logitoffsetlink: 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)
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.
Arguments
theta
Numeric or character.
See below for further details.
offset
The offset value(s), which must be non-negative.
It is called \(K\) below.
inverse, deriv, short, tag
Details at Links.
Author
Thomas W. Yee
Details
This link function allows for some asymmetry compared to the
ordinary logitlink link.
The formula is
$$\log(\theta/(1-\theta) - K)$$
and the default value for the offset \(K\) is corresponds to the
ordinary logitlink link.
When inverse = TRUE will mean that the value will
lie in the interval \((K / (1+K), 1)\).
References
Komori, O. and Eguchi, S. et al., 2016.
An asymmetric logistic model for ecological data.
Methods in Ecology and Evolution,
7.