

   family {base}                                R Documentation

   FFaammiillyy OObbjjeeccttss ffoorr MMooddeellss

   DDeessccrriippttiioonn::

        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.

   UUssaaggee::

        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, ...)

   AArrgguummeennttss::

       link: a specification for the model link function.  The
             `binomial' family admits the links `"logit"',
             `"probit"', `"log"', and `"cloglog"' (complemen-
             tary log-log); the `Gamma' family the links
             `"identity"', `"inverse"', and `"log"'; the `pois-
             son' family the links `"identity"', `"log"', and
             `"sqrt"'; 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 `"con-
             stant"', `"mu(1-mu)"', `"mu"', `"mu^2"' and
             `"mu^3"' for the variance function.

     object: the function `family' accesses the `family'
             objects which are stored within objects created by
             modelling functions (e.g. `glm').

   RReeffeerreenncceess::

        McCullagh P. and J. A. Nelder (1989).  Generalized Lin-
        ear 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.

   SSeeee AAllssoo::

        `glm', `power'.

   EExxaammpplleess::

        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

        ## tests of quasi
        x <- rnorm(100)
        y <- rpois(100, exp(1+x))
        glm(y ~x, family=quasi(var="mu", link="log"))
        # which is the same as
        glm(y ~x, family=poisson)
        glm(y ~x, family=quasi(var="mu^2", link="log"))
        glm(y ~x, family=quasi(var="mu^3", link="log")) # should fail
        y <- rbinom(100, 1, plogis(x))
        # needs to set a starting value for the next fit
        glm(y ~x, family=quasi(var="mu(1-mu)", link="logit"), start=c(0,1))

