identitylink: Identity Link Function

Description

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

Usage

identitylink(theta, inverse = FALSE, deriv = 0, short = TRUE, tag = FALSE)
 negidentitylink(theta, inverse = FALSE, deriv = 0, short = TRUE, tag = FALSE)

Arguments

theta

Numeric or character. See below for further details.

inverse, deriv, short, tag

Details at Links.

Value

For identitylink(): 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 eta / d theta as a function of theta if inverse = FALSE, else if inverse = TRUE then it returns the reciprocal.

For negidentitylink(): the results are similar to identitylink() 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 function negidentitylink 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 gevff 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.

Examples

Run this code

# NOT RUN {
identitylink((-5):5)
identitylink((-5):5, deriv = 1)
identitylink((-5):5, deriv = 2)
negidentitylink((-5):5)
negidentitylink((-5):5, deriv = 1)
negidentitylink((-5):5, deriv = 2)
# }

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