VGAM (version 0.8-1)

identity: 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.

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.

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 $\xi$.

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)