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)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.
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.
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.
Links,
loglink,
logofflink.
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)) # 0?
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