```
# NOT RUN {
require(utils) # for str
nf <- gaussian() # Normal family
nf
str(nf)
gf <- Gamma()
gf
str(gf)
gf$linkinv
gf$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())
# }
# NOT RUN {
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)
# }
# NOT RUN {
## Example of user-specified link, a logit model for p^days
## See Shaffer, T. 2004. Auk 121(2): 526-540.
logexp <- function(days = 1)
{
linkfun <- function(mu) qlogis(mu^(1/days))
linkinv <- function(eta) plogis(eta)^days
mu.eta <- function(eta) days * plogis(eta)^(days-1) *
binomial()$mu.eta(eta)
valideta <- function(eta) TRUE
link <- paste0("logexp(", days, ")")
structure(list(linkfun = linkfun, linkinv = linkinv,
mu.eta = mu.eta, valideta = valideta, name = link),
class = "link-glm")
}
(bil3 <- binomial(logexp(3)))
# }
# NOT RUN {
## in practice this would be used with a vector of 'days', in
## which case use an offset of 0 in the corresponding formula
## to get the null deviance right.
## Binomial with identity link: often not a good idea.
# }
# NOT RUN {
binomial(link = make.link("identity"))
# }
# NOT RUN {
## tests of quasi
x <- rnorm(100)
y <- rpois(100, exp(1+x))
glm(y ~ x, family = quasi(variance = "mu", link = "log"))
# which is the same as
glm(y ~ x, family = poisson)
glm(y ~ x, family = quasi(variance = "mu^2", link = "log"))
# }
# NOT RUN {
glm(y ~ x, family = quasi(variance = "mu^3", link = "log")) # fails
# }
# NOT RUN {
y <- rbinom(100, 1, plogis(x))
# needs to set a starting value for the next fit
glm(y ~ x, family = quasi(variance = "mu(1-mu)", link = "logit"), start = c(0,1))
# }
```

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