identity {VGAM} | R Documentation

## Identity Link Function

### Description

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

### Usage

    identity(theta, earg = list(), inverse = FALSE, deriv = 0,
             short = TRUE, tag = FALSE)
    nidentity(theta, earg = list(), inverse = FALSE, deriv = 0,
              short = TRUE, tag = FALSE)

### Arguments

`theta` | Numeric or character. See below for further details.
`earg` | Extra argument for passing in additional information. Here, the argument is unused.
`inverse` | Logical. If `TRUE` the inverse function is computed.
`deriv` | Order of the derivative. Integer with value 0, 1 or 2.
`short` | Used for labelling the `blurb` slot of a `vglmff-class` object.
`tag` | Used for labelling the linear/additive predictor in the `initialize` slot of a `vglmff-class` object. Contains a little more information if `TRUE`.

### Details

The identity link function g(theta)=theta should be available to every parameter estimated by the VGAM library. However, it usually results in numerical problems because the estimates lie outside the permitted range. Consequently, the result may contain `Inf`, `-Inf`, `NA` or `NaN`. The arguments `short` and `tag` are used only if `theta` is character.

The function `nidentity` is the negative-identity link function and corresponds to g(theta)=-theta. This is useful for some models, e.g., in the literature supporting the `egev` function it seems that half of the authors use xi=-k for the shape parameter and the other half use k instead of xi.

### Value

For `identity()`: for `deriv = 0`, the identity of `theta`, i.e., `theta` when `inverse = FALSE`, and if `inverse = TRUE` then `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.
For `nidentity()`: the results are similar to `identity()` except for a sign change in most cases.

### 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`, `logit`, `probit`, `powl`.

### Examples

    identity((-5):5)
    identity((-5):5, deriv=1)
    identity((-5):5, deriv=2)
    nidentity((-5):5)
    nidentity((-5):5, deriv=1)
    nidentity((-5):5, deriv=2)

[Package VGAM version 0.7-9 Index]