emph{Generalized Linear Models}.
London: Chapman and Hall.

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

Cox, D. R. and E. J. Snell (1981).
\emph{Applied Statistics; Principles and Examples}.
London: Chapman and Hall.\end{References}
\begin{SeeAlso}
\texttt{\Link{glm}}, \texttt{\Link{power}}.\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
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
\end{ExampleCode}
\end{Examples}

