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 K below.
`inverse, deriv, short, tag` | Details at `Links`.

### 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).

### 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 `logit`.

### 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

`Links`, `logit`.

### 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

[Package VGAM version 1.0-4 Index]