Identity Link Function
Computes the identity transformation, including its inverse and the first two derivatives.
identitylink(theta, inverse = FALSE, deriv = 0, short = TRUE, tag = FALSE) negidentitylink(theta, inverse = FALSE, deriv = 0, short = TRUE, tag = FALSE)
theta |
Numeric or character. See below for further details. |
inverse, deriv, short, tag |
Details at |
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.
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.
Thomas W. Yee
McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models, 2nd ed. London: Chapman & Hall.
identitylink((-5):5) identitylink((-5):5, deriv = 1) identitylink((-5):5, deriv = 2) negidentitylink((-5):5) negidentitylink((-5):5, deriv = 1) negidentitylink((-5):5, deriv = 2)
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