For deriv = 0, the log of theta+offset, i.e.,
log(theta+offset) when inverse = FALSE,
and if inverse = TRUE then
For deriv = 1, then the function returns
dtheta / deta 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-offset link function is very commonly used for parameters that
are greater than a certain value.
In particular, it is defined by log(theta + offset) where
offset is the offset value. For example,
if offset = 0.5 then the value of theta is restricted
to be greater than \(-0.5\).
Numerical values of theta close to -offset or out of range
Inf, -Inf, NA or NaN.
McCullagh, P. and Nelder, J. A. (1989)
Generalized Linear Models, 2nd ed. London: Chapman & Hall.