VGAM (version 1.1-12)

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.

Arguments

theta

Numeric or character. See below for further details.

bvalue

See Links.

inverse, deriv, short, tag

Details at Links.

Author

Thomas W. Yee

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