logofflink {VGAM} | R Documentation

## Log Link Function with an Offset

### Description

Computes the log transformation with an offset, including its inverse and the first two derivatives.

### Usage

    logofflink(theta, offset = 0, inverse = FALSE, deriv = 0,
               short = TRUE, tag = FALSE)

### Arguments

`theta` | Numeric or character. See below for further details.
`offset` | Offset value. See `Links`.
`inverse, deriv, short, tag` | Details at `Links`.

### Details

The log-offset link function is very commonly used for parameters that are greater than a certain value. In particular, it is defined by `log(theta + offset)` where `offset` is the offset value. For example, if `offset = 0.5` then the value of `theta` is restricted to be greater than -0.5.

Numerical values of `theta` close to `-offset` or out of range result in `Inf`, `-Inf`, `NA` or `NaN`.

### Value

For `deriv = 0`, the log of `theta+offset`, i.e., `log(theta+offset)` when `inverse = FALSE`, and if `inverse = TRUE` then `exp(theta)-offset`.

For `deriv = 1`, then the function returns d `theta` / d `eta` 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

The default means this function is identical to `loglink`.

Numerical instability may occur when `theta` is close to `-offset`.

### Author(s)

Thomas W. Yee

### References

McCullagh, P. and Nelder, J. A. (1989) Generalized Linear Models, 2nd ed. London: Chapman & Hall.

### See Also

`Links`, `loglink`.

### Examples

    ## Not run:
    logofflink(seq(-0.2, 0.5, by = 0.1))
    logofflink(seq(-0.2, 0.5, by = 0.1), offset = 0.5)
           log(seq(-0.2, 0.5, by = 0.1) + 0.5)
    ## End(Not run)

[Package VGAM version 1.1-1 Index]