loglog {VGAM} | R Documentation |
Computes the log-log transformation, including its inverse and the first two derivatives.
loglog(theta, bvalue = NULL, inverse = FALSE, deriv = 0, short = TRUE, tag = FALSE)
theta |
Numeric or character. See below for further details. |
bvalue |
Values of |
inverse, deriv, short, tag |
Details at |
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
.
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 bvalue
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, 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