## Description

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

## Usage

 ```1 2``` ```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`.

Thomas W. Yee

## References

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

`Links`, `loglink`.
 ```1 2 3 4 5``` ```## 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) ```