VGAM (version 1.0-4)

## 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`.

## 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.

## 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`.

## References

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

`Links`, `loge`, `cloglog`, `loglog`, `logoff`.

## Examples

Run this code
```# NOT RUN {
logc(seq(-0.2, 1.1, by = 0.1))  # Has NAs
# }
# NOT RUN {
logc(seq(-0.2, 1.1, by = 0.1), bvalue = 1 - .Machine\$double.eps)  # Has no NAs
# }
```

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