reciprocal {VGAM} | R Documentation

## Reciprocal Link Function

### Description

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

### Usage

       reciprocal(theta, bvalue = NULL, inverse = FALSE, deriv = 0,
                  short = TRUE, tag = FALSE)
    negreciprocal(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 `reciprocal` 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 `negreciprocal` link function computes the negative reciprocal, i.e., -1/theta.

### Value

For `reciprocal`: 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.

### Author(s)

Thomas W. Yee

### References

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

### See Also

`identity`, `powerlink`.

### Examples

       reciprocal(1:5)
       reciprocal(1:5, inverse = TRUE, deriv = 2)
    negreciprocal(1:5)
    negreciprocal(1:5, inverse = TRUE, deriv = 2)

    x <- (-3):3
    reciprocal(x)  # Has Inf
    reciprocal(x, bvalue = .Machine$double.eps)  # Has no Inf

[Package VGAM version 1.0-4 Index]