logc {VGAM} | R Documentation

## Complementary-log Link Function

### Description

Computes the complentary-log transformation, including its inverse and the first two derivatives.

### Usage

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

### Arguments

`theta` | Numeric or character. See below for further details.
`earg` | Optional list. Extra argument for passing in additional information. Values of `theta` which are less than or equal to 1 can be replaced by the `bvalue` component of the list `earg` before computing the link function value. The component name `bvalue` stands for ``boundary 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 complementary-log link function is suitable for parameters that are less than unity. Numerical values of `theta` close to 1 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`, i.e., `log(1-theta)` when `inverse = FALSE`, and if `inverse = TRUE` then `1-exp(theta)`.
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

Numerical instability may occur when `theta` is close to 1. One way of overcoming this is to use `earg`.

### 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`, `cloglog`, `loglog`, `logoff`.

### Examples

    ## Not run:
    logc(seq(-0.2, 1.1, by=0.1))  # Has NAs
    ## End(Not run)
    logc(seq(-0.2, 1.1, by=0.1), earg=list(bval=1-.Machine$double.eps))  # Has no NAs

[Package VGAM version 0.7-9 Index]