VGAM (version 1.0-4)

reciprocal: 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.

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 negreciprocal 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, powerlink.

Examples

# NOT RUN {
   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
# }