VGAM (version 1.0-4)

logitoffsetlink: 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)



Numeric or character. See below for further details.


The offset value(s), which must be non-negative. It is called \(K\) below.

inverse, deriv, short, tag

Details at Links.


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 link function allows for some asymmetry compared to the ordinary logit link. The formula is $$\log(\theta/(1-\theta) - K)$$ and the default value for the offset \(K\) is corresponds to the ordinary logit link. When inverse = TRUE will mean that the value will lie in the interval \((K / (1+K), 1)\).


Komori, O. and Eguchi, S. et al., 2016. An asymmetric logistic model for ecological data. Methods in Ecology and Evolution, 7.

See Also

Links, logit.


Run this code
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
# }

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