R: Complementary-log Link Function

logc {VGAM} | R Documentation

## Complementary-log Link Function

### Description

Computes the Complementary-log Transformation, Including its Inverse and the First Two Derivatives.

### Usage

    logc(theta, bvalue = NULL, inverse = FALSE, deriv = 0,
         short = TRUE, tag = FALSE)

### Arguments

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

### 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`.

### 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 `eta` / d `theta` 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 `bvalue`.

### 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), bvalue = 1 - .Machine$double.eps)  # Has no NAs

[Package VGAM version 1.0-3 Index]