loglog {VGAM}R Documentation

Log-log Link Function

Description

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

Usage

loglog(theta, earg = list(), inverse = 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 less than or equal to 1 can be replaced by the bvalue component of the list earg before computing the link function value. The component name bvalue stands for ``boundary value''. See Links for general information about earg.
inverse 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.

Details

The log-log link function is commonly used for parameters that are greater than unity. Numerical values of theta close to 1 or out of range result in Inf, -Inf, NA or NaN. The arguments short and tag are used only if theta is character.

Value

For deriv = 0, the log of theta, i.e., log(log(theta)) when inverse = FALSE, and if inverse = TRUE then exp(exp(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.
Here, all logarithms are natural logarithms, i.e., to base e.

Note

Numerical instability may occur when theta is close to 1 unless earg is used.

Author(s)

Thomas W. Yee

References

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

See Also

Links, loge, logoff.

Examples

x = seq(0.8, 1.5, by=0.1)
loglog(x)  # Has NAs
loglog(x, earg=list(bvalue=1.0 + .Machine$double.eps))  # Has no NAs

x = seq(1.01, 10, len=100)
loglog(x)
max(abs(loglog(loglog(x), inverse=TRUE) - x)) # Should be 0

[Package VGAM version 0.7-7 Index]