Computes the two transformations, including their inverse and the first two derivatives.
logloglink(theta, bvalue = NULL, inverse = FALSE, deriv = 0,
short = TRUE, tag = FALSE)
loglogloglink(theta, bvalue = NULL, inverse = FALSE, deriv = 0,
short = TRUE, tag = FALSE)Numeric or character. See below for further details.
Values of theta which are less than or equal to
1 or bvalue
before computing the link function value.
The component name bvalue stands for ``boundary value''.
See Links for more information.
Details at Links.
For logloglink():
for deriv = 0, the log of log(theta), i.e.,
log(log(theta)) when inverse = FALSE,
and if inverse = TRUE then
exp(exp(theta)).
For loglogloglink():
for deriv = 0, the log of log(log(theta)), i.e.,
log(log(log(theta))) when inverse = FALSE,
and if inverse = TRUE then
exp(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.
The log-log link function is commonly used for parameters that
are greater than unity.
Similarly, the log-log-log link function is applicable
for parameters that
are greater than theta close to 1 or Inf, -Inf, NA or NaN.
One possible application of loglogloglink() is to
the size)
of negbinomial to Poisson-like data but with
only a small amount of overdispersion; then munb.
In such situations a loglink or loglog
link may not be sufficient to draw the estimate toward
the interior of the parameter space.
Using a more stronger link function can help mitigate the
Hauck-Donner effect hdeff.
McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models, 2nd ed. London: Chapman & Hall.
# NOT RUN {
x <- seq(0.8, 1.5, by = 0.1)
logloglink(x) # Has NAs
logloglink(x, bvalue = 1.0 + .Machine$double.eps) # Has no NAs
x <- seq(1.01, 10, len = 100)
logloglink(x)
max(abs(logloglink(logloglink(x), inverse = TRUE) - x)) # Should be 0
# }
Run the code above in your browser using DataLab