linkfcn {geoBayes} | R Documentation |
Calculate the link function for exponential families
Description
Link function for the exponential family.
Usage
linkfcn(mu, linkp, family = "gaussian")
linkinv(z, linkp, family = "gaussian")
Arguments
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. |
Details
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
In the other case, the usual Box-Cox link is used.
For the Poisson and gamma families, if the link parameter is positive, then the link is defined by
where
. In the other case, the usual
Box-Cox link is used.
For the GEV binomial family, the link function is defined by
for any real . At
it reduces to the complementary log-log
link.
The Wallace binomial family is a fast approximation to the robit family. It is defined as
where
Value
A numeric array of the same dimension as the function's first argument.
References
Evangelou, E., & Roy, V. (2019). Estimation and prediction for spatial generalized linear mixed models with parametric links via reparameterized importance sampling. Spatial Statistics, 29, 289-315.
Examples
## 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)