VGAM (version 1.0-4)

# logoff: 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, 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`.

## 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.

## 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`.

## References

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

`Links`, `loge`.

## Examples

Run this code
```# NOT RUN {
logoff(seq(-0.2, 0.5, by = 0.1))
logoff(seq(-0.2, 0.5, by = 0.1), offset = 0.5)
log(seq(-0.2, 0.5, by = 0.1) + 0.5)
# }
```

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