logoff {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

    logoff(theta, earg = list(offset=0), inverse = FALSE, deriv = 0,
           short = TRUE, tag = FALSE)

### Arguments

`theta` | Numeric or character. See below for further details.
`earg` | List. Extra argument for passing in additional information. The `offset` component of the list `earg` is the offset value. See `Links` for general information about `earg`.
`inverse` | Logical. If `TRUE` the inverse function is computed.
`deriv` | Order of the derivative. Integer with value 0, 1 or 2.
`short` | Used for labelling the `blurb` slot of a `vglmff-class` object.
`tag` | Used for labelling the linear/additive predictor in the `initialize` slot of a `vglmff-class` object. Contains a little more information if `TRUE`.

### 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`. The arguments `short` and `tag` are used only if `theta` is character.

### 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 `loge`.

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`, `loge`.

### Examples

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

[Package VGAM version 0.7-9 Index]