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, ...)
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:
|
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). |
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.
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.
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))