## Description

Computes the reciprocal transformation, including its inverse and the first two derivatives.

## Usage

 ```1 2 3 4``` ``` reciprocallink(theta, bvalue = NULL, inverse = FALSE, deriv = 0, short = TRUE, tag = FALSE) negreciprocallink(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 `reciprocallink` link function is a special case of the power link function. Numerical values of `theta` close to 0 result in `Inf`, `-Inf`, `NA` or `NaN`.

The `negreciprocallink` link function computes the negative reciprocal, i.e., -1/theta.

## Value

For `reciprocallink`: for `deriv = 0`, the reciprocal of `theta`, i.e., `1/theta` when `inverse = FALSE`, and if `inverse = TRUE` then `1/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.

## Note

Numerical instability may occur when `theta` is close to 0.

Thomas W. Yee

## References

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

`identitylink`, `powerlink`.
 ```1 2 3 4 5 6 7 8``` ``` reciprocallink(1:5) reciprocallink(1:5, inverse = TRUE, deriv = 2) negreciprocallink(1:5) negreciprocallink(1:5, inverse = TRUE, deriv = 2) x <- (-3):3 reciprocallink(x) # Has Inf reciprocallink(x, bvalue = .Machine\$double.eps) # Has no Inf ```