VGAM (version 1.1-14)

logclink: Complementary-log Link Function

Description

Computes the Complementary-log Transformation, Including its Inverse and the First Two Derivatives.

Usage

logclink(theta, bvalue = NULL, inverse = FALSE, deriv = 0,
         short = TRUE, tag = FALSE)

Value

For deriv = 0, the log of theta, i.e.,

log(1-theta) when inverse = FALSE, and if inverse = TRUE then

1-exp(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.

Here, all logarithms are natural logarithms, i.e., to base e.

Details

The complementary-log link function is suitable for parameters that are less than unity. Numerical values of theta close to 1 or out of range result in Inf, -Inf, NA or NaN.

References

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

See Also

Links, loglink, clogloglink, logloglink, logofflink.

Examples

if (FALSE) {
logclink(seq(-0.2, 1.1, by = 0.1))  # Has NAs
}
logclink(seq(-0.2,1.1,by=0.1),bvalue=1-.Machine$double.eps) # Has no NAs