Log Link Function, and Variants
Computes the log transformation, including its inverse and the first two derivatives.
loglink(theta, bvalue = NULL, inverse = FALSE, deriv = 0,
short = TRUE, tag = FALSE)
negloglink(theta, bvalue = NULL, inverse = FALSE, deriv = 0,
short = TRUE, tag = FALSE)
logneglink(theta, bvalue = NULL, inverse = FALSE, deriv = 0,
short = TRUE, tag = FALSE)The log link function is very commonly used for parameters that
are positive.
Here, all logarithms are natural logarithms, i.e., to base e.
Numerical values of theta close to 0 or out of range
result in
Inf, -Inf, NA or NaN.
The function loglink computes
log(theta) whereas negloglink computes
-log(theta)=log(1/theta).
The function logneglink computes
log(-theta), hence is suitable for parameters
that are negative, e.g.,
a trap-shy effect in posbernoulli.b.
The following concerns loglink.
For deriv = 0, the log of theta, i.e., log(theta)
when inverse = FALSE, and if inverse = TRUE then
exp(theta).
For deriv = 1, then the function returns
d eta / d theta as a function of theta
if inverse = FALSE,
else if inverse = TRUE then it returns the reciprocal.
This function was called loge to avoid conflict with the
log function.
Numerical instability may occur when theta is close to 0 unless
bvalue is used.
Thomas W. Yee
McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models, 2nd ed. London: Chapman & Hall.
## Not run: loglink(seq(-0.2, 0.5, by = 0.1)) loglink(seq(-0.2, 0.5, by = 0.1), bvalue = .Machine$double.xmin) negloglink(seq(-0.2, 0.5, by = 0.1)) negloglink(seq(-0.2, 0.5, by = 0.1), bvalue = .Machine$double.xmin) ## End(Not run) logneglink(seq(-0.5, -0.2, by = 0.1))
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.