Description Usage Arguments Details Value References Examples
Link function for the exponential family.
1 2 3 
mu 
Numeric. The mean of the response variable. 
linkp 
The link function parameter. A scalar. 
family 
The distribution of the response variable from

z 
Numeric. The linear predictor. 
linkfcn
maps the mean of the response variable mu
to
the linear predictor z
. linkinv
is its inverse.
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 usual BoxCox link is used.
For the Poisson and gamma families, if the link parameter is positive, then the link is defined by
z = sign(w)*expm1(nu*w)/nu
where w = log(mu). In the other case, the usual BoxCox link is used.
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.
Evangelou, E., & Roy, V. (2019). Estimation and prediction for spatial generalized linear mixed models with parametric links via reparameterized importance sampling. Spatial Statistics, 29, 289315.
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, , "binomial.logit") # 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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