VGAM (version 0.8-4.1)

reciprocal: Reciprocal link function

Description

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

Usage

reciprocal(theta, earg = list(), inverse.arg = FALSE, deriv = 0,
        short = TRUE, tag = FALSE)
nreciprocal(theta, earg = list(), inverse.arg = FALSE, deriv = 0,
        short = TRUE, tag = FALSE)

Arguments

theta

Numeric or character. See below for further details.

earg

Optional list. Extra argument for passing in additional information. Values of theta which are equal to 0 can be replaced by the bvalue component of the list earg before computing the link function value. The

inverse.arg

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 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.

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 arguments short and tag are used only if theta is character.

The nreciprocal link function computes the negative reciprocal, i.e., $-1/ \theta$.

References

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

See Also

identity, powl.

Examples

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

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