logoff {VGAM} | R Documentation |
Computes the log transformation with an offset, including its inverse and the first two derivatives.
logoff(theta, earg = list(offset=0), inverse = FALSE, deriv = 0, short = TRUE, tag = FALSE)
theta |
Numeric or character.
See below for further details.
|
earg |
List. Extra argument for passing in additional information.
The offset component of the list earg
is the offset value.
See Links for general information about earg .
|
inverse |
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 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
.
The arguments short
and tag
are used only if
theta
is character.
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 loge
.
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: logoff(seq(-0.2, 0.5, by=0.1)) logoff(seq(-0.2, 0.5, by=0.1), earg=list(offset=0.5)) log(seq(-0.2, 0.5, by=0.1) + 0.5) ## End(Not run)