glm
,
bdGlm
, and
gam
.
family(object) binomial(link=logit) gaussian() Gamma(link=inverse) inverse.gaussian() poisson(link=log) quasi(link=identity, variance=constant)
logit
,
probit
,
cloglog
,
identity
,
inverse
,
log
,
"1/mu^2"
, and
sqrt
.
Not all links are suitable for all families.
constant
,
mu(1-mu)
,
mu
,
mu^2
, and
mu^3
. This argument may be used only with
quasi
; each of the other families implies a variance function.
gaussian
.
glm
,
bdGlm
, and
gam
in their iteratively reweighted least-squares algorithms.
See
family.object
for details.
Each of the names, except for
quasi
and the family extractor
function
family
, are associated with a member of the exponential family
of distributions.
As such, they have a fixed variance function.
There is typically a choice of link functions, with the default
corresponding to the
canonicallink for that family.
The
quasi
name represents
Quasi-likelihoodand need not correspond to any particular distribution; rather
quasi
can be used to combine any available link and variance function.
The following table summarizes the suitable pairings:
binomial gaussian Gamma inverse.gaussian poisson quasi logit * * probit * * cloglog * * identity * * * * inverse * * log * * * 1/mu^2 * * sqrt * *
power
can also be used to generate a
powerlink function object for use with
quasi
;
power
takes an argument
lambda
.
binomial
.
The easiest way is to use
quasi
with home-made
link
and
variance
objects; otherwise
make.family
can be used, or else direct
construction of the family object.
When passed as an argument to
glm
,
bdGlm
, or
gam
with the default link, the empty parentheses
()
can be omitted.
There is a
print
method for the class
"family"
.
See
GAMMA
for the functions related to the
gamma distribution:
dgamma
(density),
pgamma
(probability),
qgamma
(quantile),
rgamma
(sample).
See
gamma
for the gamma function.
binomial(link = probit) # generate binomial family with probit link glm(formula, family = binomial) robust(gaussian) # create a robust version of the gaussian family gam(formula, family = robust(quasi(link = power(2)))) # the works!