| reciprocal {VGAM} | R Documentation |
Computes the reciprocal transformation, including its inverse and the first two derivatives.
reciprocal(theta, earg = list(), inverse.arg = FALSE, deriv = 0,
short = TRUE, tag = FALSE)
nreciprocal(theta, earg = list(), inverse.arg = FALSE, deriv = 0,
short = TRUE, tag = FALSE)
theta |
Numeric or character.
See below for further details.
|
earg |
Optional list. Extra argument for passing in additional information.
Values of theta which are equal to 0 can be
replaced by the bvalue component of the list earg
before computing the link function value.
The component name bvalue stands for ``boundary value''.
See Links for general information about earg.
|
inverse.arg |
Logical. If TRUE the inverse function is computed
|
deriv |
Order of the derivative. Integer with value 0, 1 or 2.
|
short |
Used for labelling the blurb slot of a
vglmff-class object.
|
tag |
Used for labelling the linear/additive predictor in the
initialize slot of a vglmff-class object.
Contains a little more information if TRUE.
|
The reciprocal 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 arguments
short and tag are used only if theta is character.
The nreciprocal link function computes the negative reciprocal,
i.e., -1/theta.
For reciprocal:
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.
reciprocal(1:5) reciprocal(1:5, inverse=TRUE, deriv=2) nreciprocal(1:5) nreciprocal(1:5, inverse=TRUE, deriv=2) x = (-3):3 reciprocal(x) # Has Inf reciprocal(x, earg=list(bvalue= .Machine$double.eps)) # Has no Inf