Reciprocal Link Function
Computes the reciprocal transformation, including its inverse and the first two derivatives.
reciprocallink(theta, bvalue = NULL, inverse = FALSE, deriv = 0,
short = TRUE, tag = FALSE)
negreciprocallink(theta, bvalue = NULL, inverse = FALSE, deriv = 0,
short = TRUE, tag = FALSE)The reciprocallink link function
is a special case of the power link function.
Numerical values of theta close to 0 result in
Inf, -Inf, NA or NaN.
The negreciprocallink link function computes the negative reciprocal,
i.e., -1/theta.
For reciprocallink:
for deriv = 0, the reciprocal of theta, i.e.,
1/theta when inverse = FALSE,
and if inverse = TRUE then
1/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.
Numerical instability may occur when theta is
close to 0.
Thomas W. Yee
McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models, 2nd ed. London: Chapman & Hall.
reciprocallink(1:5) reciprocallink(1:5, inverse = TRUE, deriv = 2) negreciprocallink(1:5) negreciprocallink(1:5, inverse = TRUE, deriv = 2) x <- (-3):3 reciprocallink(x) # Has Inf reciprocallink(x, bvalue = .Machine$double.eps) # Has no Inf
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