Logit-with-an-Offset Link Function
Computes the logitoffsetlink transformation, including its inverse and the first two derivatives.
logitoffsetlink(theta, offset = 0, inverse = FALSE, deriv = 0,
short = TRUE, tag = FALSE)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 |
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).
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.
This function is numerical less stability than
logitlink.
Thomas W. Yee
Komori, O. and Eguchi, S. et al., 2016. An asymmetric logistic model for ecological data. Methods in Ecology and Evolution, 7.
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 0Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.