VGAM (version 1.0-6)

logc: Complementary-log Link Function

Description

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

Usage

logc(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 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, loge, cloglog, loglog, logoff.

Examples

# NOT RUN {
logc(seq(-0.2, 1.1, by = 0.1))  # Has NAs
# }
# NOT RUN {
logc(seq(-0.2, 1.1, by = 0.1), bvalue = 1 - .Machine$double.eps)  # Has no NAs
# }