Log Link Function with an Offset
Computes the log transformation with an offset, including its inverse and the first two derivatives.
logofflink(theta, offset = 0, inverse = FALSE, deriv = 0,
short = TRUE, tag = FALSE)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
result in
Inf, -Inf, NA or NaN.
For deriv = 0, the log of theta+offset, i.e.,
log(theta+offset) when inverse = FALSE,
and if inverse = TRUE then
exp(theta)-offset.
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 default means this function is identical to loglink.
Numerical instability may occur when theta is
close to -offset.
Thomas W. Yee
McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models, 2nd ed. London: Chapman & Hall.
## Not run:
logofflink(seq(-0.2, 0.5, by = 0.1))
logofflink(seq(-0.2, 0.5, by = 0.1), offset = 0.5)
log(seq(-0.2, 0.5, by = 0.1) + 0.5)
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.