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 |
inverse |
Logical. If |
deriv |
Order of the derivative. Integer with value 0, 1 or 2. |
short |
Used for labelling the |
tag |
Used for labelling the linear/additive predictor in the
|
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