Link function for the exponential family.
1 2 3 4 5 
mu 
Numeric. The mean of the response variable. 
linkp 
The link function parameter. A scalar but for the binomial family is also allowed to have the character values "logit" or "probit". 
family 
The distribution of the response variable. 
z 
Numeric. The linear predictor. 
linkfcn
maps the mean of the response variable mu
to
the linear predictor z
. linkinv
is its inverse.
Note that the logit link for the binomial family is defined as the quantile of the logistic distribution with scale 0.6458.
For the Gaussian family, if the link parameter is positive, then the extended link is used, defined by
z = (sign(mu)*abs(mu)^nu  1)/nu
In the other case, the link function is the same as for the Poisson and gamma families.
For the Poisson and gamma families, the BoxCox transformation is used, defined by
z = (mu^nu  1)/nu
For the GEV binomial family, the link function is defined by
mu = 1  exp[max(0, 1 + nu z)^(1/nu)]
for any real nu. At nu = 0 it reduces to the complementary loglog link.
The Wallace binomial family is a fast approximation to the robit family. It is defined as
mu = Phi(sign(z) c(nu) sqrt{nu log(1 + z^2/nu)})
where c(nu) = (8*nu+1)/(8*nu+3)
A numeric array of the same dimension as the function's first argument.
1 2 3 4 5 6 7 8 9 10 11  ## Not run:
mu < seq(0.1, 0.9, 0.1)
linkfcn(mu, 7, "binomial") # robit(7) link function
linkfcn(mu, "logit", "binomial") # logit link function
mu < seq(3, 3, 1)
linkfcn(mu, 0.5, "gaussian") # sqrt transformation
linkinv(linkfcn(mu, 0.5, "gaussian"), 0.5, "gaussian")
curve(linkfcn(x, 0.5, "gaussian"), 3, 3)
## End(Not run)

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