| loglog {VGAM} | R Documentation |
Computes the log-log transformation, including its inverse and the first two derivatives.
loglog(theta, earg = list(), inverse = FALSE, deriv = 0,
short = TRUE, tag = FALSE)
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 value.
The component name bvalue stands for ``boundary value''.
See Links for general information about earg.
|
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.
|
The log-log link function is commonly used for parameters that
are greater 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.
For deriv = 0, the log of theta, i.e.,
log(log(theta)) when inverse = FALSE,
and if inverse = TRUE then
exp(exp(theta)).
For deriv = 1, then the function returns
d theta / d eta 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.
Numerical instability may occur when theta is
close to 1 unless earg is used.
Thomas W. Yee
McCullagh, P. and Nelder, J. A. (1989) Generalized Linear Models, 2nd ed. London: Chapman & Hall.
x = seq(0.8, 1.5, by=0.1) loglog(x) # Has NAs loglog(x, earg=list(bvalue=1.0 + .Machine$double.eps)) # Has no NAs x = seq(1.01, 10, len=100) loglog(x) max(abs(loglog(loglog(x), inverse=TRUE) - x)) # Should be 0