R: Family Objects for Models

family {base}

R Documentation

Family Objects for Models

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.

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")
quasibinomial(link = "logit")
quasipoisson(link = "log")

Arguments

link

a specification for the model link function. The binomial family admits the links "logit", "probit", "log", and "cloglog" (complementary log-log); the Gamma family the links "identity", "inverse", and "log"; the poisson 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 "constant", "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).

...

further arguments passed to methods.

Details

The quasibinomial and quasipoisson families differ from the binomial and poisson families only in that the dispersion parameter is not fixed at one, so they can “model” over-dispersion. For the binomial case see McCullagh and Nelder (1989, pp. 124–8). Although they show that there is (under some restrictions) a model with variance proportional to mean as in the quasi-binomial model, note that glm does not compute maximum-likelihood estimates in that model. The behaviour of S-PLUS is closer to the quasi- variants.

References

McCullagh P. and Nelder, J. A. (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 Snell, E. J. (1981). Applied Statistics; Principles and Examples. London: Chapman and Hall.

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

## quasipoisson. compare with example(glm)
counts <- c(18,17,15,20,10,20,25,13,12)
outcome <- gl(3,1,9)
treatment <- gl(3,3)
d.AD <- data.frame(treatment, outcome, counts)
glm.qD93 <- glm(counts ~ outcome + treatment, family=quasipoisson())
glm.qD93
anova(glm.qD93, test="F")
summary(glm.qD93)
## for Poisson results use
anova(glm.qD93, dispersion = 1, test="Chisq")
summary(glm.qD93, dispersion = 1)


## 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"))
## Not run: 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))

[Package base version 1.5.0 ]