logitoffsetlink {VGAM} | R Documentation |
Logit-with-an-Offset Link Function
Description
Computes the logitoffsetlink transformation, including its inverse and the first two derivatives.
Usage
logitoffsetlink(theta, offset = 0, inverse = FALSE, deriv = 0,
short = TRUE, tag = FALSE)
Arguments
theta |
Numeric or character. See below for further details. |
offset |
The offset value(s), which must be non-negative.
It is called |
inverse , deriv , short , tag |
Details at |
Details
This link function allows for some asymmetry compared to the
ordinary logitlink
link.
The formula is
and the default value for the offset is corresponds to the
ordinary
logitlink
link.
When inverse = TRUE
will mean that the value will
lie in the interval .
Value
For logitoffsetlink
with deriv = 0
, the
logitoffsetlink of theta
, i.e.,
log(theta/(1-theta) - K)
when inverse = FALSE
,
and if inverse = TRUE
then
(K + exp(theta))/(1 + exp(theta) + K)
.
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.
Here, all logarithms are natural logarithms, i.e., to base e.
Note
This function is numerical less stability than
logitlink
.
Author(s)
Thomas W. Yee
References
Komori, O. and Eguchi, S. et al., 2016. An asymmetric logistic model for ecological data. Methods in Ecology and Evolution, 7.
See Also
Examples
p <- seq(0.05, 0.99, by = 0.01); myoff <- 0.05
logitoffsetlink(p, myoff)
max(abs(logitoffsetlink(logitoffsetlink(p, myoff),
myoff, inverse = TRUE) - p)) # Should be 0