VGAM (version 1.0-4)

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)

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.

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.

Details

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 \((K / (1+K), 1)\).

References

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.

Examples

# NOT RUN {
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
# }