## Description

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

## Usage

 ```1 2``` ```logclink(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`.

Thomas W. Yee

## References

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

`Links`, `loglink`, `clogloglink`, `logloglink`, `logofflink`.
 ```1 2 3 4 5``` ```## Not run: logclink(seq(-0.2, 1.1, by = 0.1)) # Has NAs ## End(Not run) logclink(seq(-0.2,1.1,by=0.1),bvalue=1-.Machine\$double.eps) # Has no NAs ```