Computes the complentary-log transformation, including its inverse and the
first two derivatives.
Usage
logc(theta, earg = list(), inverse = FALSE, deriv = 0,
short = TRUE, tag = FALSE)
Arguments
theta
Numeric or character.
See below for further details.
earg
Optional list. Extra argument for passing in additional information.
Values of theta which are less than or equal to 1 can be
replaced by the bvalue component of the list earg
before computing the link function
inverse
Logical. If TRUE the inverse function is computed.
deriv
Order of the derivative. Integer with value 0, 1 or 2.
short
Used for labelling the blurb slot of a
vglmff-class object.
tag
Used for labelling the linear/additive predictor in the
initialize slot of a vglmff-class object.
Contains a little more information if TRUE.
Value
For deriv = 0, the log of theta, i.e.,
log(1-theta) when inverse = FALSE,
and if inverse = TRUE then
1-exp(theta).
For deriv = 1, then the function returns
dtheta / deta as a function of theta
if inverse = FALSE,
else if inverse = TRUE then it returns the reciprocal.
Here, all logarithms are natural logarithms, i.e., to base e.
Details
The complementary-log link function is suitable for parameters that
are less than unity.
Numerical values of theta close to 1 or out of range
result in
Inf, -Inf, NA or NaN.
The arguments short and tag are used only if
theta is character.
References
McCullagh, P. and Nelder, J. A. (1989)
Generalized Linear Models, 2nd ed. London: Chapman & Hall.