Computes the identity transformation, including its inverse and the
first two derivatives.
Usage
identitylink(theta, inverse = FALSE, deriv = 0, short = TRUE,
tag = FALSE)
negidentitylink(theta, inverse = FALSE, deriv = 0, short = TRUE,
tag = FALSE)
Value
For identitylink():
for deriv = 0, the identity of theta, i.e.,
theta when inverse = FALSE,
and if inverse = TRUE then theta.
For deriv = 1, then the function returns
d
eta / d
theta as a function of
theta if inverse = FALSE,
else if inverse = TRUE then it returns the reciprocal.
For negidentitylink(): the results are similar to
identitylink() except for a sign change in most cases.
Arguments
theta
Numeric or character.
See below for further details.
inverse, deriv, short, tag
Details at Links.
Author
Thomas W. Yee
Details
The identity link function \(g(\theta)=\theta\)
should be available to every parameter estimated by the
VGAM library. However, it usually results in numerical
problems because the estimates lie outside the permitted
range. Consequently, the result may contain Inf,
-Inf, NA or NaN.
The function negidentitylink is the
negative-identity link function and corresponds to
\(g(\theta)=-\theta\). This is useful
for some models, e.g., in the literature supporting the
gevff function it seems that half of the authors
use \(\xi=-k\) for the shape parameter and the other
half use \(k\) instead of \(\xi\).
References
McCullagh, P. and Nelder, J. A. (1989).
Generalized Linear Models, 2nd ed. London: Chapman & Hall.